As of: 2026-11-13 13:49 CET.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code), with a human editor. How we work: https://postcutoff.com/about/
Canonical page: https://postcutoff.com/science/

# AI and open problems: claimed vs checked

Since July, AI systems have been credited with results on problems that stood for decades. Most claims still await review. Here is each one, how it was checked, and by whom.

AI-assisted mathematics results as a dataset (CSV, JSON, CC BY 4.0): https://github.com/icyklop/ai-math-catalogue

194 claims since July 2026: 29 confirmed, 164 awaiting review, 1 disputed. Median 52 years open. 8,338 problem-years in total, from the 151 claims with a known start year.

## How we count

A claim counts when an entry dated after 30 June 2026 reports an AI result on a named open problem, has importance 4 or 5, and credits an AI system. Formal proofs of theorems already proved, batches of many results and other science (forecasts, drug and protein design, competitions) are listed under ‘All AI science results’ instead. The status says where the field stands on the claim: ‘confirmed’, ‘awaiting review’ (no verdict yet from peer review or the experts in the area) or ‘disputed’. The ‘How it was checked’ column says what checking exists so far: peer review, a Lean proof, named experts, or a preprint only. A Lean proof whose formal statement nobody has reviewed is labelled ‘Lean proof, not yet reviewed’. A Lean proof can check a theorem while experts still dispute what it settles, so a row can be both ‘Lean-verified’ and ‘disputed’.

How the 194 claims were checked: Peer-reviewed 20; Lean-verified 76; Expert-checked 11; Lean proof, not yet reviewed 12; Preprint only 67; Unverified claim 8.

## Claims (194, oldest problem first)

| Problem | Posed | Years open | AI credited | Status | How it was checked | Date | Result | Human role | Entry |
|---|---|---|---|---|---|---|---|---|---|
| Gauss class number problem | 1801 | 225 | OpenAI internal model (Siegel-zero proof and its Lean formalization); Claude Opus 5.5 (Claude Code) | Awaiting review | Lean-verified | 2026-10-15 | Unconditional determination of all imaginary quadratic fields with class number ≤ 2000 (16,453,493 fields), via an explicit, Lean-verified version of OpenAI's Landau–Siegel zero exclusion. | Human-directed: the author chose the problem, checks and trusted base; Claude did constants, Lean, code and most text; the underlying theorem is OpenAI's | https://postcutoff.com/e/2026-10-15-imaginary-quadratic-fields-class-number-2000-claude-lean/ |
| Quasi-Riemann hypothesis for Dedekind zeta functions of arbitrary number fields | 1859 | 167 | AxiomProver | Awaiting review | Lean-verified | 2026-10-12 | For every number field K, ζ_K has no zeros with Re s > 31/32; likewise finite-order Hecke L-functions over K. | AI-assisted: Cureton and Thorner directed the research and made the mathematical judgments; AxiomProver generated the proofs and the Lean formalization | https://postcutoff.com/e/2026-10-12-cureton-thorner-dedekind-zeta-zero-free-axiomprover/ |
| Quasi-Riemann hypothesis | 1859 | 167 | OpenAI internal model (unreleased) | Awaiting review | Lean proof, not yet reviewed | 2026-10-06 | Claimed: ζ, all Dirichlet L-functions and finite-order Hecke L-functions over ℚ(√−3) have no zeros with Re s > 7/8; real zeros of real primitive Dirichlet L-functions satisfy 1 − β ≥ c/log q. | Listed by OpenAI as an exception to its fixed automated procedure (details not given); the 11/12 write-up was human-edited | https://postcutoff.com/e/2026-10-06-quasi-riemann-hypothesis-openai/ |
| Sylvester's conjecture | 1879 | 147 | ChatGPT; Claude; unnamed AI (Yin, Oct 2026) | Awaiting review | Preprint only | 2026-09-14 | Proved in full: the 4, 7 cases by Yin (arXiv 2605.25917, May 2026), the 8 case by Burungale–Tian (arXiv 2609.14893, Sept 2026), who show E_p: y² = x³ + p²/4 has analytic rank one; a shorter proof of the 8 case followed from Yin (arXiv 2610.08015, Oct 2026). | Human-led with AI tools. Burungale–Tian used ChatGPT and Claude for exploratory computations, editing and reorganization. In Yin's Oct 2026 short proof, the ideas are his and the detailed working-out was done by AI and then rewritten by him. | https://postcutoff.com/e/2026-09-14-sylvester-conjecture-proved-burungale-tian/ |
| Hilbert's sixteenth problem, second part | 1900 | 126 | OpenAI internal model (math release) | Awaiting review | Lean-verified | 2026-10-06 | Claimed existence of a finite, non-effective bound B(d) for every degree d; companion theorem (in Lean): quintic classical Liénard systems have at most two limit cycles, and two are attained | Released as model output under OpenAI's fixed procedure, with no human author named; no human exposition or check yet | https://postcutoff.com/e/2026-10-06-openai-hilbert-sixteenth-uniform-limit-cycle-bound-claim/ |
| Carathéodory's conjecture | 1924 | 102 | Claude (Anthropic); ChatGPT (GPT-6.1) | Awaiting review | Preprint only | 2026-08-19 | Explicit C^∞ counterexamples: umbilics of index 1 + k/2 for every positive integer k, and a strictly convex smooth closed surface with exactly one umbilic (index 2); simplified independently by Ando and Umehara | AI-assisted: Alpöge and John-Paul Smith worked on the problem with Claude, which also checked it; Ando and Umehara used GPT-6.1 to search for candidate seed functions | https://postcutoff.com/e/2026-08-19-caratheodory-loewner-smooth-counterexamples-alpoge-claude/ |
| Artin's primitive root conjecture | 1927 | 99 | OpenAI internal model (openai/math release) | Awaiting review | Preprint only | 2026-10-06 | Claimed: for every admissible a, at least c_a·x/(log x)² primes in (x, 2x) have primitive root a (infinitude, not the conjectured density); a positive lower density was added by a follow-up | Autonomous AI output released by OpenAI; follow-ups by human mathematicians with AI assistance | https://postcutoff.com/e/2026-10-06-openai-artin-primitive-root-conjecture-infinitude/ |
| Schiffer's conjecture | 1929 | 97 | GPT-5.6; GPT-5.5; Claude Opus 4.8; Claude Fable 5; ChatGPT/Codex | Awaiting review | Lean-verified | 2026-08-03 | Non-circular bounded planar domains carrying a nonconstant Neumann eigenfunction that is constant on the boundary, which disproves both Schiffer's conjecture and the Pompeiu conjecture in the plane (one explicit domain, and an infinite family). | Human-led. Colbrook–Stepaniants: AI only helped debug code. Cao-Labora–de Dios Pont: humans devised the bifurcation strategy; LLMs checked estimates numerically and drafted some lemma proofs, and GPT-5.6 wrote the Lean formalisation | https://postcutoff.com/e/2026-08-03-schiffer-pompeiu-conjectures-disproved/ |
| Tammes problem for 15 points | 1930 | 96 | unnamed AI system(s) | Awaiting review | Lean-verified | 2026-09-30 | Tammes optimum for N = 15 determined, with exactly two optimal configurations; V > 2 for Robbins' problem; frog model recurrent on the 3-ary and transient on the 4-ary tree; plus three smaller conjectures settled. | Claimed fully AI-generated ('results, proofs and code were found and written by AI'); the human operator is anonymous. One Tammes theorem came from a third party using Claude | https://postcutoff.com/e/2026-09-30-mt0-svg-ai-generated-tammes-15-robbins-frog-model-lean/ |
| Köthe conjecture | 1930 | 96 | GPT-6 Astra (pre-release) | Result confirmed | Lean-verified | 2026-09-07 | Explicit counterexample disproving the Köthe conjecture, formally verified in Lean. | Autonomous discovery; humans checked and wrote up | https://postcutoff.com/e/2026-09-07-koethe-conjecture-disproved/ |
| Hopf's conjecture | 1931 | 95 | GPT-6 Astra | Awaiting review | Preprint only | 2026-10-15 | Proved for manifolds and orbifolds admitting an effective isometric T³-action (previously T⁴), with the rational cohomology of fixed-point components classified. | AI-assisted: GPT-6 Astra produced the first proof of Theorem A with minimal human input; the stronger structure theorem, orbifold case and the write-up are human | https://postcutoff.com/e/2026-10-15-hopf-conjecture-t3-symmetry-chatgpt-astra/ |
| Hopf's sign conjecture | 1931 | 95 | Odin Automatic AI Research Agent | Awaiting review | Preprint only | 2026-09-06 | Claimed smooth metric of strictly positive sectional curvature on S³×S³ (χ = 0), a counterexample in dimension 6; preceded by a claimed metric on S²×S³ | Autonomous per the authors: the agent 'discovered' the metric and the proof; human authors posted and presumably edited the paper | https://postcutoff.com/e/2026-09-06-odin-ai-agent-positive-curvature-s3xs3-hopf-sign-conjecture/ |
| Erdős problems #1, #74, #126 and #571 | 1931 | 95 | GPT-6 Astra (pre-release) | Result confirmed | Lean-verified | 2026-09-03 | #1 disproved (N ≤ ε·2^n possible for arbitrarily large n); #571 proved (every rational α in [1,2) is a Turán exponent of a bipartite graph); #74 answered in the negative direction; #126 proved with \|S(A)\| ≫ n^(1/2). | Autonomous: the model worked in an agent harness without human steering; humans chose the problems, wrote the Lean statements and wrote informal expositions afterwards | https://postcutoff.com/e/2026-09-03-frontiermath-erdos-astra-disproves-erdos-problem-1/ |
| Banach's isometric subspace conjecture | 1932 | 94 | ChatGPT 5.5 Pro; ChatGPT 5.6 Pro; GPT-5.6 Sol | Awaiting review | Preprint only | 2026-08-13 | Real case completed (all odd n, with Gromov's even n); complex and quaternionic analogues also proved. | AI-assisted: the humans made the reduction; the key approach came out of dialogue with ChatGPT Pro, and GPT-5.6 Sol drafted proofs that the authors checked and rewrote | https://postcutoff.com/e/2026-08-13-banach-isometric-conjecture-solved/ |
| Borsuk's conjecture | 1933 | 93 | OpenAI internal model (openai/math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed: the compact projector image of ℝP³ in the 9-dimensional trace-one space needs more than ten pieces, so the conjecture fails in every dimension d ≥ 9 (previous smallest known dimension 63, for finite sets). Every finite subset needs at most eight pieces (Damásdi), so the finite version below 63 stays open | Autonomous output released without named authors; the construction was known (Kahn–Kalai, Kalai 2015), the covering obstruction is the model's | https://postcutoff.com/e/2026-10-06-openai-borsuk-conjecture-dimension-nine-counterexample/ |
| Uniqueness of Leray–Hopf weak solutions of the unforced 3D incompressible Navier–Stokes equations | 1934 | 92 | Claude Opus; Codex | Awaiting review | Lean proof, not yet reviewed | 2026-11-06 | Claimed continuum of distinct suitable Leray–Hopf solutions from one compactly supported axisymmetric datum in L^{3,∞}, without force | AI-generated text and proofs; authors understood the broad steps of the construction | https://postcutoff.com/e/2026-11-06-navier-stokes-unforced-leray-hopf-nonuniqueness-buckmaster-coiculescu-li/ |
| Landau–Siegel zeros | 1935 | 91 | OpenAI internal model (original proof); Claude | Awaiting review | Lean-verified | 2026-10-11 | Explicit version of OpenAI's claimed exclusion: (1 − β) log q ≥ 3.0 × 10⁻³ for every primitive real character of conductor q ≥ 3 (with Lu–Zaman–Zhao for small q). | Expert reconstruction: the proof is OpenAI's; Claude drafted the report, expansion and constants; Banks checked every line | https://postcutoff.com/e/2026-10-11-landau-siegel-zeros-banks-explicit-account/ |
| Bloch constant conjecture | 1937 | 89 | ChatGPT; OpenAI Codex | Awaiting review | Lean proof, not yet reviewed | 2026-10-12 | Disproved: B < A_AG − 1.3 × 10⁻⁹. | Human-led: proofs developed and written by the author; ChatGPT for exploring approaches and editing; Codex generated the Lean formalization | https://postcutoff.com/e/2026-10-12-bloch-constant-conjecture-disproved/ |
| Collatz conjecture | 1937 | 89 | OpenAI GPT models via Codex; ProofAtlas.ai harness; Claude (manuscript review); AxiomProver (formalization of Kenny Lau's refinement) | Result confirmed | Lean-verified | 2026-09-06 | A positive lower natural density of integers reach 1 within 10.46 ln n ordinary Collatz steps (linear count cX, with explicit but astronomically small c), improving earlier sublinear bounds X^0.84 and X^0.90. | AI-led: 'developed primarily by AI agents' with high-level guidance from Lech Mazur, who directed the work and is responsible for the claims | https://postcutoff.com/e/2026-09-06-collatz-positive-density-log-time-mazur-codex/ |
| Mahler's conjecture on the minimal volume product \|K\|\|K°\| of convex bodies, symmetric and general, with equality cases | 1939 | 87 | OpenAI internal model (openai/math release) | Awaiting review | Lean-verified | 2026-10-06 | Claimed: sharp lower bounds 4ⁿ/n! (symmetric; equality for Hanner polytopes) and (n+1)ⁿ⁺¹/(n!)² (general; equality for simplices) in every dimension; Gromov width of K × K° equals 4 | Autonomous AI output released by OpenAI under its fixed procedure (README) | https://postcutoff.com/e/2026-10-06-openai-mahler-conjecture-lean/ |
| Jacobian conjecture | 1939 | 87 | Claude Fable 5 | Result confirmed | Unverified claim | 2026-07-20 | Explicit non-injective polynomial map C³→C³ with constant Jacobian determinant, disproving the conjecture for all n≥3. | AI-assisted: human chose the problem and verified; Claude found the counterexample | https://postcutoff.com/e/2026-07-20-jacobian-conjecture-counterexample/ |
| Kaplansky's zero-divisor conjecture | 1940 | 86 | OpenAI internal model (math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed counterexamples: zero divisors in F₂[G] for a finitely presented torsion-free G with a 2-dimensional classifying space; one-sided inverses in K[G] in characteristic 2 (finitely presented G), odd characteristic and over F₂ for torsion-free G; injective non-surjective cellular automata; a Z[G]-matrix with Fuglede–Kadison determinant in (0, 1) | Released as model output under OpenAI's fixed procedure, with no human author named; specialists have commented on presentation and consequences, not on correctness | https://postcutoff.com/e/2026-10-06-openai-kaplansky-zero-divisor-direct-finiteness-counterexamples-claim/ |
| Hilbert–Smith conjecture | 1941 | 85 | OpenAI internal model (math release); Claude Opus 5.5; GPT 6.1 | Awaiting review | Lean-verified | 2026-10-06 | Claimed proof in every finite dimension (OpenAI manuscript); separate AI-agent proof with a registered Lean 4 formalization under second-countability assumptions | OpenAI: autonomous output released without named authors. Separate proof: AI agents run 'under human guidance' by the repository owner (adbrw) | https://postcutoff.com/e/2026-10-06-openai-hilbert-smith-conjecture-claim/ |
| Maximum number of Hamiltonian cycles in an n-vertex tournament | 1943 | 83 | GPT-5.6 | Awaiting review | Preprint only | 2026-10-16 | C(n) = (cosh 1/cos 1 ± o(1))(n−1)!/2ⁿ, attained asymptotically by the cyclic regular tournament; asymptotic maximum number of Hamiltonian paths follows | Authors chose the problem and the strategy hint (permanent estimates); GPT-5.6 found the lower-bound proof and a second instance the upper bound; authors rewrote, simplified and exposited | https://postcutoff.com/e/2026-10-16-max-hamiltonian-cycles-tournaments-gpt-5-6-wormald/ |
| Hadwiger's conjecture | 1943 | 83 | OpenAI internal model (math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed arbitrarily large counterexamples with independence number at most two, beating even the fractional form (Lean covers the ordinary form; an independent Lean project derives the fractional one); companion claims: Colin de Verdière chromatic conjecture false, linear list-Hadwiger bound true | Released as model output under OpenAI's fixed procedure, with no human author named; independent Lean re-packaging by a volunteer; no human exposition yet | https://postcutoff.com/e/2026-10-06-openai-hadwiger-conjecture-counterexample-claim/ |
| Linear Hadwiger conjecture | 1943 | 83 | GPT-6 Astra; OpenAI Codex (6 Sol, Astra) | Awaiting review | Lean proof, not yet reviewed | 2026-10-04 | Proved: a universal C with χ(G) ≤ Ct for all K_t-minor-free G | AI-generated proof under human direction: authors set the strategy and sub-goals; GPT-6 Astra wrote essentially all of the proof; Codex produced the Lean formalization | https://postcutoff.com/e/2026-10-04-linear-hadwiger-conjecture-proved-gpt-6-astra/ |
| Linnik's constant | 1944 | 82 | Claude Opus 5.5; GPT-6 Astra; Grok 4.7 | Awaiting review | Lean-verified | 2026-10-02 | Claimed L ≤ 3.99 (P(a, q) < q^3.99 for all large q), improving Xylouris's L ≤ 5 | Naslund prompted and supervised; the models did the research and wrote the paper; Grok helped with formalization | https://postcutoff.com/e/2026-10-02-linnik-constant-3-99-naslund-claude-gpt-astra/ |
| Erdős unit distance problem | 1946 | 80 | OpenAI internal model (math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed u(n) = O(n^(4/3−δ)) for an absolute, unspecified δ > 0, and the weak pinned distance theorem; both formalized in Lean | Released as model output under OpenAI's fixed procedure, with no human author named; detailed public reading by an outside mathematician (forum comment), no written check | https://postcutoff.com/e/2026-10-06-openai-unit-distance-upper-bound-power-saving-claim/ |
| Hopf problem | 1947 | 79 | Claude (internal research model) | Awaiting review | Lean proof, not yet reviewed | 2026-08-23 | Claimed explicit construction of integrable complex structures on S⁶ (answer: yes). | AI-assisted: human mathematician (Alpöge) directed and wrote up | https://postcutoff.com/e/2026-08-23-hopf-problem-s6-complex-structure/ |
| Weil conjectures | 1949 | 77 | Axiom agents | Awaiting review | Lean-verified | 2026-11-06 | Claimed sorry-free Lean 4 proof of rationality, functional equation, Riemann hypothesis and Betti-number statement for smooth projective varieties over finite fields | AI agents wrote the library on top of Axiom's Stacks formalization; no human code review yet | https://postcutoff.com/e/2026-11-06-axiom-weil-conjectures-lean-formalization/ |
| Hodge conjecture (CM abelian varieties) | 1950 | 76 | OpenAI internal model (unreleased) | Result confirmed | Lean-verified | 2026-10-06 | Claimed: every rational Hodge class on a complex CM abelian variety is a ℚ-linear combination of algebraic cycle classes; consequences for Tate and the Hodge standard conjecture. | Listed by OpenAI as an exception to its fixed automated procedure (details not given) | https://postcutoff.com/e/2026-10-06-hodge-conjecture-cm-abelian-varieties-openai/ |
| Hadwiger–Nelson problem | 1950 | 76 | OpenAI internal model (math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed proof that 5 colours never suffice, for arbitrary colour classes, so χ(R²) ∈ {6, 7}; Lean formalization of both bounds | Released as model output under OpenAI's fixed procedure, with no human author named; no human exposition yet; already used as a tool by human authors (with AI help) | https://postcutoff.com/e/2026-10-06-openai-plane-not-five-colourable-hadwiger-nelson-claim/ |
| Kaplansky's quasitrace conjecture | 1951 | 75 | Unreleased OpenAI model; GPT-6 Astra | Awaiting review | Preprint only | 2026-10-19 | Counterexample to the quasitrace conjecture (from an unreleased OpenAI model, reproduced with a modified construction) and a finite AW*-factor that is not monotone complete | OpenAI model produced the original quasitrace counterexample; Arulseelan and Hanson re-derived it, devised the monotone completeness argument, and reworked GPT 6 Astra's preliminary write-up | https://postcutoff.com/e/2026-10-19-quasitrace-monotone-completeness-counterexamples-openai/ |
| Irrationality exponent of π | 1953 | 73 | OpenAI internal model (unreleased) | Awaiting review | Lean-verified | 2026-10-06 | Claimed: μ(π) = 2 (ineffective); hence Σ 1/(n³ sin² n) converges, and Σ 1/(n^a \|sin n\|^b) converges iff a > max{1, b}. | Autonomous per OpenAI's README: 'The vast majority of results were obtained with the same procedure using an unreleased internal OpenAI model' (about three hours of ChatGPT Pro thinking compute per result on average); family 017 is not among the listed exceptions; no human author is named | https://postcutoff.com/e/2026-10-06-irrationality-exponent-pi-openai/ |
| Is every group good | 1953 | 73 | OpenAI internal model (math release) | Awaiting review | Preprint only | 2026-10-06 | Claimed: disk embedding fails in general and F₂ is not good; a PD4 group with no closed aspherical manifold model; homotopy-equivalent but non-homeomorphic closed aspherical 4-manifolds with hyperbolic fundamental group | Autonomous AI output released by OpenAI | https://postcutoff.com/e/2026-10-06-openai-borel-conjecture-dimension-four-free-group-not-good/ |
| Existence of four-dimensional interacting quantum field theories | 1954 | 72 | OpenAI internal model | Awaiting review | Lean-verified | 2026-10-26 | Claimed rigorous existence proof; details, method and paper not public | Unknown; a physics panel led by David Gross reviews it and will write its own account | https://postcutoff.com/e/2026-10-26-openai-yang-mills-qcd-existence-claim/ |
| Harary–Hill conjecture on cr(K_n); Zarankiewicz's crossing-number conjecture for K_m,n | 1954 | 72 | OpenAI internal model (openai/math release); ChatGPT (Astra) for Balko's exposition | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed exact formulas for all n and all m, n, with Lean proofs of both equalities; independent simplified human proof of the K_n case (Balko) | Manuscripts credited to 'OpenAI' as model output with no human author; human reading, simplification and exposition by Balko (with ChatGPT's help in understanding the proof), another exposition in preparation by Salazar | https://postcutoff.com/e/2026-10-06-harary-hill-zarankiewicz-crossing-numbers-openai/ |
| Linear MDS conjecture | 1955 | 71 | ChatGPT; Claude; Claude Opus 5.5 | Awaiting review | Lean-verified | 2026-10-20 | For q even and 2 ≤ k ≤ q, the maximum length of a k-dimensional linear MDS code over F_q is q + 1, or q + 2 when k ∈ {3, q − 1} | Human-led with AI tools: Kumar devised the argument and Claude helped formalize it in Lean; Chen and Huang used ChatGPT to explore proof strategies and check calculations | https://postcutoff.com/e/2026-10-20-mds-conjecture-even-characteristic-chatgpt-claude-lean/ |
| Kadison's similarity problem | 1955 | 71 | OpenAI internal model (openai/math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed: yes, for every unital C*-algebra and every Hilbert space, together with a uniform amplified commutator estimate and one hyperreflexivity constant for all von Neumann algebras | Autonomous AI output released by OpenAI under its fixed procedure (README) | https://postcutoff.com/e/2026-10-06-openai-kadison-similarity-problem-lean/ |
| Optimal constant in the i.i.d. Berry–Esseen inequality | 1956 | 70 | ChatGPT; Codex; Gemini; Antigravity | Awaiting review | Expert-checked | 2026-10-29 | Claimed: C_n ≤ C_E = (3+√10)/(6√(2π)) ≈ 0.40973 for every n ≥ 1, so the optimal constant equals Esseen's lower bound | AI-assisted: the two authors directed the reductions, certificate schemas and verification runs; AI systems helped with exploration, checking code, distributed verification and drafting; Hexagon text label 'primarily AI-generated', understanding 'some parts' | https://postcutoff.com/e/2026-10-29-berry-esseen-constant-esseen-sharp-certificate-claim/ |
| Pierce–Birkhoff conjecture | 1956 | 70 | GPT-5.6; GPT-6; Claude Opus 5; Claude Fable 5.1 | Awaiting review | Lean proof, not yet reviewed | 2026-09-09 | Explicit continuous piecewise-quadratic function on R^30 that is not a finite lattice combination of polynomials; further counterexamples in dimensions 5, 6, 7, 22, 24 and 72. | Humans gave high-level direction on which targets mattered and wrote the final exposition; a multi-model agent system found and reviewed the construction | https://postcutoff.com/e/2026-09-09-pierce-birkhoff-conjecture-disproved/ |
| Simon's Problem 2 | 1958 | 68 | OpenAI internal model (math release) | Awaiting review | Lean proof, not yet reviewed | 2026-10-06 | Claimed for uniform site potentials: pure-point spectrum throughout the spectrum in 2D at every disorder; purely absolutely continuous spectrum on an open energy interval in every d ≥ 3 at small disorder | Autonomous AI output released by OpenAI; an expert appendix shortens one step; a third-party AI-assisted Lean formalization of the 3D result | https://postcutoff.com/e/2026-10-06-openai-anderson-localization-2d-delocalization-3d/ |
| Sendov's conjecture | 1958 | 68 | GPT-5.6 Pro | Result confirmed | Lean-verified | 2026-08-05 | Proof of Sendov's conjecture for all degrees, formally verified in Lean. | Human orchestrated (Mazur); Tao simplified and formalised with AI agents | https://postcutoff.com/e/2026-08-05-sendov-conjecture-proved/ |
| Nagata's conjecture on plane curves | 1959 | 67 | OpenAI internal model (unreleased) | Result confirmed | Preprint only | 2026-10-21 | For r ≥ 10 very general points in P², every nonzero curve of degree d with multiplicities m_i satisfies Σ m_i < d√r (claimed by OpenAI; reorganized and re-proved by Tevelev). | Autonomous AI proof (OpenAI release, no human author); Tevelev re-derived, simplified and presented it, using ChatGPT Astra only for editing and figures | https://postcutoff.com/e/2026-10-21-nagata-conjecture-openai-proof-tevelev-exposition/ |
| Serre's 1960 conjecture | 1960 | 66 | GPT-6 Astra | Awaiting review | Preprint only | 2026-10-28 | Proof in mixed characteristic, completing the conjecture (positive characteristic: Abe 2025; residue characteristic zero: classical) | Kisin directed the work; GPT Astra was used extensively to find the proofs and write the first draft; Kisin checked, refined and rewrote | https://postcutoff.com/e/2026-10-28-kisin-serre-artin-character-conjecture-gpt-astra/ |
| Ulam's problem | 1960 | 66 | GPT-6 Astra | Awaiting review | Preprint only | 2026-10-13 | Yes: every Lie group, and hence every locally compact second countable group, embeds in Sym(N). | AI-assisted: GPT-6 Astra produced the key countable-index deformation for SL3(R) after three weeks of discussion; the authors extended it to all simple Lie groups, checked it and rewrote the proof | https://postcutoff.com/e/2026-10-13-ulam-problem-lie-groups-countably-representable-gpt-6-astra/ |
| Complexity of optimal prefix-free coding with unequal letter costs | 1961 | 65 | Codex | Awaiting review | Preprint only | 2026-11-04 | NP-complete even for letter costs (M, M+1) given in the input | AI-assisted: authors posed the question and guided; Codex produced the reduction strategy and much of the proof | https://postcutoff.com/e/2026-11-04-huffman-unequal-letter-costs-np-complete-codex/ |
| Vaught's conjecture for L_ω1,ω | 1961 | 65 | Claude Code; Codex; Claude Opus 4.5–5.5; Claude Fable 5/5.1; GPT-5.2–GPT-6; GPT Pro | Awaiting review | Lean-verified | 2026-10-10 | Disproved for L_ω1,ω: an explicit sentence with exactly ℵ1 countable models and no perfect set of non-isomorphic models. | Human-led: Knight's framework and draft; Ackerman and Freer directed the work; coding agents did the Lean formalization and helped search for the combinatorial template, with SMT/Horn-clause solvers | https://postcutoff.com/e/2026-10-10-vaught-conjecture-infinitary-counterexample-lean/ |
| Erdős–Sós conjecture | 1962 | 64 | GPT-6 Astra (pre-release) | Result confirmed | Lean-verified | 2026-09-03 | Full proof: every n-vertex graph with more than (k−2)n/2 edges contains every tree on k vertices. | Autonomous discovery and Lean proof in Epoch's benchmark harness; humans checked, simplified and generalised it afterwards | https://postcutoff.com/e/2026-09-03-erdos-sos-conjecture-proved-gpt-6-astra/ |
| Non-uniqueness of weak solutions of the unforced 2D Euler equations with vorticity in L^p, 2 < p < ∞ | 1963 | 63 | GPT-6.1 Sol; Claude Opus 5.5; ChatGPT 5.6; ChatGPT 6.0; ChatGPT 6.1; GPT-6 Astra | Awaiting review | Lean-verified | 2026-10-17 | Three independent claimed constructions of two distinct solutions with the same initial vorticity: vanishing-viscosity solutions for every p > 2 (Pappalettera–Sorella, fully AI-generated), renormalized weak solutions in L¹ ∩ L^q for every q < ∞ (Coiculescu, Lean-formalized), and finite-energy solutions in every finite L^p (Choi) | Ranges from none (Pappalettera–Sorella: prompted only, no edits, no claim of authorship) to human strategy with AI-written details (Coiculescu: idea and strategy his, proofs, code and text largely by Claude; Choi: main ideas his, ChatGPT completed technical details) | https://postcutoff.com/e/2026-10-17-2d-euler-unforced-nonuniqueness-lp-vorticity-ai/ |
| Formalization of Hironaka's resolution of singularities in characteristic zero | 1964 | 62 | Claude Fable 5.1; GPT-6 Astra | Result confirmed | Lean-verified | 2026-10-06 | Sorry-free Lean 4 + Mathlib library (~500–600k lines) of Hironaka's main theorems and modern refinements, for schemes and analytic spaces | Humans wrote the 112-page plan, chose sources and intervened ~30 times; agents wrote the proofs and Lean code | https://postcutoff.com/e/2026-10-06-hironaka-resolution-of-singularities-lean-fable-agents/ |
| Erdős Matching Conjecture | 1965 | 61 | unnamed generative AI | Awaiting review | Preprint only | 2026-10-12 | Tail conjecture proved for all k; Erdős Matching Conjecture proved for fixed k ≥ 3, s sufficiently large, all n ≥ k(s+1). | AI-assisted: humans built the framework and the k = 2–5 and k ≥ 10^100 cases; AI produced the unified k ≥ 6 argument and the idea that closed a gap | https://postcutoff.com/e/2026-10-12-erdos-matching-conjecture-large-matchings-ai/ |
| Birch and Swinnerton-Dyer conjecture in rank ≤ 1 | 1965 | 61 | OpenAI internal model (openai/math release) | Awaiting review | Preprint only | 2026-10-06 | Claimed: full BSD formula whenever some p-power Selmer group has corank 0 or 1; Goldfeld's 50/50 density and mean analytic rank 1/2 for the quadratic twists of every E/ℚ; hence full BSD for a density-one set of twists of every curve | Autonomous AI output released by OpenAI under its fixed procedure (README) | https://postcutoff.com/e/2026-10-06-openai-bsd-low-selmer-corank-goldfeld-claim/ |
| Lehmer's permutation conjecture | 1965 | 61 | Claude Opus 5.5; Aristotle | Awaiting review | Lean-verified | 2026-10-01 | Proof of Verhoeff's reformulation (Hamiltonicity of the non-stutter-word graph N(S), with two exceptional families), and hence of Lehmer's conjecture. | Human-led long project; the final short proof was found and developed by Claude Opus 5.5 in a multi-agent setup, then re-derived and checked by the author | https://postcutoff.com/e/2026-10-01-lehmer-permutation-conjecture-opus-5-5/ |
| Kinetic Krylov–Safonov theorem and Pucci's conjecture | 1966 | 60 | GPT-6 Astra Ultra; GPT-6 Astra; GPT-6 Pro | Awaiting review | Preprint only | 2026-10-09 | Aleksandrov estimate sup u ≤ C‖f‖_{L^p} for Kolmogorov equations with rough coefficients, giving the kinetic Krylov–Safonov theorem; AI manuscripts also claim Pucci's conjecture in every dimension and its parabolic version. | Autonomous per the authors: each AI source is marked 'Human contribution: None' (the authors wrote the prompt and research instructions). The six mathematicians checked the kinetic proof, wrote a human exposition and published the chats | https://postcutoff.com/e/2026-10-09-kinetic-krylov-safonov-pucci-conjecture-gpt-6-astra/ |
| Lonely Runner Conjecture | 1967 | 59 | ChatGPT 6 Pro; GPT-6 Astra | Awaiting review | Preprint only | 2026-10-16 | ML(V) > (1+c)/(2n) for an absolute constant c > 0, the first constant-factor improvement over the union bound 1/(2n) | Human-led: authors developed the strategy; ChatGPT 6 Pro/Astra proposed the GCD-sum ingredient, pointed to Green–Walker, fixed gaps and turned informal proofs into rigorous ones | https://postcutoff.com/e/2026-10-16-lonely-runner-constant-gap-hu-jing-chatgpt/ |
| Stein's Fourier restriction conjecture in ℝ³ | 1967 | 59 | OpenAI internal model (openai/math release) | Awaiting review | Preprint only | 2026-10-06 | Claimed full resolution of each in three dimensions (planar endpoint for Carleson) in OpenAI manuscripts of 24 Sept 2026, released 6 Oct; not formally verified and not yet reviewed | Credited to 'OpenAI' with no named human authors; OpenAI marks the release's review status as unchecked | https://postcutoff.com/e/2026-10-06-openai-release-3d-restriction-bochner-riesz-claims/ |
| Grad's conjecture | 1967 | 59 | GPT-6 Astra Pro; GPT-5.6 Sol; Claude Fable 5; Claude Opus 5; GPT-6 Astra; Claude Fable 5.1 | Result confirmed | Lean-verified | 2026-09-21 | Three families of smooth, non-symmetric toroidal equilibria with nested pressure surfaces and non-constant pressure: one C_N-symmetric family proved with Nash–Moser methods and certified in Lean (Gómez-Serrano–Liehr–Taylor), and two explicit analytic families (Landreman). | Landreman: solutions discovered by GPT-6 Astra Pro, equations checked by hand. Gómez-Serrano–Liehr–Taylor: human roadmap, LLMs filled in technical details and wrote the Lean proof under guidance. | https://postcutoff.com/e/2026-09-21-grad-conjecture-counterexamples/ |
| Barnette's conjecture | 1969 | 57 | OpenAI internal model (unreleased) | Result confirmed | Lean proof, not yet reviewed | 2026-10-21 | Every cubic 3-connected bipartite planar graph has a Hamiltonian cycle; indeed G − e is Hamiltonian for every edge e (claimed by OpenAI; written out and partly re-proved by Li). | Autonomous AI proof (OpenAI release); Zhentao Li re-derived it by hand with combinatorial replacements, using LLMs to read the preprint and format the note | https://postcutoff.com/e/2026-10-21-barnette-conjecture-openai-proof-zhentao-li-exposition/ |
| Exponent ω of matrix multiplication | 1969 | 57 | OpenAI internal model (openai/math release) | Result confirmed | Lean-verified | 2026-10-06 | ω ≤ 9/4 over ℂ (OpenAI, non-constructive, Lean-formalized); re-proved over every field and made constructive by independent authors within three weeks | Autonomous AI output released by OpenAI; independent human-led re-proofs (Amanov–van den Berg–Zuiddam, Pass), both AI-assisted | https://postcutoff.com/e/2026-10-06-openai-matrix-multiplication-omega-9-4/ |
| Erdős problem #108 | 1969 | 57 | ChatGPT; Codex; GPT-6 Astra | Result confirmed | Lean-verified | 2026-09-15 | Negative answer: for every M there is a triangle-free graph with χ > M whose C4-free subgraphs are all 6-colourable (Kohlmeyer–Kruer, Lean-verified); improved to 3-colourable by Nguyen–Walczak. | AI-assisted: two Purdue authors developed the construction and the Lean proof with substantial ChatGPT/Codex help. In the follow-up, GPT-6 Astra found the proof of the 3-colourable lemma and the experts streamlined it. | https://postcutoff.com/e/2026-09-15-erdos-108-high-girth-problem-disproved-conjectures-io/ |
| Matrix mortality problem in dimension 2 | 1970 | 56 | OpenAI Codex; GPT-5.6 Sol; Claude Code | Awaiting review | Lean-verified | 2026-11-04 | Claimed undecidable for finite families (5,799 matrices) of 2×2 integer matrices | AI-assisted: authors chose the final proof architecture and reworked the exposition; AI used for research, proofs and Lean code | https://postcutoff.com/e/2026-11-04-matrix-mortality-2x2-undecidable-codex-claude-lean/ |
| Golomb–Welch conjecture | 1970 | 56 | ChatGPT | Awaiting review | Preprint only | 2026-10-25 | Claimed full proof, in both the lattice and the arbitrary-centre forms | AI-assisted: authors used ChatGPT to explore proof strategies and check calculations; the authors say they wrote all results and proofs | https://postcutoff.com/e/2026-10-25-golomb-welch-conjecture-perfect-lee-codes-chatgpt/ |
| Erdős–Szemerédi sunflower conjecture, all k | 1970 | 56 | ChatGPT 6 Astra Pro | Awaiting review | Lean-verified | 2026-10-19 | Claimed proof for every k ≥ 3, with the bound 2^((1 − 1/(16k³))n), via a new polynomial-method bound for vector sunflowers. | AI-assisted: the authors posed the generalization of Naslund–Sawin and rewrote the argument; ChatGPT 6 Astra Pro found the proof of the key Theorem 2 | https://postcutoff.com/e/2026-10-19-erdos-szemeredi-sunflower-conjecture-gpt-6-astra-pro/ |
| Open Erdős problems | 1970 | 56 | AlphaProof Nexus; Gemini 3.1 Pro; AlphaProof | Result confirmed | Peer-reviewed | 2026-10-08 | Lean-verified resolutions of 9 of 353 attempted open Erdős (sub-)problems, 44 of 492 open OEIS conjectures, 2 of 4 open Hilbert-function problems, and an exact O(1/t) rate for anchored GDA. | Autonomous on the Erdős and OEIS evaluation (humans chose and formalized problems, reviewed formalizations); AI-assisted collaboration in the deployment results | https://postcutoff.com/e/2026-10-08-alphaproof-nexus-science-paper/ |
| Hilbert's tenth problem over ℚ | 1970 | 56 | OpenAI internal model (openai/math release) | Awaiting review | Preprint only | 2026-10-06 | Claimed negative answer: rational solvability is undecidable (number of variables part of the input), via a Turing reduction from integer solvability to finitely many rational tests | Autonomous AI output released by OpenAI under its fixed procedure (README) | https://postcutoff.com/e/2026-10-06-openai-hilbert-tenth-problem-rationals-claim/ |
| Singmaster's conjecture on multiplicities of binomial coefficients | 1971 | 55 | Claude Opus 5.5 | Awaiting review | Lean-verified | 2026-11-05 | Claimed unconditional bound N(t) = O((log t)^(1/2+o(1))) | AI-generated proofs, formalization and most text; human contributor checked some parts | https://postcutoff.com/e/2026-11-05-singmaster-bound-claude-opus-5-5-whitmore/ |
| Chvátal's conjecture | 1972 | 54 | ChatGPT; GPT-6 Astra; Codex | Result confirmed | Lean-verified | 2026-09-16 | Proof of Chvátal's conjecture via a sharp correlation inequality, followed by an AI-found short spectral proof and a Lean formalization. | AI-assisted, human-led original proof (ChatGPT tested inequalities and proved a guiding special case); the short spectral proof was found by GPT-6 Astra under human direction | https://postcutoff.com/e/2026-09-16-chvatal-conjecture-proved/ |
| Hochster's small Cohen–Macaulay module conjecture | 1973 | 53 | OpenAI internal model (unreleased); ChatGPT; Claude | Awaiting review | Lean-verified | 2026-10-21 | A 3-dimensional complete Noetherian normal local domain over C with no nonzero finitely generated maximal Cohen–Macaulay module (OpenAI); Anghel extends the obstruction to all dimensions ≥ 3. | Counterexample autonomous (OpenAI release), building on human preprints by Anghel, Lopez and Chen; Anghel's survey re-proves and generalizes it, with proofs drafted with ChatGPT and Claude | https://postcutoff.com/e/2026-10-21-hochster-small-cohen-macaulay-counterexample-openai-anghel-survey/ |
| Penrose conjecture | 1973 | 53 | Claude | Awaiting review | Preprint only | 2026-10-14 | Spacetime Penrose inequality in all dimensions n ≥ 3 for 'maximally parameterized' initial data (with a horizon nondegeneracy condition), via new generalized Schoen–Yau identities; the general case is reduced to solving a degenerate PDE system | Human-led: the key t = 1 identity was derived by hand; Claude did and checked the algebra for general t and made 'useful mathematical suggestions' the authors call co-author level but 'not decisive' | https://postcutoff.com/e/2026-10-14-penrose-conjecture-bray-khuri-claude-openai-provenance/ |
| Amenability of Thompson's group F | 1973 | 53 | OpenAI internal model (unreleased) | Result confirmed | Lean-verified | 2026-10-13 | Claimed by OpenAI and re-proved in streamlined form by Kim and Lodha: F is nonamenable. | Autonomous AI proof (OpenAI release); human experts simplified, generalized and wrote it out without AI | https://postcutoff.com/e/2026-10-13-thompson-group-f-nonamenable-kim-lodha-exposition/ |
| Cycle double cover conjecture | 1973 | 53 | GPT-5.6 Sol Ultra | Result confirmed | Expert-checked | 2026-07-17 | Proof that every bridgeless graph admits a cycle double cover. | Autonomous proof per OpenAI; human experts wrote independent expositions | https://postcutoff.com/e/2026-07-17-cycle-double-cover-conjecture-proved/ |
| Double-cap conjecture / Witsenhausen's problem on spherical sets without orthogonal pairs | 1974 | 52 | Codex; AI-assisted tools (unspecified) | Awaiting review | Lean-verified | 2026-10-20 | For n ≥ 3, sets in S^(n−1) with no orthogonal pair have measure at most that of two opposite caps of radius π/4, with equality only for double caps (claimed) | Human-led paper with an assistive AI role; the separate Lean proof was produced almost entirely with AI-assisted tools | https://postcutoff.com/e/2026-10-20-double-cap-conjecture-witsenhausen-lean-ai/ |
| Rauch's hot spots conjecture, simply connected planar case | 1974 | 52 | OpenAI internal model (openai/math release); ChatGPT (follow-ups by Burdzy and Bañuelos) | Awaiting review | Lean-verified | 2026-10-06 | Claimed: on every smooth bounded simply connected planar domain, every first nonconstant Neumann eigenfunction has no interior critical point, so its extrema lie only on the boundary; eigenvalue multiplicity allowed | Autonomous AI output released by OpenAI under its fixed procedure (README); the follow-ups were generated with ChatGPT from prompts by Burdzy and by Bañuelos | https://postcutoff.com/e/2026-10-06-openai-hot-spots-conjecture-simply-connected-lean/ |
| Strong cosmic censorship near Kerr, in Christodoulou's formulation | 1974 | 52 | OpenAI internal model (math release) | Awaiting review | Preprint only | 2026-10-06 | Claimed local strong cosmic censorship near every fixed subextremal rotating Kerr spacetime (C⁰ ∩ W^{1,2}_loc, plus C¹ and C² versions), without symmetry | Autonomous AI output released by OpenAI; reading group of specialists organised by Sung-Jin Oh | https://postcutoff.com/e/2026-10-06-openai-strong-cosmic-censorship-near-kerr/ |
| Kung–Traub conjecture on the maximal order of multipoint iterations without memory | 1974 | 52 | ChatGPT 6; ChatGPT 5.6 | Awaiting review | Lean-verified | 2026-09-20 | Local order ≤ 2^(n−1) for any memoryless method with n evaluations per step, for real and complex scalar evaluations; sharper bound for grouped evaluations | Human-led: proofs by the author; ChatGPT 6 assisted the Lean formalization and ChatGPT 5.6/6 were used to discuss and check arguments | https://postcutoff.com/e/2026-09-20-kung-traub-conjecture-proved-colbrook-lean-chatgpt/ |
| Murty–Simon conjecture | 1975 | 51 | GPT-5.6 Sol; GPT-6 Astra | Awaiting review | Preprint only | 2026-10-28 | Claimed proof for every n (previously known only for n beyond a tower-type bound, Füredi 1992) | AI-assisted: GPT-5.6 Sol found the n²/4 bound and the even-n equality case; the authors simplified it, proved the odd-n equality case and wrote the paper | https://postcutoff.com/e/2026-10-28-murty-simon-conjecture-proof-gpt-5-6-sol-das-fox/ |
| Erdős–Lovász problem | 1975 | 51 | unnamed generative AI tools | Awaiting review | Preprint only | 2026-10-27 | m(k) ≥ k^k·exp(−50√(k log k)) for log k ≥ 32, so m(k) = k^k·exp(−k^(1/2+o(1))) with Zakharov's bound; the Frankl–Ota–Tokushige conjecture is false for large k | AI found the construction; the authors verified the proofs, reworked the arguments and wrote the exposition | https://postcutoff.com/e/2026-10-27-erdos-lovasz-intersecting-covering-number-frankl-ai-construction/ |
| Polyakov's conjecture | 1975 | 51 | OpenAI internal model (math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed: exponential decay for all n ≥ 3 and all β (Lean-formalized in finite volume); an Osterwalder–Schrader continuum O(3) theory with unique vacuum, mass gap and an isolated particle pole; exact O(4) lattice mass asymptotics | Released as model output under OpenAI's fixed procedure, with no human author named; first reactions by mathematical physicists quoted in the press | https://postcutoff.com/e/2026-10-06-openai-polyakov-o3-sigma-model-mass-gap-claim/ |
| Erdős's conjecture on arithmetic progressions | 1976 | 50 | OpenAI internal model (math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed proof via quasipolynomial bounds r_k(N) ≤ C_k N exp(−c_k (log N)^ε_k) for every k ≥ 3; the qualitative conjecture is proved in Lean (with, per Bloom, a weaker quantitative bound inside the formal proof) | Released as model output under OpenAI's fixed procedure, with no human author named; no human exposition or check yet | https://postcutoff.com/e/2026-10-06-openai-erdos-arithmetic-progressions-conjecture-claim/ |
| Serre's cyclicity problem | 1977 | 49 | GPT-6; ChatGPT | Awaiting review | Unverified claim | 2026-10-31 | Claimed positive lower density c_E/(32 log 32) for every E/ℚ without full rational 2-torsion, CM and non-CM alike (known before under GRH, or for CM curves) | Human-led with AI writing: Bhargava's handwritten argument; GPT-6 added writing and details and helped with the Lean formalisation; builds on OpenAI's AI-generated analytic estimates | https://postcutoff.com/e/2026-10-31-bhargava-cyclic-reduction-elliptic-curves-positive-proportion-gpt-6/ |
| Erdős–Hajnal for all paths | 1977 | 49 | ChatGPT-6 Astra; Google DeepMind internal model; Claude Opus 5.5 | Awaiting review | Lean-verified | 2026-10-17 | Claimed proof that every path P_t (and the subdivided claws S_{1,2,t}) has the Erdős–Hajnal property; DeepMind's model and a Claude-assisted manuscript claim the P_t case independently. | Human-led (Nguyen): the author's framework, with Astra proving parts of key lemmas; DeepMind's and the Claude manuscripts are described as AI-generated | https://postcutoff.com/e/2026-10-17-erdos-hajnal-all-paths-nguyen-astra-deepmind/ |
| Asymptotic value of Delsarte's linear programming bound for binary codes and spherical codes | 1977 | 49 | Claude Opus 5.5; GPT-5.6 Sol; GPT-6 Astra; Codex | Awaiting review | Preprint only | 2026-10-15 | Exact asymptotic rates of the binary and spherical Delsarte LPs for all distances, in closed form via elliptic integrals (matching upper and lower bounds). | AI-assisted: human-led program; GPT-5.6 Sol co-formulated the upper bounds; Opus 5.5 found the key compatibility and the obstacle-problem reformulation 'with light direction'; Codex drafted | https://postcutoff.com/e/2026-10-15-delsarte-lp-bound-exact-rate-salmon-opus/ |
| Brennan's conjecture on integrability of \|g′\|^p for conformal maps; Kraetzer's t²/4 conjecture for the universal integral-means spectrum | 1978 | 48 | OpenAI internal model (openai/math release) | Result confirmed | Lean-verified | 2026-10-16 | OpenAI's internal model proved Brennan's conjecture and disproved Kraetzer's conjecture at t = −1 (preprints dated 24 Sept, released 6 Oct). Four experts checked the work and gave a short independent proof that B_b(t) ≤ t²/4 on [−2, 2], strict except at 0 and ±2 | AI-generated original proof; Binder, Ivrii, Prause and Smirnov validated it and wrote a shorter, stronger proof without AI help (some used AI agents to understand the AI proof) | https://postcutoff.com/e/2026-10-16-brennan-conjecture-openai-proof-binder-ivrii-prause-smirnov/ |
| De Giorgi's conjecture | 1978 | 48 | OpenAI internal model (math release) | Awaiting review | Preprint only | 2026-10-06 | Claimed proof in the sharp dimension 8 without Savin's limit assumption; classification of stable solutions in ℝ⁷ without energy growth | Autonomous AI output released by OpenAI | https://postcutoff.com/e/2026-10-06-openai-de-giorgi-conjecture-dimension-eight/ |
| Irrationality of ζ(5) | 1978 | 48 | Claude Opus 5; Claude Opus 5.5; Claude Code; unnamed generative AI tool (paper) | Result confirmed | Lean-verified | 2026-09-17 | ζ(5) is irrational, with integer polynomials Q_n of degree 37n satisfying 0 < Q_n(ζ(5)) < exp(−139n²/5), and irrationality measure at most 260. | Paper by a single human author who discloses AI only for editing and consistency checks (disputed by Calegari). One Lean formalization was written by Claude agents directed by Dan Romik; the other, by Moritz Firsching, does not say how it was produced. | https://postcutoff.com/e/2026-09-17-zeta-5-irrational-fauzan-lean-verified/ |
| Abundance conjecture | 1980 | 46 | OpenAI internal model (math release); Liu: DeepSeek, Fable, GLM, ChatGPT, Danus, Rethlas | Awaiting review | Preprint only | 2026-10-06 | OpenAI claims log abundance for rational-boundary lc pairs and canonical nonvanishing in every dimension in characteristic zero. Liu (human-led, AI-assisted) proves nonvanishing ⇒ abundance for lc pairs | OpenAI: autonomous AI output released by OpenAI. Liu: human-led paper written with several AI models and agent systems | https://postcutoff.com/e/2026-10-06-openai-log-abundance-nonvanishing-claim/ |
| Smale's mean value problem | 1981 | 45 | Claude; ChatGPT | Awaiting review | Lean-verified | 2026-11-11 | Claimed: the best constant over all degrees is exactly 4 (Smale's original bound), approached but not attained as the degree grows | Author steered AI models in dialogue; work 'done overwhelmingly by AI models' | https://postcutoff.com/e/2026-11-11-smale-mean-value-constant-equals-4-goel-lean/ |
| Smale's mean value conjecture | 1981 | 45 | GPT-6 Astra (pre-release); Grok 4.6 | Result confirmed | Lean-verified | 2026-09-03 | Disproved: a polynomial with p(0) = 0, p'(0) = 1 and \|p(c)/c\| > 1 at every critical point exists (Lean). Follow-up: Smale's constant M > 1.1018. | Autonomous (benchmark run, no human steering); follow-up bound by Jatar & Ng with AI drafts rewritten by the authors | https://postcutoff.com/e/2026-09-03-smale-mean-value-conjecture-disproved-gpt-6-astra/ |
| Erdős's question | 1982 | 44 | GPT-6 Pro; GPT-6.1; Claude Opus 5.5 | Awaiting review | Preprint only | 2026-10-30 | Claimed affirmative answer (previous best upper bound 2^{1.0819…n^{3/2}}, Kleitman–Winston 1982) | Human-led: main ideas by the author; GPT-6 Pro helped complete the proofs; GPT-6.1 and Opus 5.5 revised the text | https://postcutoff.com/e/2026-10-30-number-of-c4-free-graphs-erdos-question-tianchi-yang-gpt-6-pro/ |
| Baum–Connes conjecture without coefficients | 1982 | 44 | OpenAI internal model (math release) | Awaiting review | Preprint only | 2026-10-06 | Claimed counterexamples: failure of rational injectivity for a torsion-free group, failure of surjectivity via an irrational-trace projection, and a torsion-free group with a nontrivial projection; the surjectivity failure re-proved in a stronger form by Guoliang Yu | Autonomous AI output released by OpenAI; follow-up construction by Guoliang Yu, who states all proofs in it are his own | https://postcutoff.com/e/2026-10-06-openai-baum-connes-kadison-kaplansky-counterexamples/ |
| Yau's conjecture | 1982 | 44 | OpenAI internal model (math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed: upper bound true on all smooth surfaces (completing the conjecture in dimension 2); upper bound false for smooth metrics in dimensions 3 and 4, and by a power of λ on S⁴×S¹ | Autonomous AI output released by OpenAI, with Lean formalizations | https://postcutoff.com/e/2026-10-06-openai-yau-nodal-conjecture-surfaces-counterexamples/ |
| Classification of Finite Simple Groups | 1983 | 43 | AxiomProver; Axiom agents (models not disclosed) | Awaiting review | Lean-verified | 2026-10-27 | Claimed complete, sorry-free Lean 4 formalization of the first-generation CFSG proof against TauCeti's statement, plus a repaired step in one published route to the Unbalanced Group Theorem | AI agents formalized the literature from a human-written blueprint; about 34 named mathematicians and engineers; experts Lyons and Solomon consulted | https://postcutoff.com/e/2026-10-27-axiom-cfsg-classification-finite-simple-groups-lean/ |
| Haldane conjecture / Haldane gap for the spin-one antiferromagnetic Heisenberg chain | 1983 | 43 | OpenAI internal model (math release); ChatGPT Astra (Tasaki follow-up) | Awaiting review | Preprint only | 2026-10-06 | Uniform positive spectral gap above a unique ground state on even periodic rings (Δ₁ ≥ log 20/784), plus a boundary-field gap for odd open chains with a nontrivial topological index | Autonomous AI output released by OpenAI; Tasaki's follow-up is AI-assisted (he set problems and strategy, ChatGPT Astra developed proofs) | https://postcutoff.com/e/2026-10-06-openai-spin-one-haldane-gap-proof/ |
| Rigorous critical storage capacity of the Hopfield associative-memory model at zero temperature | 1985 | 41 | Claude Opus 5.5; GPT-6.1 Sol | Awaiting review | Unverified claim | 2026-11-05 | Claimed bracket αc ∈ [0.138198129, 0.13820106] | Mainly AI-generated; human contributor checked parts | https://postcutoff.com/e/2026-11-05-hopfield-critical-capacity-claude-opus-5-5/ |
| Falconer's distance conjecture | 1985 | 41 | OpenAI internal model (openai/math release) | Awaiting review | Lean-verified | 2026-10-06 | Claimed in every dimension d ≥ 2, with a Lean proof of the exact statement (comparator accepted) | Autonomous AI output released by OpenAI under its fixed procedure (README) | https://postcutoff.com/e/2026-10-06-openai-falconer-distance-conjecture-lean/ |
| Large-data global classical existence for the three-dimensional relativistic Vlasov–Maxwell system | 1986 | 40 | OpenAI internal model (openai/math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed: every smooth compactly supported nonnegative particle density with smooth finite-energy fields satisfying the Gauss laws has a unique global classical solution, smooth on every finite time interval | Autonomous AI output released by OpenAI under its fixed procedure (README); a summary of the model's reasoning is published | https://postcutoff.com/e/2026-10-06-openai-relativistic-vlasov-maxwell-global-solutions-lean/ |
| Sidorenko's conjecture | 1986 | 40 | OpenAI internal model (math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed counterexample: an explicit 35-vertex, 66-edge bipartite incidence graph H and a (non-explicit) finite host G with t(H,G) < p(G)^66; the same H is not forcing | Released as model output under OpenAI's fixed procedure, with no human author named; no human exposition or check yet | https://postcutoff.com/e/2026-10-06-openai-sidorenko-conjecture-counterexample-claim/ |
| Erdős #993: forest independence sequences are unimodal | 1987 | 39 | Claude Opus 5.5; Claude Fable 5.1; GPT-6 Astra; GPT-5.6 Sol; GPT-6 Sol; GPT-6.1 Sol | Awaiting review | Lean-verified | 2026-09-27 | Claimed: yes for every finite forest. Two proofs: Zhang–Li (27 Sept 2026, computer-assisted, GPT-6 Astra for computations) and Li–Vallier–Zhang (6 Oct 2026, new arguments and Lean 4 proof attributed to AI agents). | First proof: human strategy with GPT-6 Astra for computations. Second proof: AI-generated per the paper (all new mathematics, the Lean proof and most of the prose), in a project directed by Kevin Vallier and built on Zhang and Li's reductions | https://postcutoff.com/e/2026-09-27-erdos-993-forest-independence-polynomials-unimodal/ |
| Aggarwal–Vitter | 1988 | 38 | ChatGPT; Codex | Awaiting review | Lean-verified | 2026-10-14 | Deterministic external-memory sort of Θ(log N)-bit integers with asymptotically fewer block transfers than the comparison bound in a range of parameters, via a new network-coding-over-routing construction | AI-assisted: the authors (two of them the conjecture's original proposers) directed the work; ChatGPT/Codex 'materially affected' constructions, analyses and the Lean proofs | https://postcutoff.com/e/2026-10-14-external-memory-integer-sorting-beats-comparison-bound-network-coding/ |
| k-server conjecture | 1988 | 38 | GPT-6 Astra (ChatGPT); ChatGPT 5.5 Pro; Gemini 3.1 Pro | Awaiting review | Preprint only | 2026-09-14 | Deterministic k-competitiveness of the work function algorithm on every metric space. | Human-designed potential and k = 3 proof; the AI generalised it to all k; humans adapted and verified the final proof | https://postcutoff.com/e/2026-09-14-k-server-conjecture-proved/ |
| Hardy–Littlewood–Chowla conjecture, case Σ_{p≤x} µ(p+h) | 1989 | 37 | ChatGPT; OpenAI internal model (via the OpenAI Math Release preprint) | Awaiting review | Preprint only | 2026-10-14 | Claimed: Σ_{p≤x} µ(p+2) = o(π(x)), and each sign of µ(p+2) has density 1/2 among primes with p+2 squarefree | Human-written proof; ChatGPT helped the authors understand the OpenAI preprint's method, establish Appendix A and check the manuscript | https://postcutoff.com/e/2026-10-14-hardy-littlewood-chowla-mobius-shifted-primes-lu-wang-wu/ |
| Planar Mumford–Shah conjecture | 1989 | 37 | GPT-6 Astra (ChatGPT, Work mode) | Awaiting review | Preprint only | 2026-09-22 | Claimed classification of planar Mumford–Shah generalized global minimizers, which would imply the conjecture. | The human supplied his thesis, unpublished results and a research protocol; the model produced the proof text; checking by the author is ongoing | https://postcutoff.com/e/2026-09-22-mumford-shah-conjecture-astra-claim/ |
| Alon–Seymour–Thomas conjecture | 1990 | 36 | GPT-6 Astra; Claude Opus 5.5; ChatGPT 6 Pro; GPT-6.1 Sol | Awaiting review | Lean-verified | 2026-11-03 | Claimed proved twice: 21h√n (Lin) and O(h√n) with Lean formalization (Conroy–Le–Spalding-Jamieson) | Conroy et al.: AI-originated ideas, humans verified and rewrote; Lin: human-guided AI-assisted proof checked by hand | https://postcutoff.com/e/2026-11-03-alon-seymour-thomas-separator-conjecture-gpt-6-astra-two-proofs/ |
| Deligne–Drinfeld conjecture | 1990 | 36 | OpenAI internal model (openai/math release) | Result confirmed | Lean-verified | 2026-10-06 | Proved in full by OpenAI's internal model (dimension upper bound via characteristic two). An expert simplified the proof over 𝔽₂ and accepted that it settles the conjecture (Willwacher), and a second, independent proof identifies the motivic Galois group of mixed Tate motives over ℤ with GRT (Hirose) | AI-generated original proof; Schneps and Enriquez reworked it, Willwacher simplified and re-proved it with AI help, Hirose gave an independent proof (discussing the mathematics with GPT-6 Astra Pro) | https://postcutoff.com/e/2026-10-06-openai-deligne-drinfeld-conjecture-proof/ |
| Delocalization | 1991 | 35 | AxiomProver; unnamed LLMs | Awaiting review | Lean-verified | 2026-11-11 | QUE for W²/N → ∞ and a DMPK-described critical law at W² ≍ N for the Gaussian periodic block model | Authors provided the architecture; LLMs drafted proofs, edited by authors; AxiomProver autoformalized everything | https://postcutoff.com/e/2026-11-11-band-matrix-que-critical-crossover-axiomprover-lean/ |
| Laczkovich's Lipschitz mapping problem | 1991 | 35 | ChatGPT | Awaiting review | Preprint only | 2026-10-28 | Claimed positive answer for every d (previously only d ≤ 2), plus Kolmogorov's contraction problem for Jordan measurable sets | AI-assisted: ChatGPT produced the key proposition and lemma; the author had the framework and lower bound, rewrote the proof and wrote the paper | https://postcutoff.com/e/2026-10-28-laczkovich-lipschitz-mapping-problem-chatgpt-gaspar/ |
| Sogge's local smoothing conjecture in all dimensions; consequences | 1991 | 35 | OpenAI internal model (openai/math release) | Awaiting review | Lean-verified | 2026-10-26 | Claimed proof of local smoothing for the Euclidean wave equation in every dimension n ≥ 2 with ε loss, with Bochner–Riesz, restriction in the interior of the range, Nikodym/Kakeya maximal bounds and full Hausdorff dimension of Kakeya sets as corollaries | Credited to 'OpenAI'; released as 'model output directly', with no named human authors and no designated reviewers | https://postcutoff.com/e/2026-10-26-openai-local-smoothing-kakeya-all-dimensions-claim/ |
| Is ℤ a Diophantine subset of ℚ? | 1992 | 34 | GPT-6 Astra; GPT-6.1 Sol; Claude Opus 5.5; Claude Fable 5.1; Claude Fable 5.2; ChatGPT; Claude | Awaiting review | Lean-verified | 2026-11-05 | Two claimed proofs that ℤ is Diophantine in ℚ, with explicit quartics (Glazer: 222 variables; Burungale: degree at most four), refuting Mazur's conjecture on the topology of rational points | Glazer: manuscript produced with Astra, Sol and Opus, audited by Fable and by human-run AI reviews; Burungale: human proof, ChatGPT assisted Sections 4–5 | https://postcutoff.com/e/2026-11-05-z-diophantine-in-q-glazer-burungale/ |
| Satisfiability conjecture for random k-SAT | 1992 | 34 | OpenAI internal model (math release) | Awaiting review | Peer-reviewed | 2026-10-05 | Existence of α_k for every fixed k ≥ 3, proved twice: by Carenini via an O(n^{1/2+1/k}) scaling window plus Abbe–Montanari, and by OpenAI's models via a capped last-satisfiable-index argument; OpenAI adds Θ(n) hitting-time variance and computability of α_3 | Carenini: human proof, no LLM-generated arguments by her statement. OpenAI: autonomous output released without named authors, crediting Carenini with priority | https://postcutoff.com/e/2026-10-05-random-k-sat-satisfiability-conjecture-carenini-openai/ |
| Odlyzko–Poonen conjecture | 1993 | 33 | GPT-6 Astra | Result confirmed | Lean-verified | 2026-09-22 | Unconditional proof that random 0/1 polynomials are irreducible with probability tending to one, with the sharp asymptotic for the reducible probability. | AI-generated proofs and formalisation; the author directed the work, rewrote and checked it; an expert (Breuillard) checked the proof | https://postcutoff.com/e/2026-09-22-odlyzko-poonen-conjecture-proved/ |
| LeBrun–Salamon conjecture | 1994 | 32 | ChatGPT; OpenAI internal model (unreleased) | Awaiting review | Preprint only | 2026-10-07 | Claimed proof for all real dimensions 4n with n ≥ 2 (the 4-dimensional case was already known), via transverse rational curves on the twistor space; independently claimed in OpenAI's family 062. | Human-led with AI tools for Hu–Liu–Wan (ChatGPT as an 'auxiliary tool', role not specified); autonomous for OpenAI's family 062 | https://postcutoff.com/e/2026-10-07-lebrun-salamon-conjecture-proof/ |
| Rapid mixing of Glauber dynamics for proper colourings | 1995 | 31 | GPT-6 Astra Pro | Awaiting review | Preprint only | 2026-11-04 | Claimed spectral gap Ω(1/n) for q ≥ (1+1/e+γ)Δ, large Δ, any graph | AI-originated ideas; author simplified, verified and wrote the text | https://postcutoff.com/e/2026-11-04-glauber-dynamics-colorings-1-plus-1-over-e-gpt-6-astra-pro/ |
| 3SUM hypothesis | 1995 | 31 | Claude (Anthropic internal research model) | Awaiting review | Lean-verified | 2026-10-05 | Deterministic O(n^1.9992) 3SUM and O(n^2.9995) integer APSP, refuting the 3SUM, APSP, Exact Triangle and Zero-Weight k-Clique hypotheses and three hinted OMv conjectures | AI-originated: the core algorithm was found autonomously by Claude (16M output tokens, no human input) during an unrelated cryptography task; Alman and Vassilevska Williams simplified, extended and wrote the paper | https://postcutoff.com/e/2026-10-05-claude-refutes-3sum-apsp-hypotheses/ |
| Kannan–Lovász–Simonovits conjecture | 1995 | 31 | GPT-6 Astra; GPT-5.6 Sol; Claude Fable 5; Claude Fable 5.1; ChatGPT | Awaiting review | Preprint only | 2026-10-02 | Universal O(1) bound on the KLS constant ψ_n (Song–Zhang); a second, AI-generated proof via Song–Zhang's criterion (Bizeul–Klartag–Lehec) | AI-assisted (Song–Zhang: human-chosen approaches, AI co-developed); largely AI-generated (Bizeul–Klartag–Lehec: authors mainly understood and exposited ChatGPT's proofs) | https://postcutoff.com/e/2026-10-02-kls-conjecture-proved-ai-assisted/ |
| Pach–Shahrokhi–Szegedy conjecture | 1996 | 30 | ChatGPT-6 | Awaiting review | Expert-checked | 2026-11-05 | Proof produced by ChatGPT-6; simplified self-contained proof by Pach, Tardos and Zeng | AI produced the proof (relying on Beeker–Lazarovich); human experts rewrote and simplified it | https://postcutoff.com/e/2026-11-05-quasiplanar-graphs-linear-edges-chatgpt-6-pach-tardos-zeng/ |
| Competitive ratio of greedy for online Steiner forest; Awerbuch–Azar–Bartal conjectured O(log k) | 1996 | 30 | GPT-6 Astra; Gemini 4 Argon | Awaiting review | Lean-verified | 2026-10-29 | Claimed tight bound Θ(log k log log k), so the O(log k) conjecture is false | AI-assisted: GPT Astra helped develop some proofs and the write-up, Gemini Argon assisted in parts; the authors take responsibility | https://postcutoff.com/e/2026-10-29-online-steiner-forest-greedy-log-k-loglog-k-gpt-astra-lean/ |
| Exact overlaps conjecture (dimension one) | 1996 | 30 | GPT-6 Astra | Awaiting review | Lean-verified | 2026-10-07 | Proof that every self-similar measure on the line has dim ν = min{1, h_μ/\|χ_μ\|}, so dimension drop occurs only with exact overlaps; no separation or algebraicity assumptions. | AI-found, human-rewritten: GPT-6 Astra produced the first full proof in a ~2.5-hour session and the Lean formalization; Kittle found a new deduction of the main theorem and the authors rewrote the paper and checked it | https://postcutoff.com/e/2026-10-07-exact-overlaps-conjecture-gpt-6-astra/ |
| Periodic tiling conjecture | 1996 | 30 | OpenAI internal model (openai/math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed: a finite tile of ℤ³, and its unit-cube thickening in ℝ³, that tiles but has no fully periodic tiling, the lowest possible lattice dimension (Greenfeld–Tao had a counterexample only in very high dimension) | Autonomous output released without named authors; method adapted from Greenfeld and Tao's Sudoku construction | https://postcutoff.com/e/2026-10-06-openai-periodic-tiling-conjecture-dimension-three/ |
| Benjamini–Schramm conjecture | 1996 | 30 | OpenAI internal model; Claude Opus 5.5 | Awaiting review | Lean-verified | 2026-09-24 | Claimed for bond percolation (OpenAI, Lean) and for site percolation (Pei, Claude agents) | OpenAI: not stated per paper; Pei: chose problem and strategy, reviewed key lemmas, AI found and wrote proofs | https://postcutoff.com/e/2026-09-24-benjamini-schramm-pc-pu-nonamenable-openai-lean/ |
| List total colouring conjecture | 1997 | 29 | GPT-6 Astra Ultra | Awaiting review | Preprint only | 2026-09-29 | Disproved: an explicit 20-vertex cubic graph with total chromatic number 4 and list total chromatic number 5. | AI-found counterexample: the author prompted the model to disprove the conjecture; he checked the proof and rewrote the drafts | https://postcutoff.com/e/2026-09-29-list-total-colouring-conjecture-false-astra/ |
| Alon–Krivelevich conjecture | 1998 | 28 | GPT-6 Astra; xean; Claude Opus 5.5 | Awaiting review | Preprint only | 2026-10-30 | Disproved: bipartite graphs with ch(G) ≥ (1/32 − o(1))(ln Δ)²/(ln ln Δ)³ | AI-found: GPT-6 Astra found the counterexample and proof; authors verified it; Claude rewrote the text | https://postcutoff.com/e/2026-10-30-alon-krivelevich-conjecture-disproved-gpt-6-astra-xean/ |
| Smale's 6th problem, five bodies in the plane | 1998 | 28 | unnamed generative AI tools | Awaiting review | Peer-reviewed | 2026-10-09 | Claimed: finitely many planar central configurations for every five positive masses, removing the codimension-two exceptional set of Albouy–Kaloshin. | AI-generated per the author's disclosure (AI found and proved the results, wrote the programs, the Lean formalization and the draft); the human role is not described | https://postcutoff.com/e/2026-10-09-smale-sixth-problem-five-bodies-lean-tomar/ |
| Existence of the q-colourability threshold of G(n, d/n) | 1999 | 27 | Claude Opus 5.5; GPT-6 Astra; GPT-6 Luna; GPT-6.1 Sol | Awaiting review | Lean-verified | 2026-10-29 | Claimed: for every q ≥ 3 a constant threshold d_q exists for G(n, d/n) (d_q/2 for G(n, ⌊cn⌋)), with an O(n(log n)^(−3/2)) hitting-time window | Authors supervised; the models did proof discovery, verification, Lean formalization and all writing; human understanding 'some parts' | https://postcutoff.com/e/2026-10-29-q-colorability-threshold-existence-aronow-lopatto-ai/ |
| Exponential Time Hypothesis | 1999 | 27 | internal Claude research model (Anthropic) | Awaiting review | Lean-verified | 2026-10-27 | Claimed deterministic 2^O(n log log n/√log n)-time (fixed k) algorithm for #k-SAT, refuting ETH and SETH, found independently of OpenAI's | Autonomous discovery (14M output tokens, 'no human input'); Anthropic researchers worked with Claude on the presentation; Lean formalization written by AI models | https://postcutoff.com/e/2026-10-27-anthropic-claude-eth-refutation-3sat-subexponential/ |
| Exponential Time Hypothesis | 1999 | 27 | OpenAI internal model (openai/math release) | Awaiting review | Lean-verified | 2026-10-26 | Claimed deterministic (n+m)^O_k(1)·2^(n/(log n)^(1/2+o(1)))-time, polynomial-space algorithm for #k-SAT, every fixed k ≥ 2, which would refute ETH and its variants | Credited to 'OpenAI' with no named human authors; OpenAI says it is model output. Human examination is assigned to an outside working group (Impagliazzo, Paturi, Williams) | https://postcutoff.com/e/2026-10-26-openai-eth-false-subexponential-sat-claim/ |
| Reed–Solomon list decoding up to capacity | 1999 | 27 | GPT-5.6 Sol; ChatGPT 5.6 Pro; ChatGPT 6 Pro | Awaiting review | Expert-checked | 2026-09-04 | Deterministic polynomial-time list decoding of RS codes over prime fields up to capacity for every constant rate and evaluation set, and near-optimal mutual correlated agreement (proximity gaps) up to capacity with fixed slack. | AI-assisted: humans extracted the idea from a crowd-sourced prize submission and directed the work; GPT-5.6 Sol helped produce most of the remaining results (BCPZZ); ChatGPT 5.6 Pro interactions were 'crucial' (Jeronimo); authors verified everything | https://postcutoff.com/e/2026-09-04-reed-solomon-list-decoding-capacity-ai/ |
| Barry Simon's multidimensional L² conjecture | 2000 | 26 | ChatGPT | Awaiting review | Expert-checked | 2026-10-22 | False in every dimension d ≥ 2: smooth, bounded, nonnegative, arbitrarily small potentials satisfying the (even weighted) L² condition for which −Δ + V has only pure point spectrum on (0, ∞). | AI-assisted: authors chose the problem and suspected falsity; ChatGPT developed the construction and the extension to the full spectrum; authors rewrote the argument | https://postcutoff.com/e/2026-10-22-simon-l2-conjecture-disproved-chatgpt/ |
| Woodin's question | 2000 | 26 | GPT-6 Astra (ultra reasoning); GPT-6.1 Sol | Awaiting review | Preprint only | 2026-10-06 | Yes, in ZFC; the argument also works for ω₁-strongly compact cardinals. | AI-assisted; the author acknowledges GPT-6 Astra and GPT-6.1 Sol 'during the investigation' without detailing their contribution and takes responsibility | https://postcutoff.com/e/2026-10-06-gch-above-strongly-compact-woodin-question/ |
| Navier–Stokes existence and smoothness | 2000 | 26 | OpenAI internal model (≈10,000 parallel agents) | Disputed | Lean-verified | 2026-09-08 | Claimed proof, formalised in Lean, of finite-time blow-up for 3D incompressible Navier–Stokes with smooth external forcing. | Largely autonomous agent swarm; builds on human techniques of Córdoba and Martínez-Zoroa | https://postcutoff.com/e/2026-09-08-openai-navier-stokes-blowup/ |
| Is there a binary search tree satisfying Iacono's unified bound? | 2001 | 25 | Claude Opus 5.5; Claude Fable 5.1; Claude Fable 5.2; GPT-6 Astra; GPT-5.6 Sol | Awaiting review | Preprint only | 2026-11-12 | A deterministic online BST with cost O(m + UB(X)); dynamic optimality now implies the unified bound for splay trees | AI-assisted design, analysis, proof checking and drafting; authors take responsibility | https://postcutoff.com/e/2026-11-12-binary-search-tree-unified-bound-ai/ |
| Mézard–Parisi formula for the free energy of diluted spin-glass models, including random K-SAT | 2001 | 25 | ChatGPT Astra; Claude Fable | Awaiting review | Preprint only | 2026-10-30 | Claimed matching lower bound for diluted p-spin models with even p and random K-sat under symmetry and integrability assumptions, completing the formula (upper bound: Franz–Leone) | AI-found proof directed by the field's main expert: Panchenko asked for a new perturbation in his earlier argument; ChatGPT Astra found the proof; Panchenko rewrote it with ChatGPT Astra and Claude Fable | https://postcutoff.com/e/2026-10-30-mezard-parisi-formula-panchenko-proof-found-by-chatgpt-astra/ |
| Period-index conjecture | 2001 | 25 | ChatGPT | Awaiting review | Preprint only | 2026-08-04 | Varieties of every dimension d ≥ 3 with a Brauer class of period 2 and index 2^d, contradicting the conjecture; a corrected conjecture is proposed. | Human-led: a wrong AI example inspired the construction; the human found and proved the correct one, with AI help on literature search and lattice calculations | https://postcutoff.com/e/2026-08-04-period-index-conjecture-false/ |
| Spectral isometry conjecture | 2002 | 24 | GPT-6 Astra; ChatGPT 6 | Awaiting review | Lean-verified | 2026-10-29 | Claimed full proof for arbitrary unital C*-algebras, plus the non-unital-map variant; Lean-checked per the authors (Palomar) | AI found the proof; the authors studied it, rewrote it as a human-readable paper and checked it | https://postcutoff.com/e/2026-10-29-spectral-isometry-conjecture-c-star-algebras-gpt-6-astra/ |
| Finite index over treeable (JKL 2002) | 2002 | 24 | ChatGPT 6 Astra Ultra | Awaiting review | Preprint only | 2026-10-06 | Yes, in the purely Borel setting (hence also measurably); with consequences for strongly treeable groups. | Human-led: the authors designed the staged construction; GPT contributed one key coherence observation; the paper was written by the authors | https://postcutoff.com/e/2026-10-06-finite-index-over-treeable-jkl-problem/ |
| Zilber–Pink conjecture for abelian varieties | 2002 | 24 | OpenAI internal model (openai/math release) | Awaiting review | Preprint only | 2026-10-06 | Claimed: finiteness of maximal atypical subvarieties for every subvariety of an abelian variety over Q̄ (hence over any characteristic-zero field by Barroero–Dill); Zilber–Pink for Hodge-generic curves in A2 | Autonomous AI output released by OpenAI under its fixed procedure (README) | https://postcutoff.com/e/2026-10-06-openai-abelian-zilber-pink-claim/ |
| Exact polynomial-time approximability of metric k-median | 2002 | 24 | unreleased internal OpenAI model | Awaiting review | Lean-verified | 2026-10-06 | Claimed: deterministic polynomial-time (1 + 2/e + ε)-approximation for every fixed ε > 0, matching the NP-hardness bound, so the threshold is exactly 1 + 2/e; plus a randomized (2 − σ)-approximation | Autonomous per OpenAI: produced by the model in OpenAI's open-problem evaluation; humans curated and released | https://postcutoff.com/e/2026-10-06-openai-k-median-optimal-approximation-1-plus-2-over-e/ |
| Unique Games Conjecture | 2002 | 24 | OpenAI internal model (unreleased) | Awaiting review | Lean proof, not yet reviewed | 2026-10-06 | Claimed: NP-hardness of (1−ε, δ)-gap Unique Games for every fixed ε, δ; hence optimal NP-hardness for Max-Cut (Goemans–Williamson) and Vertex Cover (factor 2). | Autonomous by OpenAI's fixed procedure (per README) | https://postcutoff.com/e/2026-10-06-unique-games-conjecture-openai/ |
| Multiple-unicast network coding conjecture | 2004 | 22 | GPT-6 (ChatGPT) | Awaiting review | Preprint only | 2026-10-07 | Disproved: an explicit linear network code over 𝔽₉ on a 182-vertex PG(2, 9) incidence subgraph beats fractional multicommodity flow (rate 1 vs ≤ 147/157), giving Ω((log n)^ε) coding gaps by amplification. | AI found the counterexample to a strengthened version the authors formulated; humans steered the search, converted it to a causal code and checked the proof | https://postcutoff.com/e/2026-10-07-multiple-unicast-conjecture-false-gpt-6/ |
| Crouzeix's conjecture | 2004 | 22 | GPT-5.6 Sol | Result confirmed | Expert-checked | 2026-07-27 | Proof that the numerical range W(A) is a 2-spectral set for every matrix A. | Autonomous: non-specialist prompted; experts verified | https://postcutoff.com/e/2026-07-27-crouzeix-conjecture-proved/ |
| Explicit matrices with the restricted isometry property beyond the square-root bottleneck | 2007 | 19 | GPT-6 Astra; ChatGPT; Claude Opus 5.5 | Awaiting review | Lean-verified | 2026-11-10 | Explicit real RIP matrices with k = m^(2/3−o(1)), plus a proof that absolute-value Gram-matrix methods cannot exceed exponent 2/3 | AI-generated main proof; humans digested it, found the 2/3 barrier with ChatGPT and rewrote the paper | https://postcutoff.com/e/2026-11-10-explicit-rip-matrices-two-thirds-gpt-6-astra/ |
| Area law for entanglement entropy of ground states of gapped local Hamiltonians in two dimensions | 2007 | 19 | OpenAI internal model (original proof); Axiom agent tooling; OpenAI Codex | Awaiting review | Lean-verified | 2026-10-16 | Lean 4 proof, with no sorry, of OpenAI's theorem that the unique ground state of a globally gapped finite-range Hamiltonian on any finite induced square-lattice domain has entanglement entropy at most C × (number of boundary edges), with C independent of domain size and shape. | AI-generated proof (OpenAI release); formalization by AI agents directed by Ruiz Chen (Axiom), who froze and audited the Lean statement layer and checked each result | https://postcutoff.com/e/2026-10-16-openai-2d-area-law-lean-formalized-axiom/ |
| Matroid secretary conjecture | 2007 | 19 | GPT-6 Astra; GPT-5.6 Sol; ChatGPT Pro | Awaiting review | Preprint only | 2026-09-13 | O(1) (4-probability-competitive) secretary algorithm for every matroid; merged paper claims the optimal ratio e and a ratio-2 single-sample prophet inequality | AI-assisted: authors chose approaches and ran the LP computations; GPT Astra used in obtaining the main theorems; authors checked the proofs | https://postcutoff.com/e/2026-09-13-matroid-secretary-conjecture-resolved-gpt-astra/ |
| Aaronson–Ambainis conjecture | 2008 | 18 | non-public Anthropic model; PSI research system | Awaiting review | Lean-verified | 2026-11-06 | Max influence ≥ c·v^(5/2)/d^6 (≥ (v/d)^7) for bounded degree-d polynomials of variance v, claimed with a Lean-checked proof | AI found the proof in an autonomous run; a human scoped the problem, reviewed the AI-drafted paper and advisers audited it | https://postcutoff.com/e/2026-11-06-psi-aaronson-ambainis-conjecture-proof/ |
| Gurvits's conjecture that mixed volumes admit no FPRAS in the oracle model | 2009 | 17 | GPT-6 Astra | Awaiting review | Preprint only | 2026-11-03 | FPRAS for mixed volumes of n convex bodies in R^n | AI-originated: main ideas from GPT-6 Astra, humans simplified and wrote the exposition | https://postcutoff.com/e/2026-11-03-mixed-volume-fpras-gurvits-conjecture-disproved-gpt-6-astra/ |
| Toms–Winter conjecture (C*-algebras) | 2009 | 17 | ChatGPT 6 Astra (GPT-6 Astra via Codex); unnamed AI (Thiel) | Awaiting review | Preprint only | 2026-10-07 | Claimed complete: Thiel proves strict comparison implies pureness (5 Oct 2026); Evington, Hua, Schafhauser, Seth, Tikuisis and White prove pureness implies Z-stability (7 Oct 2026). | Human-led with AI input: one prompt gave a 4-page proof of a lemma in a special case (W*-bundles); the authors built the general theory and the 70-page proof without further AI use. Thiel: AI collaboration at an initial stage led to the key idea of two lemmas | https://postcutoff.com/e/2026-10-07-toms-winter-conjecture-completed-chatgpt-astra-lemma/ |
| Courtade–Kumar conjecture | 2013 | 13 | Gemini (Stellar Colosseum); ChatGPT; unnamed generative AI systems | Awaiting review | Lean-verified | 2026-09-21 | Proved in full (all n, all noise levels, no balance assumption) by three independent teams on 21–22 Sep 2026; the Google–CUHK proof is computer-assisted and verified end-to-end in Lean. | Google–CUHK: humans supplied the reduction and the Bellman function, AI generated most new ideas and the region-by-region proof; Ky–Tran: human approach, ChatGPT developed the proofs; Mahdavifar–Beirami: AI generated the single-bit proof under human direction | https://postcutoff.com/e/2026-09-21-courtade-kumar-conjecture-proved/ |
| Bounded gaps between primes | 2014 | 12 | GPT-6 Astra | Awaiting review | Lean proof, not yet reviewed | 2026-08-30 | Claimed proof that infinitely many pairs of primes differ by at most 186. | Largely AI-generated per OpenAI | https://postcutoff.com/e/2026-08-30-bounded-prime-gaps-186/ |
| Dimension of the SO(3) instanton homology J♯ of the dodecahedron web | 2015 | 11 | ChatGPT Astra 6; ChatGPT; Claude | Awaiting review | Unverified claim | 2026-11-03 | Proposed proof that the dimension is 64 | Leading gauge theorists posed the question and supplied earlier AI-computed data; the text is primarily AI-generated and only partly checked | https://postcutoff.com/e/2026-11-03-kronheimer-mrowka-dodecahedron-web-instanton-homology-64-chatgpt/ |
| 3-Uniform Hyperclique Hypothesis | 2018 | 8 | ChatGPT Sol 6.1 | Awaiting review | Preprint only | 2026-11-05 | Truly subquartic (O(n^3.957)) algorithm for detecting or counting 4-hypercliques in 3-uniform hypergraphs; the hypothesis is false | AI-assisted: authors prompted the model with different suggestions; both proofs came from the model, the authors verified and rewrote them | https://postcutoff.com/e/2026-11-05-3-uniform-hyperclique-hypothesis-false-chatgpt-sol/ |
| Benson–Etingof–Ostrik conjecture on symmetric tensor categories of moderate growth in positive characteristic | 2023 | 3 | GPT-6 Astra | Awaiting review | Expert-checked | 2026-11-11 | Claimed full proof: every such category admits a symmetric tensor functor to a higher Verlinde category, possibly of infinite height | AI-generated paper; five specialists (including two of the conjecture's authors) directed it with questions, reductions and ideas | https://postcutoff.com/e/2026-11-11-benson-etingof-ostrik-conjecture-gpt-6-astra/ |
| Hyperelliptic Schottky problem | not recorded |  | unnamed AI tools | Awaiting review | Preprint only | 2026-11-11 | Codim Sing(Θ) = 3 characterizes hyperelliptic Jacobians; IT₀ criterion for GV-subschemes; generic reducedness of codim-2 base loci | Human-led; AI suggested the final step of the main proof and constructed the sharpness example | https://postcutoff.com/e/2026-11-11-hyperelliptic-schottky-problem-huang-jiang-ai/ |
| Talagrand's Ultimate Matching Conjecture | not recorded |  | GPT-6 | Awaiting review | Preprint only | 2026-11-11 | Claimed proof for all finite critical exponent pairs α₁, α₂ > 2 with 1/α₁ + 1/α₂ = 1/2; claimed failure at the endpoints (2, ∞), (∞, 2) | AI-assisted: specialists steered weeks of LLM interaction; GPT-6 found the critical and endpoint proofs; text mostly LLM-written | https://postcutoff.com/e/2026-11-11-talagrand-ultimate-matching-conjecture-gpt-6/ |
| Rational points on X_ns+(121); the level-121 case of the Rouse–Sutherland–Zureick-Brown conjecture on ℓ-adic images | not recorded |  | Claude Opus 5.5; GPT-6.1 Sol; GPT-6 Astra; Claude Code | Awaiting review | Unverified claim | 2026-11-09 | Claimed: X_ns+(121)(Q) consists of 7 CM points, so the 11-adic images of non-CM elliptic curves over Q are determined | Humans chose the problem and directed; AI produced almost all the mathematics, computations and text; partial (2611.00231) or no (2611.00255) human checking | https://postcutoff.com/e/2026-11-09-non-split-cartan-121-two-ai-proofs/ |
| Order of the weak-coupling Hawking–Page/deconfinement transition in N=4 SYM; optimal large-c spinless modular bootstrap bound | not recorded |  | internal Claude research model; Claude Opus 5.5 | Awaiting review | Unverified claim | 2026-11-07 | b = −1.48×10⁻³ λ² (first-order transition); optimal slope Λ_V = 12π²/(π²+4 arcsinh²1) ≈ 9.1266 | Autonomous AI result with a physicist prompting and checking | https://postcutoff.com/e/2026-11-07-anthropic-claude-hawking-page-modular-bootstrap-hexagon/ |
| Tusnády's problem | not recorded |  | Claude; Codex; ChatGPT | Awaiting review | Preprint only | 2026-11-06 | Claimed Θ_d((log N)^(d−1/2)) in every fixed dimension d ≥ 2 (two independent proofs) | AI-assisted: authors credit the tools with proof development and checking (Wengiel) and with generating ideas (Lei) | https://postcutoff.com/e/2026-11-06-tusnady-problem-settled-two-ai-assisted-preprints/ |
| Formalizing the Stacks Project in Lean | not recorded |  | Axiom agents | Awaiting review | Lean-verified | 2026-11-04 | Claimed Lean 4 formalization of every formalizable Stacks tag, in human-reviewed and agent-written tiers | AI agents wrote StacksFrontier; humans reviewed StacksCore | https://postcutoff.com/e/2026-11-04-axiom-stacks-project-lean-formalization/ |
| Torsion groups of elliptic curves over number fields of fixed degree d | not recorded |  | GPT-6.1 Sol; Claude Opus 5.5; ChatGPT-6 Astra | Awaiting review | Unverified claim | 2026-11-04 | Complete list of torsion groups for d = 6–9, with three groups new | Human posed questions and guided; AI produced the mathematics, computations and manuscript; human checked degree 6 only | https://postcutoff.com/e/2026-11-04-elliptic-curve-torsion-degrees-6-9-gpt-6-1-sol-najman/ |
| Best proven running time of deterministic integer factoring | not recorded |  | Claude Opus 5.5 | Awaiting review | Lean-verified | 2026-10-29 | Lean-proved: deterministic factoring in time N^o(1) (C_k·2^(n/k) for every k) | Authors posed the question and designed and audited the 13-line Lean statement; Claude agents produced the reduction, method, proof plan and all Lean code; the authors did not read the proof | https://postcutoff.com/e/2026-10-29-deterministic-factoring-n-o1-lean-claude-rudich-rousseau/ |
| Kervaire's conjecture | not recorded |  | OpenAI internal model (unreleased, unnamed) | Result confirmed | Lean-verified | 2026-10-29 | OpenAI's proofs accepted as solutions in the Kourovka Notebook after confirmation by N. V. Bogachev | Proofs from OpenAI's internal model run; human confirmation by N. V. Bogachev for the Notebook | https://postcutoff.com/e/2026-10-29-kervaire-conjecture-openai-kourovka-confirmed-bogachev/ |
| Petty's equilateral-set conjecture | not recorded |  | Tencent Hunyuan hyprover | Awaiting review | Preprint only | 2026-10-29 | Claimed proof in dimension 5 (dimensions 3 and 4 were known) | Author wrote the prompt with a methodological hint; the agent generated the proof; the author organised, verified and rewrote it | https://postcutoff.com/e/2026-10-29-petty-equilateral-set-conjecture-dimension-five-tencent-hyprover/ |
| Pure semisimplicity conjecture | not recorded |  | GPT-6 Astra; GPT-6.1 Sol; Claude Opus 5.5 | Awaiting review | Lean-verified | 2026-10-29 | Claimed counterexample via a division ring extension with right dimension sequence (1, 2, 2, 2, …), through Simson's reduction | AI-assisted: GPT-6 Astra helped choose the criterion and construct the division rings; the author verified the proofs and completed the Lean formalisation with GPT-6.1 Sol and Claude Opus 5.5 | https://postcutoff.com/e/2026-10-29-pure-semisimplicity-conjecture-counterexample-gpt-6-astra-lean/ |
| Coloring 3-colorable graphs with few colors in polynomial time | not recorded |  | GPT-6 Astra; GPT-6 Pro | Awaiting review | Preprint only | 2026-10-26 | O(n^0.1537) colors, improving O(n^0.1954); also an n^(1/6+o(1)) framework | Human–AI collaboration: the models generated each successive algorithm; the authors studied the analyses, suggested ideas (incl. the generalization to vector k-coloring), simplified the arguments and wrote the paper | https://postcutoff.com/e/2026-10-26-three-coloring-n-0-1537-gpt-6-astra/ |
| Rigorous continuum limit of three-dimensional Yang–Mills theory | not recorded |  | Claude Opus 5.5; GPT-6 Astra; GPT-6.1 Sol | Awaiting review | Lean-verified | 2026-10-26 | Claimed convergence of flowed Wilson-loop laws of 3D SU(2) lattice Yang–Mills on a torus to a unique continuum measure on the Cao–Chatterjee state space, with short-distance and weak-coupling asymptotics | Contributors posted the work; by the Hexagon label no part is understood by a human; proof discovery, verification and writing by the models | https://postcutoff.com/e/2026-10-26-three-dimensional-su2-yang-mills-continuum-limit-aronow-lopatto-ai/ |
| Constructing a solution of the two-dimensional KPZ equation at criticality | not recorded |  | ChatGPT 5.5; ChatGPT 5.6; ChatGPT 6 | Awaiting review | Expert-checked | 2026-10-22 | Construction of the Critical 2D KPZ Process as the unique limit of centred log partition functions of critical 2D directed polymers, a functional of the Critical 2D Stochastic Heat Flow; proved non-Gaussian. | Human-led with substantial AI input: authors supplied structure, literature and judgement; ChatGPT developed key estimates and proofs, some of which failed audit | https://postcutoff.com/e/2026-10-22-critical-2d-kpz-process-chatgpt/ |
| Integer programming with exponent linear in d | not recorded |  | GPT-6 Astra Ultra | Awaiting review | Lean-verified | 2026-10-19 | Claimed deterministic f(d)·N^O(d)·poly-log(c_max) + poly(input) algorithm for bounded standard-form integer programming. | Human-led: the authors designed the proof route and core idea; GPT Astra Ultra wrote the complete proofs and a Lean check | https://postcutoff.com/e/2026-10-19-integer-programming-linear-exponent-gpt-astra-ultra/ |
| FPRAS for counting perfect matchings in general graphs | not recorded |  | OpenAI internal model (unreleased, unnamed) | Result confirmed | Lean-verified | 2026-10-19 | Claimed FPRAS for all finite simple graphs (OpenAI), re-proved in simplified form by Liu and Meng | Proof from OpenAI's model run; independent human re-proof and simplification by Liu and Meng | https://postcutoff.com/e/2026-10-19-perfect-matchings-fpras-general-graphs-openai-liu-meng/ |
| A non-sofic hyperbolic group | not recorded |  | GPT Astra; OpenAI release model (family 252) | Awaiting review | Lean-verified | 2026-10-17 | Claimed construction of a torsion-free two-dimensional word-hyperbolic group that is not sofic; independently, a claimed proof with Lean that OpenAI's non-residually-finite hyperbolic group is not sofic. | AI-assisted: AI-generated construction (Sandhu, 7 Oct) built on OpenAI's AI result; Thom reworked and checked the proof; GPT Astra helped draft | https://postcutoff.com/e/2026-10-17-non-sofic-hyperbolic-group-sandhu-thom/ |
| Gauss circle problem | not recorded |  | ChatGPT; Codex | Awaiting review | Preprint only | 2026-10-16 | θ ≤ 209/670 + ε ≈ 0.31194, improving Li–Yang's 0.314483 and going below Huxley's suggested 5/16 barrier for the Bombieri–Iwaniec method. | Human-led with AI tools: authors used ChatGPT and Codex to discuss proof strategies and to draft and check parts of the arguments; final proofs written and verified by the authors | https://postcutoff.com/e/2026-10-16-gauss-circle-problem-209-670-bound/ |
| Existence of the Smith–Toda complex V(4); V(3) exists for p ≥ 7 | not recorded |  | OpenAI internal model (openai/math release); ChatGPT | Awaiting review | Preprint only | 2026-10-16 | V(4) exists for every prime p ≥ 11. OpenAI's internal model had shown it only for p = 1009, plus a V(n) at some prime for each n | OpenAI's model wrote the original papers; Angeltveit checked, simplified and extended them, using ChatGPT as an interactive assistant; he checked all arguments himself | https://postcutoff.com/e/2026-10-16-smith-toda-v4-angeltveit-improves-openai/ |
| Yang–Mills existence (YM4) | not recorded |  | Claude; Codex; GPT-5.6 Sol | Awaiting review | Preprint only | 2026-10-16 | Claimed, not established: a very long Claude-generated argument for the existence of SU(2) Yang–Mills on ℝ⁴ (continuum limit with Osterwalder–Schrader properties and non-triviality), conditional on listed inputs; no mass gap, no uniqueness of the infinite-volume limit. | Alpöge 'coaxing Claude' with 'some small amount of direction'; Sussman proposed the program and ran the earlier Codex QED3 experiment; both say they cannot yet tell how reliable the output is | https://postcutoff.com/e/2026-10-16-yang-mills-claude-balaban-program-alpoge-sussman/ |
| Erdős–Simonovits rational exponents conjecture | not recorded |  | GPT-6 Astra | Result confirmed | Lean-verified | 2026-10-13 | Human-written exposition of the AI-found proof: for every rational r in [1, 2] there is a graph H with ex(n, H) = Θ(n^r). | The proof was found by GPT-6 Astra in Epoch AI's FrontierMath Erdős runs (Sept 2026); eight human experts wrote, explained and situated it in this paper | https://postcutoff.com/e/2026-10-13-rational-exponents-conjecture-proof-paper-conlon/ |
| How mathematics should respond to AI-driven 'proof abundance' after OpenAI's 722-manuscript release | not recorded |  | n/a | Result confirmed | Unverified claim | 2026-10-09 | Public lecture and slides arguing that problem-solving has become a misaligned proxy and proposing 'Math 2.0' uses of AI (exposition problems, living result networks, formal libraries, open interpretable maths models). | Human-led | https://postcutoff.com/e/2026-10-09-tao-math-2-0-caltech-lecture/ |
| Dualization lower bound under ETH | not recorded |  | GPT-6 Astra | Awaiting review | Preprint only | 2026-10-08 | No, under the Exponential Time Hypothesis: a 3SAT reduction rules out N^o(√(log N/log log N)) algorithms, leaving a gap only between √(log N) and log N in the exponent. | AI found the proof of the main theorem; the authors reconstructed, revised and verified it and rewrote the exposition | https://postcutoff.com/e/2026-10-08-dualization-eth-lower-bound-gpt-6-astra/ |
| Hyperkähler SYZ conjecture | not recorded |  | ChatGPT Astra (proofreading only) | Awaiting review | Preprint only | 2026-10-08 | Proved (preprint): every nef line bundle on a compact irreducible hyperkähler manifold is semiample; finitely many deformation classes in each dimension for b2 ≥ 5. | Human-led; the proof was written by the authors, AI used only to proofread after OpenAI's release | https://postcutoff.com/e/2026-10-08-hyperkahler-syz-conjecture-engel-mauri/ |
| Artin–Davenport conjecture | not recorded |  | ChatGPT 6.0 (GPT-6); ChatGPT 5.5/5.6/6.1; OpenAI Codex | Awaiting review | Preprint only | 2026-10-06 | Proved in full: n ≥ 10 suffices (previous record n ≥ 14, Heath-Brown 2007); 10 is sharp. | Human-led over two years; ChatGPT 6.0 supplied the improved incidence-variety dimension bound (Lemma 3.8) and the Galois-descent approach of Lemma 3.6; GPT models helped combine estimates and proofread; Codex produced a partial Lean auto-formalisation | https://postcutoff.com/e/2026-10-06-artin-davenport-cubic-forms-ten-variables/ |
| Free group factor isomorphism problem | not recorded |  | OpenAI internal model (unreleased) | Result confirmed | Expert-checked | 2026-10-06 | Claimed: yes; all interpolated free group factors L(F_r), 1 < r ≤ ∞, are isomorphic, with fundamental group ℝ₊. | Autonomous by OpenAI's fixed procedure (per README) | https://postcutoff.com/e/2026-10-06-free-group-factors-isomorphism-openai/ |
| Generalized Lax conjecture | not recorded |  | unnamed AI system (Kummer–Netzer); OpenAI internal model | Awaiting review | Lean-verified | 2026-10-06 | Claimed: true for strictly hyperbolic polynomials (Kummer–Netzer, AI-found); false in general, even for shadows (OpenAI family 095) | Kummer–Netzer: AI produced the proof, humans posed the question, suggested approaches, checked and edited. OpenAI: autonomous model output, Lean statement | https://postcutoff.com/e/2026-10-06-generalized-lax-conjecture-openai-counterexample-kummer-netzer-generic-case/ |
| Bloch's conjecture | not recorded |  | OpenAI internal model (openai/math release) | Awaiting review | Expert-checked | 2026-10-06 | Claimed in full: for p_g = q = 0, CH₀(S) ≅ ℤ via the degree; hence Bloch's conjecture for all surfaces with p_g = 0 | Autonomous AI output released by OpenAI under its fixed procedure (README) | https://postcutoff.com/e/2026-10-06-openai-bloch-conjecture-surfaces-claim/ |
| Cannon's conjecture | not recorded |  | OpenAI internal model (math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed proof for all such groups (finite kernel allowed), via a fixed-scale combinatorial 2-modulus bound and the Bourdon–Kleiner criterion; Lean formalization of the conclusion | Released as model output under OpenAI's fixed procedure, with no human author named; presented in a seminar talk by Mario Bonk; no written human check yet | https://postcutoff.com/e/2026-10-06-openai-cannon-conjecture-proof-claim/ |
| Is Catalan's constant G | not recorded |  | OpenAI internal model (openai/math release) | Awaiting review | Lean-verified | 2026-10-06 | Proved irrational (OpenAI manuscript with a Lean proof of the exact statement); follow-ups give explicit irrationality measures | Autonomous AI output released by OpenAI under its fixed procedure (README) | https://postcutoff.com/e/2026-10-06-openai-catalan-constant-irrational/ |
| Does every Riemannian metric on Sⁿ have infinitely many geometrically distinct closed geodesics? | not recorded |  | OpenAI internal model (math release); OpenAI Codex | Awaiting review | Preprint only | 2026-10-06 | Claimed for all n ≥ 2 and every metric, plus every closed 3-manifold (OpenAI); independently re-proved and extended to all compact rank-one symmetric spaces' underlying manifolds (Chen–Deng–Zhang) | OpenAI: autonomous output. Chen–Deng–Zhang: human-verified proof developed with Codex, crediting OpenAI's strategy | https://postcutoff.com/e/2026-10-06-openai-closed-geodesics-spheres-infinitely-many/ |
| Finitely presented Burnside problem | not recorded |  | OpenAI internal model (math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed infinite finitely presented periodic group St₁₂(R) over an F₂-algebra, with property (T); claimed residually finite version with a finite-index 2-power-torsion subgroup; claimed finitely presented nil algebra that is not nilpotent | Released as model output under OpenAI's fixed procedure, with no human author named; no human exposition or check yet | https://postcutoff.com/e/2026-10-06-openai-finitely-presented-burnside-periodic-group-claim/ |
| Gromov–Lawson / Schoen–Yau aspherical conjecture | not recorded |  | OpenAI internal model (math release) | Awaiting review | Expert-checked | 2026-10-06 | Claimed in every dimension, without spin hypotheses, via rational inessentiality of positive-scalar-curvature manifolds; plus the integral inequality with a dimensional constant | Autonomous AI output released by OpenAI | https://postcutoff.com/e/2026-10-06-openai-gromov-lawson-aspherical-conjecture-psc/ |
| Long-range order of the quantum Heisenberg ferromagnet in d ≥ 3; Bose–Einstein condensation of an interacting continuum Bose gas at fixed density in the thermodynamic limit | not recorded |  | OpenAI internal model (math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed: magnetized KMS states at low temperature for all d ≥ 3 and all spins, Bloch's T^{3/2} law with exact coefficient; condensation in every hard-sphere ground state and at a fixed positive temperature, with the Bogoliubov depletion law | Autonomous AI output released by OpenAI, with Lean formalizations of the two core theorems | https://postcutoff.com/e/2026-10-06-openai-heisenberg-ferromagnet-bose-einstein-condensation/ |
| Is BPL | not recorded |  | OpenAI internal model (math release) | Awaiting review | Peer-reviewed | 2026-10-06 | Claimed proof of L = RL = BPL, with a Lean formalization in an explicit Turing-machine model whose statement definitions have been community-checked against the proof's | Autonomous AI output released by OpenAI; community volunteers (with Claude Code) re-checked the Lean statement | https://postcutoff.com/e/2026-10-06-openai-l-equals-rl-equals-bpl-lean-claim/ |
| Modularity of elliptic curves over imaginary quadratic fields | not recorded |  | OpenAI internal model (openai/math release) | Awaiting review | Preprint only | 2026-10-06 | Claimed: every elliptic curve over every imaginary quadratic field is modular; Le Hung's note states the method also covers all totally real fields and CM fields without ζ5 | Autonomous AI output released by OpenAI; follow-up notes by human experts written with AI drafts | https://postcutoff.com/e/2026-10-06-openai-modularity-elliptic-curves-imaginary-quadratic/ |
| Nearby Lagrangian conjecture | not recorded |  | OpenAI internal model (math release) | Awaiting review | Preprint only | 2026-10-06 | Claimed counterexample in T*(S⁹ × S^{N−1}) for some large even N: an embedded exact Lagrangian diffeomorphic to the base, not Hamiltonian isotopic to the zero section | Autonomous AI output released by OpenAI | https://postcutoff.com/e/2026-10-06-openai-nearby-lagrangian-conjecture-counterexample/ |
| ε-Dvoretzky conjecture | not recorded |  | ChatGPT | Awaiting review | Preprint only | 2026-10-02 | Polynomial bound n ≥ (C/ε)^((ℓ+1)/2)\|log ε\| for nearly ellipsoidal ℓ-dimensional sections of arbitrary (not necessarily symmetric) convex bodies, and a Euclidean-ball version. | Human-led. The key idea (the probability distribution on the Grassmannian) came out of a discussion between ChatGPT and Shahar Moshe; ChatGPT also checked and improved proofs. | https://postcutoff.com/e/2026-10-02-epsilon-dvoretzky-conjecture-klartag-moshe/ |
| Dying percolation conjecture | not recorded |  | Claude (Anthropic); Claude Fable 5.1; GPT-5.6 Sol | Awaiting review | Lean proof, not yet reviewed | 2026-09-03 | Claimed Lean-verified proof that θ(p_c)=0 for all d ≥ 2, via a new additive gluing inequality that settles Kozma–Nitzan Conjecture 3. | Autonomous formalization: Claude wrote all the Lean code under Justin Leder's direction. The follow-up proofs of stronger conjectures were produced by GPT-5.6 Sol + Claude Fable 5.1 with 'minimal human intervention' from Ahmed Bou-Rabee | https://postcutoff.com/e/2026-09-03-dying-percolation-theta-pc-zero/ |
| Matrix Spencer conjecture | not recorded |  | GPT-5.6 Sol Pro | Awaiting review | Preprint only | 2026-08-28 | O(√n) discrepancy for n symmetric n×n matrices of norm at most 1, achievable efficiently. | AI-assisted: humans chose the strategy and verified and polished; the model produced the key lemma's proof and most calculations | https://postcutoff.com/e/2026-08-28-matrix-spencer-conjecture-proved/ |
| Large gaps between consecutive primes | not recorded |  | GPT-5.6 Pro/Sol; GPT-6 Astra | Awaiting review | Lean proof, not yet reviewed | 2026-08-26 | Improved lower bound for infinitely many large prime gaps, saving a log log log n factor over FGKMT 2018. | AI-assisted: pseudonymous user DottedCalculator prompted the model; Thomas Bloom wrote the exposition | https://postcutoff.com/e/2026-08-26-erdos-rankin-large-prime-gaps-improved/ |
| Yau–Tian–Donaldson conjecture (cscK metrics) | not recorded |  | Danus (Rethlas-based agent); Claude Fable 5 (Claude Code); GPT-5.6 Sol (Codex) | Awaiting review | Preprint only | 2026-08-19 | Claimed explicit K-polystable polarized smooth projective fivefold without a cscK metric. | AI-generated main result with one key human redirection; the author checked and polished the text | https://postcutoff.com/e/2026-08-19-yau-tian-donaldson-cscK-disproof-claim/ |
| Zeros of ζ(s) on the critical line | not recorded |  | Claude (unreleased research model) in Claude Code | Result confirmed | Lean-verified | 2026-08-10 | Unconditional proof that more than 67.2% of zeta zeros are simple and lie on the critical line. | Near-autonomous: non-mathematician prompted; experts verified | https://postcutoff.com/e/2026-08-10-claude-riemann-zeta-zeros-two-thirds/ |

## All AI science results (378)

### Mathematics (274)

- 2026-11-13: AI-assisted results, 13 Nov. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-13-ai-assisted-results-november-13-listing/
- 2026-11-12: Fixed-profile soliton resolution fails (3D, 5D wave equation), with GPT-6 Astra. Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-12-fixed-profile-soliton-resolution-counterexamples-gpt-6-astra/
- 2026-11-12: Test-free PDL lacks interpolation; counterexample by Claude Fable in Lean. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-11-12-test-free-pdl-no-craig-interpolation-claude-fable/
- 2026-11-12: AI-assisted results, 12 Nov: Hexagon. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-12-ai-assisted-results-november-12-listing/
- 2026-11-11: Band-matrix QUE and critical crossover, 1.2M lines of Lean by AxiomProver. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-11-band-matrix-que-critical-crossover-axiomprover-lean/
- 2026-11-11: Benson–Etingof–Ostrik conjecture: full proof generated by GPT-6 Astra. Awaiting review; Expert-checked. https://postcutoff.com/e/2026-11-11-benson-etingof-ostrik-conjecture-gpt-6-astra/
- 2026-11-11: Hyperelliptic Schottky problem solved; AI suggested the final step. Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-11-hyperelliptic-schottky-problem-huang-jiang-ai/
- 2026-11-11: Smale's mean value constant = 4 (claimed, Lean-checked). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-11-smale-mean-value-constant-equals-4-goel-lean/
- 2026-11-11: Talagrand's Ultimate Matching Conjecture: GPT-6 proof (Hexagon). Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-11-talagrand-ultimate-matching-conjecture-gpt-6/
- 2026-11-11: Large triangles in planar sets of positive density: GPT-6 Astra Pro proof. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-11-triangles-positive-density-plane-gpt-6-astra-pro/
- 2026-11-11: AI-assisted results, 11 Nov: arXiv and Hexagon. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-11-ai-assisted-results-november-11-listing/
- 2026-11-10: Explicit RIP matrices reach k = m^(2/3): main theorem by GPT-6 Astra. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-10-explicit-rip-matrices-two-thirds-gpt-6-astra/
- 2026-11-10: AI-assisted results, 10 Nov: arXiv and Hexagon. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-10-ai-assisted-results-november-10-listing/
- 2026-11-09: X_ns+(121): two AI-generated proofs in two days. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-11-09-non-split-cartan-121-two-ai-proofs/
- 2026-11-09: Reflexive polytopes conjecture disproved, GPT-6.1 Sol. Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-09-nill-reflexive-polytopes-conjecture-disproved-gpt-6-1-sol/
- 2026-11-09: AI-assisted results, 9 Nov: arXiv and Hexagon. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-09-ai-assisted-results-november-9-listing/
- 2026-11-08: AI-assisted results, 8 Nov: Hexagon of 7 Nov and arXiv. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-08-ai-assisted-results-november-8-listing/
- 2026-11-07: AI-assisted results, 7 Nov: Hexagon of 6 Nov and arXiv. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-07-ai-assisted-results-november-7-listing/
- 2026-11-06: Axiom: the Weil conjectures proved in Lean. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-06-axiom-weil-conjectures-lean-formalization/
- 2026-11-06: Navier–Stokes: unforced Leray–Hopf non-uniqueness, AI-written. Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-11-06-navier-stokes-unforced-leray-hopf-nonuniqueness-buckmaster-coiculescu-li/
- 2026-11-06: Tusnády's problem claimed settled twice, with AI help. Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-06-tusnady-problem-settled-two-ai-assisted-preprints/
- 2026-11-06: AI-assisted results, 6 Nov: arXiv of 6 Nov and Hexagon of 5 Nov. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-06-ai-assisted-results-november-6-listing/
- 2026-11-05: ℤ is Diophantine in ℚ: Glazer (Astra, Claude) and Burungale claim Mazur's conjecture fails. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-05-z-diophantine-in-q-glazer-burungale/
- 2026-11-05: Hopfield critical capacity bracketed, by Claude Opus 5.5. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-11-05-hopfield-critical-capacity-claude-opus-5-5/
- 2026-11-05: Quasiplanar graph conjecture proved by ChatGPT-6 (Pach, Tardos, Zeng). Awaiting review; Expert-checked. https://postcutoff.com/e/2026-11-05-quasiplanar-graphs-linear-edges-chatgpt-6-pach-tardos-zeng/
- 2026-11-05: Singmaster's problem: new bound by Claude Opus 5.5. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-05-singmaster-bound-claude-opus-5-5-whitmore/
- 2026-11-05: AI-assisted results, 5 Nov: arXiv of 5 Nov and Hexagon of 4 Nov. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-05-ai-assisted-results-november-5-listing/
- 2026-11-04: Axiom: the Stacks Project formalized in Lean. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-04-axiom-stacks-project-lean-formalization/
- 2026-11-04: Elliptic-curve torsion in degrees 6–9, mostly by GPT-6.1 Sol. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-11-04-elliptic-curve-torsion-degrees-6-9-gpt-6-1-sol-najman/
- 2026-11-04: Amplituhedron magic number conjecture: counterexample found by ChatGPT. Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-04-amplituhedron-magic-number-conjecture-counterexample-chatgpt/
- 2026-11-04: Serre modularity over real quadratic fields, primarily AI-generated. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-11-04-serre-modularity-real-quadratic-fields-chatgpt-astra/
- 2026-11-04: AI-assisted results, 4 Nov: arXiv of 4 Nov and Hexagon of 2–3 Nov. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-04-ai-assisted-results-november-4-listing/
- 2026-11-03: K_h-minor-free separators O(h√n): two AI-assisted proofs. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-03-alon-seymour-thomas-separator-conjecture-gpt-6-astra-two-proofs/
- 2026-11-03: Kronheimer–Mrowka: dodecahedron instanton homology is 64 (ChatGPT Astra 6). Awaiting review; Unverified claim. https://postcutoff.com/e/2026-11-03-kronheimer-mrowka-dodecahedron-web-instanton-homology-64-chatgpt/
- 2026-11-03: D-equivalence for generalized Kummer hyperkählers (ChatGPT-6 assisted). Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-03-d-equivalence-generalized-kummer-chatgpt-6/
- 2026-11-03: RM(1,9) covering radius = 242, three proofs. Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-03-reed-muller-rm19-covering-radius-242-three-proofs/
- 2026-11-03: AI-assisted results, 3 Nov: arXiv of 3 Nov and Hexagon of 2–3 Nov. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-03-ai-assisted-results-november-3-listing/
- 2026-11-02: AI-assisted results, 2 Nov: arXiv of 2 Nov and Hexagon of 1–2 Nov. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-02-ai-assisted-results-november-2-listing/
- 2026-11-01: AI-assisted results, 1 Nov: arXiv leftovers and result repos. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-01-ai-assisted-results-november-1-listing/
- 2026-10-31: Bhargava: elliptic curves have cyclic reduction at a positive proportion of primes (claim). Awaiting review; Unverified claim. https://postcutoff.com/e/2026-10-31-bhargava-cyclic-reduction-elliptic-curves-positive-proportion-gpt-6/
- 2026-10-31: AI-assisted results, 31 Oct: arXiv of 30 Oct and Hexagon of 29–31 Oct. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-31-ai-assisted-results-october-31-listing/
- 2026-10-30: Alon–Krivelevich conjecture disproved with GPT-6 Astra. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-30-alon-krivelevich-conjecture-disproved-gpt-6-astra-xean/
- 2026-10-30: Mézard–Parisi formula: Panchenko's proof 'found by ChatGPT Astra'. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-30-mezard-parisi-formula-panchenko-proof-found-by-chatgpt-astra/
- 2026-10-30: Number of C₄-free graphs is 2^{(1+o(1))ex(n,C₄)} (claim, GPT-6 Pro). Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-30-number-of-c4-free-graphs-erdos-question-tianchi-yang-gpt-6-pro/
- 2026-10-30: AFEM rate-optimal for any bulk parameter θ < 1 (ChatGPT framework). Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-30-afem-optimal-convergence-any-bulk-parameter-diening-storn-chatgpt/
- 2026-10-30: Right-angled hyperbolic polytopes exist only up to dimension 8 (claim). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-30-right-angled-hyperbolic-polytopes-dimension-bounds-kolpakov-gpt-6-astra/
- 2026-10-30: AI-assisted results, 30 Oct: arXiv announcement of 29–30 Oct. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-30-ai-assisted-results-october-30-listing/
- 2026-10-29: Sharp Berry–Esseen constant claimed: C = Esseen's 0.4097. Awaiting review; Expert-checked. https://postcutoff.com/e/2026-10-29-berry-esseen-constant-esseen-sharp-certificate-claim/
- 2026-10-29: Kervaire's conjecture: OpenAI proof confirmed in the Kourovka Notebook. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-10-29-kervaire-conjecture-openai-kourovka-confirmed-bogachev/
- 2026-10-29: Petty's conjecture in dimension 5: proof by Tencent's hyprover agent. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-29-petty-equilateral-set-conjecture-dimension-five-tencent-hyprover/
- 2026-10-29: Pure semisimplicity conjecture: claimed counterexample, GPT-6 Astra, Lean. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-29-pure-semisimplicity-conjecture-counterexample-gpt-6-astra-lean/
- 2026-10-29: q-colourability threshold of G(n, d/n) exists, says a machine-written paper. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-29-q-colorability-threshold-existence-aronow-lopatto-ai/
- 2026-10-29: Spectral isometry conjecture for C*-algebras: GPT-6 Astra proof, Lean. Event confirmed, Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-29-spectral-isometry-conjecture-c-star-algebras-gpt-6-astra/
- 2026-10-29: Gcd in O(log a / log log a) remainder calls refutes Moschovakis's uniform-process conjecture. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-29-euclidean-algorithm-not-optimal-moschovakis-lean/
- 2026-10-29: OpenConjecture: GPT models on 200 random arXiv conjectures. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-29-openconjecture-random-conjectures-gpt-models-pnnl/
- 2026-10-29: AI-assisted results, 29 Oct 2026 (part 2). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing-2/
- 2026-10-29: AI-assisted results, 29 Oct (part 3): Hexagon's evening batch. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing-3/
- 2026-10-29: AI-assisted results in the 29 Oct 2026 sweep. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing/
- 2026-10-28: Kisin proves Serre's 1960 Artin-character conjecture with GPT Astra. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-28-kisin-serre-artin-character-conjecture-gpt-astra/
- 2026-10-28: Laczkovich's Lipschitz mapping problem: claimed answer, ChatGPT key step. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-28-laczkovich-lipschitz-mapping-problem-chatgpt-gaspar/
- 2026-10-28: Murty–Simon conjecture: proof for all n, bound found by GPT-5.6 Sol. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-28-murty-simon-conjecture-proof-gpt-5-6-sol-das-fox/
- 2026-10-28: AI-assisted results in the 28 Oct 2026 sweep. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-28-ai-assisted-results-october-28-listing/
- 2026-10-27: Axiom: Classification of Finite Simple Groups formalized in Lean. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-27-axiom-cfsg-classification-finite-simple-groups-lean/
- 2026-10-27: Erdős–Lovász covering-number problem: AI-found construction disproves Frankl's 1996 conjecture. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-27-erdos-lovasz-intersecting-covering-number-frankl-ai-construction/
- 2026-10-27: Sharp exponent 2/3 for the Banach–Mazur distance to the cube. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-27-banach-mazur-distance-cube-sharp-exponent-gpt-6/
- 2026-10-27: Morgan–Mullen conjecture confirmed with Claude, Lean-checked. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-27-morgan-mullen-conjecture-claude-lean/
- 2026-10-27: R(3,3,3,3) ≤ 61 with AI, Lean and SAT. Event confirmed, Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-27-ramsey-r3333-upper-bound-61-ai-lean-sat/
- 2026-10-27: AI-assisted results in the 27 Oct 2026 sweep. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-27-ai-assisted-results-october-27-listing/
- 2026-10-26: OpenAI claims local smoothing and Kakeya in all dimensions. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-26-openai-local-smoothing-kakeya-all-dimensions-claim/
- 2026-10-26: AI-assisted results in the 26 Oct 2026 sweep. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-26-ai-assisted-results-october-26-listing/
- 2026-10-25: Golomb–Welch conjecture (perfect Lee codes) claimed, with ChatGPT. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-25-golomb-welch-conjecture-perfect-lee-codes-chatgpt/
- 2026-10-24: AI-assisted results in the 24 Oct 2026 sweep. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-24-ai-assisted-results-october-24-listing/
- 2026-10-23: AI-assisted results in the 23 Oct 2026 arXiv listing. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-23-ai-assisted-results-october-23-listing/
- 2026-10-23: Heilman simplifies OpenAI's propeller conjecture proof. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-10-23-propeller-conjecture-openai-proof-heilman-simplification/
- 2026-10-23: Tokareva's bent-function conjecture disproved by LLM agents. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-23-tokareva-bent-functions-conjecture-disproved-minimax-agents/
- 2026-10-23: Triangle lower tail: Zhao's conjecture settled with GPT-6 Astra and Claude. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-23-triangle-lower-tail-zhao-conjecture-gpt-6-astra-claude/
- 2026-10-22: Eleven probabilists construct the Critical 2D KPZ process, a solution of the critical two-dimensional KPZ equation, 'through extensive interactions' with ChatGPT 5.5, 5.6 and 6. Awaiting review; Expert-checked. https://postcutoff.com/e/2026-10-22-critical-2d-kpz-process-chatgpt/
- 2026-10-22: Barry Simon's L² conjecture (Problem 8 of his 2000 list) disproved. Awaiting review; Expert-checked. https://postcutoff.com/e/2026-10-22-simon-l2-conjecture-disproved-chatgpt/
- 2026-10-22: AI-assisted results in the 22 Oct 2026 arXiv listing. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-22-ai-assisted-results-october-22-listing/
- 2026-10-22: ChatGPT 6 Astra outlines the argument that removes the Hodge-conjecture assumption from Nakayama's local height asymptotics. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-22-nakayama-local-height-without-hodge-conjecture-chatgpt-astra/
- 2026-10-21: Nagata's 1959 conjecture. Result confirmed; Preprint only. https://postcutoff.com/e/2026-10-21-nagata-conjecture-openai-proof-tevelev-exposition/
- 2026-10-21: Barnette's 1969 Hamiltonicity conjecture. Result confirmed; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-10-21-barnette-conjecture-openai-proof-zhentao-li-exposition/
- 2026-10-21: Hochster's 1973 small Cohen–Macaulay conjecture. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-21-hochster-small-cohen-macaulay-counterexample-openai-anghel-survey/
- 2026-10-21: AI-assisted results in the 21 Oct 2026 arXiv listing. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-21-ai-assisted-results-october-21-listing/
- 2026-10-20: Double-cap conjecture claimed in all dimensions, with a separate AI-built Lean proof. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-20-double-cap-conjecture-witsenhausen-lean-ai/
- 2026-10-20: MDS conjecture settled in even characteristic. Event confirmed, Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-20-mds-conjecture-even-characteristic-chatgpt-claude-lean/
- 2026-10-20: AI-assisted results in the 20 Oct 2026 arXiv listing. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-20-ai-assisted-results-october-20-listing/
- 2026-10-20: Borodin–Kostochka conjecture claimed for maximum degree ≥ 4583 (down from 5.3 million), then ≥ 1000 (26 Oct), with GPT-6 Astra assisting. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-20-borodin-kostochka-threshold-4583-gpt-6-astra/
- 2026-10-20: Gale's 1953 conjecture fails in 3D. Result confirmed; Unverified claim. https://postcutoff.com/e/2026-10-20-gale-conjecture-r3-counterexample-gpt-6-astra/
- 2026-10-19: Erdős–Szemerédi sunflower conjecture proved for every k ≥ 3. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-19-erdos-szemeredi-sunflower-conjecture-gpt-6-astra-pro/
- 2026-10-19: Kaplansky's quasitrace conjecture reported disproved by an unreleased OpenAI model. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-19-quasitrace-monotone-completeness-counterexamples-openai/
- 2026-10-19: AI-assisted results in the 19 Oct 2026 arXiv listing. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-19-ai-assisted-results-october-19-listing/
- 2026-10-19: AI-assisted maths on Zenodo, 17–19 Oct 2026. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-19-ai-assisted-results-zenodo-october-17-19/
- 2026-10-19: Commutative counterexamples to Arveson's hyperrigidity conjecture. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-19-arveson-hyperrigidity-commutative-counterexamples-gpt-6-astra/
- 2026-10-19: Gregory Chudnovsky, with ChatGPT, claims the lemniscate period has irrationality exponent 2, with a Lean 4 proof built on OpenAI's π-exponent library. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-19-lemniscate-irrationality-exponent-chudnovsky-chatgpt/
- 2026-10-19: Neumann–Zagier 1985 conjecture on tree lattices settled after an AI proof with ChatGPT 5.5 Pro and Opus 4.8. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-19-neumann-zagier-conjecture-tree-lattices-ai-proof/
- 2026-10-18: Bake AI's Épi agent reports 120 record results with GPT-6 Astra. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-18-bake-ai-epi-autonomous-research-agent-120-records/
- 2026-10-17: 2D Euler non-uniqueness without force claimed three times, all with AI. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-17-2d-euler-unforced-nonuniqueness-lp-vorticity-ai/
- 2026-10-17: Erdős–Hajnal conjecture proved for every path P_t. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-17-erdos-hajnal-all-paths-nguyen-astra-deepmind/
- 2026-10-17: A non-sofic word-hyperbolic group. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-17-non-sofic-hyperbolic-group-sandhu-thom/
- 2026-10-17: arXiv results with disclosed AI help, 16 Oct 2026 announcement. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-17-ai-assisted-results-october-16-listing/
- 2026-10-17: AI-assisted results, 16–17 Oct 2026 (Zenodo and arXiv leftovers). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-18-ai-assisted-results-october-17-listing/
- 2026-10-16: Brennan's conjecture: experts confirm and shorten OpenAI's proof. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-10-16-brennan-conjecture-openai-proof-binder-ivrii-prause-smirnov/
- 2026-10-16: Gauss circle problem: exponent 209/670, below 5/16. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-16-gauss-circle-problem-209-670-bound/
- 2026-10-16: Lonely runner: (1+c)/2n bound with ChatGPT 6. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-16-lonely-runner-constant-gap-hu-jing-chatgpt/
- 2026-10-16: Tournament Hamiltonian cycles: GPT-5.6 settles Alon's question. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-16-max-hamiltonian-cycles-tournaments-gpt-5-6-wormald/
- 2026-10-16: Smith–Toda V(4) for p ≥ 11, after OpenAI's p = 1009. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-16-smith-toda-v4-angeltveit-improves-openai/
- 2026-10-16: arXiv results with disclosed AI help, 15 Oct 2026 listing. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-16-ai-assisted-results-october-15-listing/
- 2026-10-16: Lee–Loh–Sudakov directed-cut conjecture proved with AI, Lean-verified. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-16-lee-loh-sudakov-directed-cuts-altifina-lean/
- 2026-10-16: Equiregular counterexample to the sub-Riemannian Sard conjecture. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-16-sub-riemannian-sard-equiregular-counterexample-claude/
- 2026-10-15: Exact asymptotic rate of Delsarte's linear programming bound for binary and spherical codes found, with key steps from Claude Opus 5.5 and GPT-5.6 Sol. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-15-delsarte-lp-bound-exact-rate-salmon-opus/
- 2026-10-15: Hopf's Euler characteristic conjecture proved under T³ symmetry. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-15-hopf-conjecture-t3-symmetry-chatgpt-astra/
- 2026-10-15: All 16,453,493 imaginary quadratic fields with class number ≤ 2000 determined unconditionally, using OpenAI's Siegel-zero proof made explicit in Lean with Claude Opus 5.5. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-15-imaginary-quadratic-fields-class-number-2000-claude-lean/
- 2026-10-15: Ghys's 1995 conjecture proved in the codimension-one case with Shanghai AI Lab's Intern-S2. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-10-15-ghys-conjecture-codimension-one-intern-s2-lean/
- 2026-10-14: Lü, Wang & Wu claim µ(p+2) = o(π(x)), a model case of the parity problem open since at least 1989, building on an OpenAI preprint with ChatGPT's help. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-14-hardy-littlewood-chowla-mobius-shifted-primes-lu-wang-wu/
- 2026-10-14: Mid-October 2026: arXiv results with disclosed AI help. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-14-ai-assisted-results-mid-october-2026/
- 2026-10-13: Eight extremal combinatorialists write up GPT-6 Astra's proof of the Erdős–Simonovits rational exponents conjecture (Conlon, Janzer, Liu et al.). Result confirmed; Lean-verified. https://postcutoff.com/e/2026-10-13-rational-exponents-conjecture-proof-paper-conlon/
- 2026-10-13: Thompson's group F is nonamenable. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-10-13-thompson-group-f-nonamenable-kim-lodha-exposition/
- 2026-10-13: Ulam's question answered. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-13-ulam-problem-lie-groups-countably-representable-gpt-6-astra/
- 2026-10-13: October 2026: the arXiv stream of conjectures settled with disclosed AI help continues. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-13-ai-assisted-results-october-2026/
- 2026-10-12: Bloch constant conjecture (Ahlfors–Grunsky, 1937) disproved. Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-10-12-bloch-constant-conjecture-disproved/
- 2026-10-12: Cureton and Thorner, with AxiomProver, extend the quasi-Riemann zero-free half-plane to every Dedekind zeta function (Re s > 31/32, Lean-formalized). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-12-cureton-thorner-dedekind-zeta-zero-free-axiomprover/
- 2026-10-12: Erdős Matching Conjecture (1965) proved for every fixed k and all large s, via a sharp tail bound whose k ≥ 6 cases generative AI completed. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-12-erdos-matching-conjecture-large-matchings-ai/
- 2026-10-12: Chow polynomials of matroids are not log-concave. Result confirmed; Expert-checked. https://postcutoff.com/e/2026-10-12-chow-polynomials-matroids-not-log-concave/
- 2026-10-11: William Banks writes out OpenAI's Landau–Siegel proof with explicit constants. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-11-landau-siegel-zeros-banks-explicit-account/
- 2026-10-11: Skryabin's 2006 conjecture proved. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-11-skryabin-conjecture-noetherian-hopf-algebra-antipode/
- 2026-10-10: Vaught's conjecture fails for infinitary logic. Event confirmed, Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-10-vaught-conjecture-infinitary-counterexample-lean/
- 2026-10-10: Erdős #1117 on maximum-modulus points answered negatively with GPT-6 help. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-10-erdos-problem-1117-maximum-modulus-gpt-6-codex/
- 2026-10-09: Thurston's geometrization conjecture formalised in Lean. Event confirmed, Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-10-09-geometrization-conjecture-lean-formalization/
- 2026-10-09: "We need ABP": six PDE specialists publish GPT-6 Astra's proofs of the kinetic Krylov–Safonov theorem and of Pucci's 1966 conjecture, with full chats (Loher, Mooney, Mouhot, Niebel, Silvestre, Zhu). Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-09-kinetic-krylov-safonov-pucci-conjecture-gpt-6-astra/
- 2026-10-09: Smale's sixth problem claimed for five bodies in the plane. Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-09-smale-sixth-problem-five-bodies-lean-tomar/
- 2026-10-09: Terence Tao's Caltech lecture 'Math 2.0'. Result confirmed; Unverified claim. https://postcutoff.com/e/2026-10-09-tao-math-2-0-caltech-lecture/
- 2026-10-09: arXiv, 5–9 October 2026. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-09-arxiv-ai-disclosed-results-early-october-2026/
- 2026-10-09: Gemini Argon shrinks Goldbach, Riemann and ZF Turing machines. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-10-09-deepmind-cryptids-smaller-turing-machines-goldbach-riemann-zf/
- 2026-10-09: Erdős #32: no O(log N) complement to the primes (Radomskii). Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-09-erdos-32-additive-complements-primes-radomskii/
- 2026-10-09: Nirenberg's 1962 conjecture on closed asymptotic curves disproved. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-09-nirenberg-conjecture-closed-asymptotic-curves-counterexample/
- 2026-10-09: Random permutations of quadratic length contain every pattern. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-09-random-permutations-universal-alon-gpt-6-pro/
- 2026-10-08: Google DeepMind's AlphaProof Nexus paper published in Science. Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-10-08-alphaproof-nexus-science-paper/
- 2026-10-08: Engel & Mauri post a 7-page proof of the hyperkähler SYZ conjecture, two days after OpenAI's catalogue claimed it; AI used only to proofread. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-08-hyperkahler-syz-conjecture-engel-mauri/
- 2026-10-08: Erdős Problem #522 (1961) resolved with a Lean-verified proof. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-10-08-erdos-522-littlewood-polynomial-zeros-lean-kawada/
- 2026-10-08: Hilbert's 16th problem. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-08-hilbert-number-lower-bound-gpt-5-6-sol-lean/
- 2026-10-08: Holomorphic Cancellation Problem (1998) answered in the negative, conditional on a newly announced exotic affine space; proofs developed with generative AI (Gaofeng Huang, Harvard). Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-08-holomorphic-cancellation-problem-counterexample/
- 2026-10-08: Set theorist Asaf Karagila refuses to review OpenAI's claimed solution of the Partition Principle problem (does PP imply AC?): 'It sucked'; calls the 722-paper release a 'Denial of Service'. Event confirmed, Awaiting review; Unverified claim. https://postcutoff.com/e/2026-10-08-karagila-openai-partition-principle/
- 2026-10-07: Exact overlaps conjecture for self-similar measures on the line proved. Event confirmed, Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-07-exact-overlaps-conjecture-gpt-6-astra/
- 2026-10-07: Two claimed proofs of the LeBrun–Salamon conjecture. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-07-lebrun-salamon-conjecture-proof/
- 2026-10-07: Toms–Winter conjecture on C*-algebras completed by two preprints in one week. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-07-toms-winter-conjecture-completed-chatgpt-astra-lemma/
- 2026-10-07: Hovey–Strickland: author says OpenAI's paper matches his ChatGPT-uploaded draft. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-07-chenglong-ma-hovey-strickland-openai-chatgpt-upload-provenance/
- 2026-10-07: Claimed proof of the cyclicity conjecture of Perron–Frobenius theory for positive operators (Dobrick, GPT-5.6 used to simplify arguments). Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-07-cyclicity-conjecture-positive-operators-dobrick/
- 2026-10-06: Artin–Davenport conjecture proved. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-artin-davenport-cubic-forms-ten-variables/
- 2026-10-06: OpenAI model claims the free group factor problem. Result confirmed; Expert-checked. https://postcutoff.com/e/2026-10-06-free-group-factors-isomorphism-openai/
- 2026-10-06: Harary–Hill and Zarankiewicz crossing-number conjectures (OpenAI, Lean). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-harary-hill-zarankiewicz-crossing-numbers-openai/
- 2026-10-06: OpenAI release proves the rational Hodge conjecture for all CM abelian varieties, giving the Tate conjecture for abelian varieties over finite fields; Lean proof added 26 Oct, human-written proof by van Hoften and Sempliner, and Milne calls it proved. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-10-06-hodge-conjecture-cm-abelian-varieties-openai/
- 2026-10-06: OpenAI claims Baum–Connes and Kadison–Kaplansky counterexamples. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-baum-connes-kadison-kaplansky-counterexamples/
- 2026-10-06: OpenAI claims 4D Borel counterexample and that F₂ is not good. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-borel-conjecture-dimension-four-free-group-not-good/
- 2026-10-06: Borsuk's conjecture fails in dimension 9 (OpenAI claim, Lean-checked). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-borsuk-conjecture-dimension-nine-counterexample/
- 2026-10-06: Cannon's conjecture claimed (OpenAI, Lean); Bonk's seminar talk. Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-cannon-conjecture-proof-claim/
- 2026-10-06: OpenAI: Catalan's constant is irrational (Lean). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-06-openai-catalan-constant-irrational/
- 2026-10-06: Deligne–Drinfeld conjecture proved; experts simplify and reprove OpenAI's proof. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-10-06-openai-deligne-drinfeld-conjecture-proof/
- 2026-10-06: Erdős's arithmetic-progression conjecture claimed (OpenAI, Lean). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-erdos-arithmetic-progressions-conjecture-claim/
- 2026-10-06: Finitely presented Burnside problem answered negatively? (OpenAI, Lean). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-finitely-presented-burnside-periodic-group-claim/
- 2026-10-06: OpenAI claims the aspherical positive-scalar-curvature conjecture. Awaiting review; Expert-checked. https://postcutoff.com/e/2026-10-06-openai-gromov-lawson-aspherical-conjecture-psc/
- 2026-10-06: Hadwiger's conjecture disproved? (OpenAI, Lean). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-hadwiger-conjecture-counterexample-claim/
- 2026-10-06: Hilbert's 16th problem: uniform limit-cycle bound claimed (OpenAI). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-06-openai-hilbert-sixteenth-uniform-limit-cycle-bound-claim/
- 2026-10-06: Hilbert–Smith conjecture claimed by OpenAI, Lean-checked by a separate AI proof. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-06-openai-hilbert-smith-conjecture-claim/
- 2026-10-06: OpenAI claims Hilbert's tenth problem over ℚ is undecidable. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-hilbert-tenth-problem-rationals-claim/
- 2026-10-06: OpenAI claims Kadison's similarity problem (Lean). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-kadison-similarity-problem-lean/
- 2026-10-06: Kaplansky's zero-divisor and direct-finiteness conjectures refuted? (OpenAI, Lean). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-kaplansky-zero-divisor-direct-finiteness-counterexamples-claim/
- 2026-10-06: OpenAI proves the Mahler conjectures (Lean). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-06-openai-mahler-conjecture-lean/
- 2026-10-06: OpenAI releases 722 AI-written math manuscripts claiming hundreds of open problems. Event confirmed, Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-10-06-openai-math-release-722-manuscripts/
- 2026-10-06: Chromatic number of the plane is 6 or 7, OpenAI claims (Lean). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-plane-not-five-colourable-hadwiger-nelson-claim/
- 2026-10-06: OpenAI claims global smoothness for 3D relativistic Vlasov–Maxwell (Lean). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-relativistic-vlasov-maxwell-global-solutions-lean/
- 2026-10-06: OpenAI: Yau's nodal bound holds on surfaces, fails in higher dimensions. Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-yau-nodal-conjecture-surfaces-counterexamples/
- 2026-10-06: OpenAI model claims the quasi-Riemann hypothesis. Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-10-06-quasi-riemann-hypothesis-openai/
- 2026-10-06: Chen, Tserunyan & Tucker-Drob solve the Jackson–Kechris–Louveau 'finite index over treeable' problem (2002); ChatGPT 6 Astra Ultra supplied a 'crucial observation'. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-finite-index-over-treeable-jkl-problem/
- 2026-10-06: Woodin's question answered. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-gch-above-strongly-compact-woodin-question/
- 2026-10-06: Generalized Lax conjecture: OpenAI counterexample claim; AI-found generic case (Kummer–Netzer). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-06-generalized-lax-conjecture-openai-counterexample-kummer-netzer-generic-case/
- 2026-10-06: Hironaka's resolution of singularities formalized in Lean by agents. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-10-06-hironaka-resolution-of-singularities-lean-fable-agents/
- 2026-10-06: OpenAI model claims the irrationality exponent of π is exactly 2 (Lean-formalized), which implies the Flint–Hills series converges. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-06-irrationality-exponent-pi-openai/
- 2026-10-06: OpenAI claims abelian Zilber–Pink. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-abelian-zilber-pink-claim/
- 2026-10-06: OpenAI claims Artin's primitive root conjecture (infinitude). Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-artin-primitive-root-conjecture-infinitude/
- 2026-10-06: OpenAI claims Bloch's conjecture for surfaces. Awaiting review; Expert-checked. https://postcutoff.com/e/2026-10-06-openai-bloch-conjecture-surfaces-claim/
- 2026-10-06: OpenAI claims BSD in Selmer corank ≤ 1 and Goldfeld's conjecture. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-bsd-low-selmer-corank-goldfeld-claim/
- 2026-10-06: Infinitely many closed geodesics on every sphere, claimed and re-proved. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-closed-geodesics-spheres-infinitely-many/
- 2026-10-06: OpenAI claims De Giorgi's conjecture in dimension eight. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-de-giorgi-conjecture-dimension-eight/
- 2026-10-06: OpenAI proves the Falconer distance conjecture (Lean). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-06-openai-falconer-distance-conjecture-lean/
- 2026-10-06: OpenAI claims the planar hot spots conjecture (Lean). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-06-openai-hot-spots-conjecture-simply-connected-lean/
- 2026-10-06: OpenAI claims the abundance conjecture; Jihao Liu raises priority. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-log-abundance-nonvanishing-claim/
- 2026-10-06: OpenAI: elliptic curves over imaginary quadratic fields are modular. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-modularity-elliptic-curves-imaginary-quadratic/
- 2026-10-06: OpenAI claims a counterexample to the nearby Lagrangian conjecture. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-nearby-lagrangian-conjecture-counterexample/
- 2026-10-06: Periodic tiling conjecture fails in dimension 3 (OpenAI claim, Lean-checked). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-periodic-tiling-conjecture-dimension-three/
- 2026-10-06: OpenAI claims 3D restriction and Bochner–Riesz conjectures. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-release-3d-restriction-bochner-riesz-claims/
- 2026-10-06: Sidorenko's conjecture disproved? (OpenAI, Lean). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-sidorenko-conjecture-counterexample-claim/
- 2026-10-06: Unit-distance bound below n^(4/3) claimed (OpenAI, Lean). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-unit-distance-upper-bound-power-saving-claim/
- 2026-10-06: doubleAI's 'Double Agent' claims explicit regular graphs of girth (8/5)·log n, beating the 4/3 constant of Margulis and Lubotzky–Phillips–Sarnak (1988). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-doubleai-high-girth-regular-graphs-8-5/
- 2026-10-06: Walter Trump's 1979 packing of 11 unit squares proved optimal, with a full Lean verification (AI involvement reported, unconfirmed). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-06-eleven-square-packing-optimality-lean/
- 2026-10-06: Optimal bound for the polynomial Littlewood–Offord problem, 'discovered autonomously by GPT-6 Pro' (exposition by Grebennikov). Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-polynomial-littlewood-offord-gpt-6-pro/
- 2026-10-05: Teen's Claude-coded proof claims rhombicosidodecahedron is not Rupert. Awaiting review; Expert-checked. https://postcutoff.com/e/2026-10-05-rhombicosidodecahedron-not-rupert-claude/
- 2026-10-04: Linear Hadwiger conjecture proved. Event confirmed, Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-10-04-linear-hadwiger-conjecture-proved-gpt-6-astra/
- 2026-10-02: Kannan–Lovász–Simonovits conjecture proved in two AI-assisted preprints. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-02-kls-conjecture-proved-ai-assisted/
- 2026-10-02: Klartag and Moshe prove the ε-Dvoretzky conjecture. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-02-epsilon-dvoretzky-conjecture-klartag-moshe/
- 2026-10-02: Linnik's constant ≤ 3.99, written by Claude Opus 5.5 and GPT Astra. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-02-linnik-constant-3-99-naslund-claude-gpt-astra/
- 2026-10-02: Meta publishes six maths papers made by mathematicians working with Muse Spark in ordinary meta.ai chat, saying five answer open questions. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-10-02-meta-muse-spark-six-math-papers/
- 2026-10-02: ChatGPT Astra finds geometric triangle-free graphs with near-optimal chromatic number, the first improvement on Burling's 1965 box bound. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-02-tomon-triangle-free-box-graphs-astra/
- 2026-10-01: Lehmer's 1965 permutation conjecture proved. Event confirmed, Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-01-lehmer-permutation-conjecture-opus-5-5/
- 2026-09-30: Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help. Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-30-ai-assisted-conjecture-wave-summer-2026/
- 2026-09-30: mt0-svg: AI-made Tammes N=15, Robbins V>2, frog model (Lean). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-09-30-mt0-svg-ai-generated-tammes-15-robbins-frog-model-lean/
- 2026-09-30: GPT-6 Astra proves Barvinok's log-concavity question for contingency tables on lines, giving lattice-point bounds for all totally unimodular polytopes. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-30-barvinok-log-concavity-totally-unimodular-astra/
- 2026-09-29: List Total Colouring Conjecture (late 1990s) disproved. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-29-list-total-colouring-conjecture-false-astra/
- 2026-09-29: EPFL's LinCodeEvolve (Viazovska, Abbe) finds seven record-breaking binary linear codes with LLM-guided program search. Result confirmed; Expert-checked. https://postcutoff.com/e/2026-09-29-lincodeevolve-record-binary-codes/
- 2026-09-29: GPT-5.6 Sol supplies key steps in a nearly linear bound for the Lovász path conjecture. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-29-lovasz-conjecture-nearly-linear-bound-gpt-5-6-sol/
- 2026-09-28: Four-body problem: uniqueness of convex central configurations for all masses claimed (Simó–Yoccoz conjecture), AI-found and formalized in Lean (Tomar). Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-28-four-body-convex-central-configurations-unique-tomar/
- 2026-09-28: Convex counterexamples to Schiffer and Pompeiu in dimensions 3, 4, 6, 8, 10 and 14, made with Claude Opus 5.5 and GPT-6 Astra/Sol. Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-28-schiffer-pompeiu-convex-higher-dimensions/
- 2026-09-28: Caltech 'Mathathon' is reworked into 'Old Problems, New Proofs' after an open letter from mathematicians. Result confirmed; Unverified claim. https://postcutoff.com/e/2026-09-28-mathathon-joint-statement/
- 2026-09-27: Erdős Problem #993 (1987). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-09-27-erdos-993-forest-independence-polynomials-unimodal/
- 2026-09-27: Perelman's proof of the Poincaré conjecture formalised in Lean, with AI-generated code. Result confirmed; Unverified claim. https://postcutoff.com/e/2026-09-27-poincare-conjecture-lean-formalization/
- 2026-09-26: GPT-6 Astra finds a proof improving the Kővári–Sós–Turán bound. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-26-mubayi-zarankiewicz-astra/
- 2026-09-25: Conjectures.io bounty platform pays out for Lean proofs of Erdős #859, #18(b), #1062(ii) and Ben Green's problems 24, 39, 40 within ten days, mostly to Purdue's 'JenW1N'. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-09-25-conjectures-io-erdos-green-bounty-solves/
- 2026-09-25: New record bound on the irrationality measure of ζ(2), μ ≤ 5.0495243, released as a 92k-line Lean proof written by Claude; beaten a week later by a Claude-assisted paper. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-09-25-zeta2-irrationality-measure-claude-lean/
- 2026-09-24: Benjamini–Schramm p_c < p_u: OpenAI bond proof in Lean, Claude site form. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-09-24-benjamini-schramm-pc-pu-nonamenable-openai-lean/
- 2026-09-22: Mathematician posts an unchecked ChatGPT Astra proof of the planar Mumford–Shah conjecture (1989), citing OpenAI's '100 open problems' claim. Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-22-mumford-shah-conjecture-astra-claim/
- 2026-09-22: Odlyzko–Poonen conjecture (1993) proved unconditionally. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-09-22-odlyzko-poonen-conjecture-proved/
- 2026-09-21: Courtade–Kumar 'most informative Boolean function' conjecture (2013) proved three times in two days, all with AI: Ky & Tran (ChatGPT), Google + CUHK (Gemini, Lean-verified end-to-end), Mahdavifar & Beirami. Event confirmed, Awaiting review; Lean-verified. https://postcutoff.com/e/2026-09-21-courtade-kumar-conjecture-proved/
- 2026-09-21: OpenAI says an internal model resolved 100+ long-standing open problems in 24 days of training (list released 6 Oct: 722 manuscripts). Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-21-openai-100-open-problems-claim/
- 2026-09-20: Kung–Traub conjecture proved, Lean check with ChatGPT 6. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-09-20-kung-traub-conjecture-proved-colbrook-lean-chatgpt/
- 2026-09-17: ζ(5) proved irrational. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-09-17-zeta-5-irrational-fauzan-lean-verified/
- 2026-09-16: Chvátal's 1972 conjecture proved (Chang–Liu–Liu, ChatGPT-assisted), then a GPT-6 Astra 'proof from The Book' and a Codex-built Lean formalization. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-09-16-chvatal-conjecture-proved/
- 2026-09-16: Lean-verified 'Liouville Goldbach' theorem goes viral as a GPT-6 Astra 'Goldbach breakthrough'; the AI role is unconfirmed and it is not the Goldbach conjecture. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-09-16-liouville-goldbach-lean-proof/
- 2026-09-15: Erdős–Hajnal high-girth problem (Erdős #108) disproved with ChatGPT/Codex help and a Lean proof, via the Conjectures.io bounty; experts sharpen it with GPT-6 Astra. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-09-15-erdos-108-high-girth-problem-disproved-conjectures-io/
- 2026-09-14: Sylvester's 1879 conjecture on sums of two cubes is fully proved. Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-14-sylvester-conjecture-proved-burungale-tian/
- 2026-09-11: Fields Medallists' open letter 'A Severe Misalignment of AI in Mathematics' criticises labs' race for famous problems. Result confirmed; Unverified claim. https://postcutoff.com/e/2026-09-11-fields-medalists-letter-ai-mathematics/
- 2026-09-11: Medvedev's logic of finite problems (1962) shown undecidable. Event confirmed, Awaiting review; Lean-verified. https://postcutoff.com/e/2026-09-11-medvedev-logic-undecidable/
- 2026-09-10: GPT-6 Astra's Epoch AI run adds more Lean-checked results. Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-09-10-astra-leanopenproblems-september-results/
- 2026-09-10: SAIR's IGP24 challenge. Result confirmed; Unverified claim. https://postcutoff.com/e/2026-09-10-igp24-inverse-galois-degree-24-humans-win/
- 2026-09-10: Irrationality measure of π lowered to 7.101862832357, the first improvement on Zeilberger–Zudilin (2019), with GPT-5.6 Sol and GPT-6 Astra; four weeks later OpenAI claimed the exact value 2. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-10-pi-irrationality-measure-bai-gpt/
- 2026-09-09: Pierce–Birkhoff conjecture disproved by a multi-agent GPT + Claude harness. Event confirmed, Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-09-09-pierce-birkhoff-conjecture-disproved/
- 2026-09-08: OpenAI claims a Millennium Prize problem. Disputed; Lean-verified. https://postcutoff.com/e/2026-09-08-openai-navier-stokes-blowup/
- 2026-09-07: Pre-release GPT-6 Astra disproves the Köthe conjecture with a Lean-verified counterexample. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-09-07-koethe-conjecture-disproved/
- 2026-09-07: Caltech team (Anandkumar) reports a stable self-similar singularity candidate for the unforced 3D Euler equations on R³, found with PINNs and LLM help. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-09-07-anandkumar-euler-singularity-r3/
- 2026-09-07: Erdős's 1946 conjecture on almost-monotone additive functions (Erdős problem #1122) proved in an anonymous Zenodo preprint whose proofs and Lean code were generated by GPT-6 Astra; Mangerel builds on it to settle Sárközy's 2001 conjectures. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-09-07-erdos-1122-monotone-additive-gpt-6-astra/
- 2026-09-06: Collatz positive-density convergence, AI-developed, Lean-checked. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-09-06-collatz-positive-density-log-time-mazur-codex/
- 2026-09-06: Preprint credits the 'Odin' AI research agent with a positively curved metric on S³×S³, which would disprove Hopf's Euler-characteristic sign conjecture (unverified). Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-06-odin-ai-agent-positive-curvature-s3xs3-hopf-sign-conjecture/
- 2026-09-04: Claude produces the first complete machine-checked proof of Fermat's Last Theorem in Lean, in 11 days. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-09-04-claude-formalizes-fermats-last-theorem/
- 2026-09-03: Claude-written Lean proof claims the dying percolation conjecture θ(p_c)=0 in every dimension. Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-09-03-dying-percolation-theta-pc-zero/
- 2026-09-03: GPT-6 Astra proves the Erdős–Sós conjecture with a short counting argument. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-09-03-erdos-sos-conjecture-proved-gpt-6-astra/
- 2026-09-03: Pre-release GPT-6 Astra disproves Erdős's 'first serious problem' (1931, $500) and proves the rational-exponents conjecture, all Lean-verified, in Epoch's FrontierMath Erdős runs. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-09-03-frontiermath-erdos-astra-disproves-erdos-problem-1/
- 2026-09-03: GPT-6 Astra autonomously disproves Smale's mean value conjecture in Lean. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-09-03-smale-mean-value-conjecture-disproved-gpt-6-astra/
- 2026-08-30: GPT-6 Astra lowers the bounded prime gaps record from 246 to 186. Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-08-30-bounded-prime-gaps-186/
- 2026-08-28: Matrix Spencer conjecture proved. Awaiting review; Preprint only. https://postcutoff.com/e/2026-08-28-matrix-spencer-conjecture-proved/
- 2026-08-26: GPT-5.6 improves the Erdős–Rankin / Ford–Green–Konyagin–Maynard–Tao bound for large prime gaps. Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-08-26-erdos-rankin-large-prime-gaps-improved/
- 2026-08-23: Claude-assisted construction claims a complex structure on the 6-sphere, answering Hopf's 1947 problem (pending verification). Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-08-23-hopf-problem-s6-complex-structure/
- 2026-08-23: Claude-assisted search breaks the elliptic curve rank record. Result confirmed; Expert-checked. https://postcutoff.com/e/2026-08-23-elliptic-curve-rank-record-31/
- 2026-08-19: Smooth Carathéodory and Loewner conjectures disproved with Claude. Awaiting review; Preprint only. https://postcutoff.com/e/2026-08-19-caratheodory-loewner-smooth-counterexamples-alpoge-claude/
- 2026-08-19: Peking University preprint claims an AI-found disproof of the Yau–Tian–Donaldson conjecture for constant scalar curvature metrics. Awaiting review; Preprint only. https://postcutoff.com/e/2026-08-19-yau-tian-donaldson-cscK-disproof-claim/
- 2026-08-18: Palomar launches: a registry of Lean-verified mathematics to curb misrepresented AI proof claims. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-08-18-palomar-lean-registry/
- 2026-08-13: Banach's isometric conjecture (1932) completed in the real case with key steps from ChatGPT 5.5/5.6 Pro; complex and quaternionic cases follow five days later. Awaiting review; Preprint only. https://postcutoff.com/e/2026-08-13-banach-isometric-conjecture-solved/
- 2026-08-12: Claude-assisted constructions complete Hadamard matrices for every order below 2000. Result confirmed; Preprint only. https://postcutoff.com/e/2026-08-12-claude-hadamard-matrices-below-2000/
- 2026-08-10: Claude proves more than two-thirds of Riemann zeta zeros are simple and on the critical line (up from 41.6%). Result confirmed; Lean-verified. https://postcutoff.com/e/2026-08-10-claude-riemann-zeta-zeros-two-thirds/
- 2026-08-05: Sendov's 1958 conjecture on polynomial roots proved with GPT-5.6 Pro. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-08-05-sendov-conjecture-proved/
- 2026-08-05: HRT conjecture (1996) disproved. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-08-05-hrt-conjecture-disproved/
- 2026-08-04: Alexander Perry disproves the period-index conjecture. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-08-04-period-index-conjecture-false/
- 2026-08-03: Planar Schiffer and Pompeiu conjectures disproved by two independent groups. Event confirmed, Awaiting review; Lean-verified. https://postcutoff.com/e/2026-08-03-schiffer-pompeiu-conjectures-disproved/
- 2026-08-01: OpenAI's unreleased 'Astra' model claims ten advances in maths and theoretical CS, with Lean proofs. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-08-01-openai-astra-ten-advances/
- 2026-07-27: Neurosurgery resident uses GPT-5.6 Sol to prove Crouzeix's conjecture in a 16-hour autonomous run. Result confirmed; Expert-checked. https://postcutoff.com/e/2026-07-27-crouzeix-conjecture-proved/
- 2026-07-25: Sharp thin-shell inequality. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-07-25-sharp-thin-shell-inequality-gpt-5-6-pro/
- 2026-07-24: Hessian conjecture refuted in five variables, derived from Claude-found Jacobian counterexample. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-07-24-hessian-conjecture-counterexample/
- 2026-07-24: Rota's 1970 unimodality conjecture for matroid flats disproved, with ChatGPT 5.6 Pro suggesting a key construction. Result confirmed; Preprint only. https://postcutoff.com/e/2026-07-24-rota-flats-unimodality-disproved/
- 2026-07-24: Terence Tao's ICM 2026 public lecture 'Mathematics in the age of AI' calls a crisis in the foundations of mathematical values. Result confirmed; Unverified claim. https://postcutoff.com/e/2026-07-24-tao-icm-mathematics-in-the-age-of-ai/
- 2026-07-23: AI systems score a perfect 42/42 at IMO 2026, officially graded. Result confirmed; Expert-checked. https://postcutoff.com/e/2026-07-23-imo-2026-ai-perfect-scores/
- 2026-07-22: Dmitry Rybin posts a GPT-5.6 Pro counterexample to the ~30-year-old Dinitz–Garg–Goemans (Goemans cost) conjecture on unsplittable flows. Awaiting review; Expert-checked. https://postcutoff.com/e/2026-07-22-dinitz-garg-goemans-conjecture-disproved-gpt-5-6-pro/
- 2026-07-22: Columbia PhD student Shouqiao Wang says he solved six open Erdős problems in five days with GPT-5.6 Sol in Codex, and publishes his workflow. Awaiting review; Expert-checked. https://postcutoff.com/e/2026-07-22-shouqiao-wang-six-erdos-problems-gpt-5-6-sol-codex/
- 2026-07-20: Claude Fable 5 finds a counterexample to the Jacobian conjecture in dimension 3. Result confirmed; Unverified claim. https://postcutoff.com/e/2026-07-20-jacobian-conjecture-counterexample/
- 2026-07-17: GPT-5.6 Sol Ultra proves the 50-year-old cycle double cover conjecture. Result confirmed; Expert-checked. https://postcutoff.com/e/2026-07-17-cycle-double-cover-conjecture-proved/
- 2026-07-14: Berkeley's Phillip Kerger uses GPT-5.6 Sol and a 10-page prompt to close a 30-year gap in derivative-free convex optimization. Awaiting review; Preprint only. https://postcutoff.com/e/2026-07-14-gpt-5-6-zeroth-order-convex-lower-bound/
- 2026-07-01: AI-assisted counterexample answers Grothendieck's question on finite flat group schemes, merged into Mathlib. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-07-01-grothendieck-group-scheme-counterexample/

### Physics (25)

- 2026-11-07: Anthropic's Claude physics papers: Hawking–Page and modular bootstrap. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-11-07-anthropic-claude-hawking-page-modular-bootstrap-hexagon/
- 2026-10-31: Onsager hard rods: AI-written first-order transition claim, not human-verified. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-10-31-onsager-hard-rods-first-order-transition-gpt-6-astra-unverified/
- 2026-10-30: Hopfield model thermodynamic limit, AI-generated proofs. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-30-hopfield-model-thermodynamic-limit-barra-durante-claude-chatgpt/
- 2026-10-26: OpenAI claims 4D Yang–Mills and QCD existence. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-26-openai-yang-mills-qcd-existence-claim/
- 2026-10-26: 3D SU(2) Yang–Mills continuum limit claimed in five AI-written papers. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-26-three-dimensional-su2-yang-mills-continuum-limit-aronow-lopatto-ai/
- 2026-10-25: AI-assisted results in the 25 Oct 2026 sweep. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-25-ai-assisted-results-october-25-listing/
- 2026-10-16: OpenAI's 2D area law proof Lean-verified by Axiom. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-16-openai-2d-area-law-lean-formalized-axiom/
- 2026-10-16: Alpöge and Sussman say Claude has an (unreadable) existence argument for 4D Yang–Mills on ℝ⁴, by finishing Bałaban's 1980s program. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-16-yang-mills-claude-balaban-program-alpoge-sussman/
- 2026-10-16: Das Sarma paper written with Claude Opus 5.5, refereed by Codex. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-16-das-sarma-exciton-superfluidity-claude-opus-codex-referee/
- 2026-10-15: CERN and Mistral plan a Large Physics Model. Event confirmed, Awaiting review; Unverified claim. https://postcutoff.com/e/2026-10-15-cern-mistral-large-physics-model/
- 2026-10-14: Bray, Dolmen, Khuri & Schmidt prove the spacetime Penrose inequality for 'maximally parameterized' data with Claude's help, and say OpenAI's Oct 6 Penrose paper appears to finish their program. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-14-penrose-conjecture-bray-khuri-claude-openai-provenance/
- 2026-10-12: "The proof presented in this paper is due to Claude Opus 5.5". Result confirmed; Preprint only. https://postcutoff.com/e/2026-10-12-drouot-claude-opus-proof-bulk-conductances/
- 2026-10-08: Full Lyapunov spectrum of the Sompolinsky–Crisanti–Sommers random neural network derived, a problem named open in 1988; GPT-6 Astra produced the first derivation (David G. Clark, Flatiron). Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-08-lyapunov-spectrum-random-neural-networks-gpt-6-astra/
- 2026-10-08: PPT-distillable entanglement can fall strictly below the regularised Rains bound. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-08-ppt-entanglement-distillation-rains-bound-chatgpt-astra/
- 2026-10-06: OpenAI claims Anderson localization in 2D and extended states in 3D. Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-10-06-openai-anderson-localization-2d-delocalization-3d/
- 2026-10-06: OpenAI claims quantum ferromagnet order and interacting Bose condensation. Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-heisenberg-ferromagnet-bose-einstein-condensation/
- 2026-10-06: OpenAI claims strong cosmic censorship near Kerr. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-strong-cosmic-censorship-near-kerr/
- 2026-10-06: 2D O(n) mass gap (Polyakov) and O(3) continuum limit claimed (OpenAI). Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-polyakov-o3-sigma-model-mass-gap-claim/
- 2026-10-06: OpenAI proves the spin-one Haldane gap (periodic chains). Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-openai-spin-one-haldane-gap-proof/
- 2026-09-25: Claude (Fable 5.1 in Claude Science) computes the nine-loop six-gluon amplitude in planar N=4 super-Yang-Mills, answering a physicist's public challenge. Result confirmed; Expert-checked. https://postcutoff.com/e/2026-09-25-claude-nine-loop-amplitude-n4-sym/
- 2026-09-21: Grad's 1967 conjecture on 3D plasma equilibria falls. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-09-21-grad-conjecture-counterexamples/
- 2026-09-05: The I3322 Bell inequality needs infinite dimensions. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-05-i3322-bell-inequality-infinite-dimensions/
- 2026-09-03: PPPL's PACMAN framework lets multiple AI models control a tokamak in ~20 ms, preventing a tearing mode. Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-09-03-pppl-pacman-fusion-ai-control/
- 2026-09-02: Nature: 'Designing physics experiments with artificial intelligence' (Krenn group) on AI-found setups that beat human designs. Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-09-02-krenn-nature-designing-physics-experiments-ai/
- 2026-07-29: Maxwell's conjecture on equilibria of point charges is false. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-07-29-maxwell-point-charge-conjecture-false/

### Computer science (44)

- 2026-11-12: A BST meets Iacono's 2001 unified bound, with Claude and GPT. Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-12-binary-search-tree-unified-bound-ai/
- 2026-11-12: Grid-minor exponent 6 in polynomial time (Hajiaghayi with Astra). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-12-grid-minor-sixth-power-hajiaghayi-astra/
- 2026-11-06: PSI claims Lean-checked proof of the Aaronson–Ambainis conjecture. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-06-psi-aaronson-ambainis-conjecture-proof/
- 2026-11-05: 3-uniform hyperclique hypothesis refuted with ChatGPT Sol 6.1. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-05-3-uniform-hyperclique-hypothesis-false-chatgpt-sol/
- 2026-11-04: Colourings Glauber dynamics above (1+1/e)Δ (GPT-6 Astra Pro). Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-04-glauber-dynamics-colorings-1-plus-1-over-e-gpt-6-astra-pro/
- 2026-11-04: Huffman coding with unequal letter costs is NP-complete (Codex). Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-04-huffman-unequal-letter-costs-np-complete-codex/
- 2026-11-04: 2×2 matrix mortality claimed undecidable (AI-assisted, Lean). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-11-04-matrix-mortality-2x2-undecidable-codex-claude-lean/
- 2026-11-03: FPRAS for mixed volumes, ideas from GPT-6 Astra. Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-03-mixed-volume-fpras-gurvits-conjecture-disproved-gpt-6-astra/
- 2026-10-29: Deterministic factoring in N^o(1) steps, Lean-checked, ideas by Claude. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-29-deterministic-factoring-n-o1-lean-claude-rudich-rousseau/
- 2026-10-29: Online Steiner forest: greedy claimed Θ(log k log log k), with GPT Astra. Event confirmed, Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-29-online-steiner-forest-greedy-log-k-loglog-k-gpt-astra-lean/
- 2026-10-27: Anthropic's Claude also refutes ETH. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-27-anthropic-claude-eth-refutation-3sat-subexponential/
- 2026-10-27: Unbounded-error communication is not closed under AND, found with GPT-6 Astra. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-27-uppcc-not-closed-under-intersection-gpt-6-astra/
- 2026-10-26: OpenAI claims ETH is false. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-26-openai-eth-false-subexponential-sat-claim/
- 2026-10-26: 3-colorable graphs: O(n^0.1537) colors with GPT-6 Astra. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-26-three-coloring-n-0-1537-gpt-6-astra/
- 2026-10-25: Formula minimization Σ₂ᵖ-complete (proof found by GPT-Sol-6.1). Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-25-formula-minimization-sigma2p-complete-gpt-sol/
- 2026-10-23: Graph connectivity communication bound settled, with ChatGPT. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-23-graph-connectivity-nondeterministic-communication-complexity-chatgpt/
- 2026-10-19: Integer programming in standard form in N^O(d) time, improving Eisenbrand–Weismantel's N^O(d²): Zhejiang team's ideas, GPT Astra Ultra's proofs (Chen, Mao, Zhang). Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-19-integer-programming-linear-exponent-gpt-astra-ultra/
- 2026-10-19: Counting perfect matchings in general graphs: OpenAI FPRAS, simplified proof. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-10-19-perfect-matchings-fpras-general-graphs-openai-liu-meng/
- 2026-10-14: Li, Li & Liu: external-memory integer sorting beats the comparison bound, answering Aggarwal–Vitter (1988) by way of network coding, with ChatGPT/Codex and Lean. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-14-external-memory-integer-sorting-beats-comparison-bound-network-coding/
- 2026-10-13: k-median breaks the factor-2 barrier. Event confirmed, Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-13-k-median-better-than-2-approximation-epfl/
- 2026-10-09: Subset Sum in O(n + N^(1+ε)) time claimed. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-09-subset-sum-near-linear-time-gpt-astra-ultra/
- 2026-10-08: GPT-6 Astra finds a 3SAT reduction showing monotone Dualization (minimal hypergraph transversals) has no polynomial algorithm under ETH. Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-08-dualization-eth-lower-bound-gpt-6-astra/
- 2026-10-08: Laderman's 23 multiplications are optimal for 3×3 matrices over F_2 and over the integers. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-08-rank-3x3-matrix-multiplication-f2-is-23-lean-tomar/
- 2026-10-07: Outside researchers using AI crowdsource a tighter exponent in OpenAI's integer-multiplication result #109, from 2^-182 to about 2^-8.4 (conditional). Event confirmed, Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-07-colkitt-codex-integer-multiplication-exponent/
- 2026-10-07: Braverman & He refute the 2004 undirected multiple-unicast (network coding) conjecture with a GPT-6-found counterexample on PG(2, 9). Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-07-multiple-unicast-conjecture-false-gpt-6/
- 2026-10-07: Bolzano (Charles University). Awaiting review; Expert-checked. https://postcutoff.com/e/2026-10-07-bolzano-automated-open-problem-solving-charles-university/
- 2026-10-06: OpenAI proves ω ≤ 9/4 for matrix multiplication. Result confirmed; Lean-verified. https://postcutoff.com/e/2026-10-06-openai-matrix-multiplication-omega-9-4/
- 2026-10-06: OpenAI model claims a proof of Khot's Unique Games Conjecture, with Lean formalization. Awaiting review; Lean proof, not yet reviewed. https://postcutoff.com/e/2026-10-06-unique-games-conjecture-openai/
- 2026-10-06: OpenAI model claims tight 1 + 2/e approximation for k-median. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-06-openai-k-median-optimal-approximation-1-plus-2-over-e/
- 2026-10-06: OpenAI claims L = RL = BPL with a Lean proof. Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-06-openai-l-equals-rl-equals-bpl-lean-claim/
- 2026-10-06: Explicit tensors of border rank 3n − o(n), past the 'linear flattening barrier'. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-06-explicit-tensors-border-rank-3n-gpt-6-astra/
- 2026-10-06: Why SAT solvers fail on multiplication. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-06-multiplier-associativity-hard-for-resolution-gpt-5-6-sol/
- 2026-10-06: Preprint claims a 4.268 upper bound for the random 3-SAT threshold, down from 4.4898, with a Lean 4 proof; 'large language models drove the research'. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-06-random-3-sat-threshold-upper-bound-4-268-llm/
- 2026-10-05: Claude discovers an algorithm that refutes the 3SUM and APSP hypotheses. Event confirmed, Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-05-claude-refutes-3sum-apsp-hypotheses/
- 2026-10-05: Random k-SAT threshold exists for every k ≥ 3: a human proof and an OpenAI Lean-checked proof. Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-10-05-random-k-sat-satisfiability-conjecture-carenini-openai/
- 2026-10-05: Decreasing diagrams are complete for confluence. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-10-05-decreasing-diagrams-complete-for-confluence-rta-problem-56/
- 2026-09-14: The k-server conjecture, the 'holy grail' of online algorithms, is proved at Oxford. Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-14-k-server-conjecture-proved/
- 2026-09-14: Friedgut's 2004 influential-coalitions conjecture resolved. Result confirmed; Expert-checked. https://postcutoff.com/e/2026-09-14-friedgut-coalition-conjecture-resolved/
- 2026-09-13: Matroid secretary conjecture resolved, with GPT Astra. Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-13-matroid-secretary-conjecture-resolved-gpt-astra/
- 2026-09-04: Reed–Solomon codes list-decoded up to capacity and proximity gaps settled, with GPT-5.6 Sol and ChatGPT 5.6 Pro (Brakensiek–Chen–Putterman–Zhang–Zheng; Jeronimo). Awaiting review; Expert-checked. https://postcutoff.com/e/2026-09-04-reed-solomon-list-decoding-capacity-ai/
- 2026-09-02: NVIDIA's Nemotron-3-Ultra-CC outscores every human at IOI 2026. Result confirmed; Expert-checked. https://postcutoff.com/e/2026-09-02-nvidia-nemotron-ioi-2026/
- 2026-08-27: Google's Antigravity 'Teamwork' multi-agent framework with Gemini 3.7 Flash solves seven open CS/math problems, incl. part of Knuth's cycles problem. Awaiting review; Lean-verified. https://postcutoff.com/e/2026-08-27-antigravity-teamwork-open-problems/
- 2026-08-17: AlphaEvolve helps lower the matrix multiplication exponent ω to below 2.371177. Result confirmed; Preprint only. https://postcutoff.com/e/2026-08-17-alphaevolve-matrix-multiplication-exponent/
- 2026-07-28: Claude Mythos Preview finds new cryptanalytic attacks on post-quantum HAWK and 7-round AES. Event confirmed, Awaiting review; Unverified claim. https://postcutoff.com/e/2026-07-28-claude-mythos-cryptanalysis-hawk-aes/

### Biology (15)

- 2026-11-11: Google DeepMind launches AlphaGenome 2, predicting how DNA variants act in specific cell types. Result confirmed; Unverified claim. https://postcutoff.com/e/2026-11-11-alphagenome-2/
- 2026-11-04: Anthropic's biology team, working with Claude, reports the first 3D structure of a vault particle from bacterial life. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-11-04-anthropic-claude-bacterial-vault-particle-structure/
- 2026-11-04: Nature: AI agents run an automated biology lab. Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-11-04-nature-ai-native-autonomous-biomolecular-lab/
- 2026-10-21: Thousands of GPT-Rosalind agents analyse millions of mouse brain cells in 32 minutes and propose a cholesterol-transport lead for Perry syndrome. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-10-21-gpt-rosalind-agents-perry-syndrome-lead/
- 2026-10-20: Claude designs binders against scorpion neurotoxins. Event confirmed, Awaiting review; Unverified claim. https://postcutoff.com/e/2026-10-20-claude-scorpion-toxin-binders/
- 2026-10-14: AI-designed proteases (Baker lab, Nature). Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-10-14-baker-lab-de-novo-designed-proteases-nature/
- 2026-10-09: Machine-learning-guided evolution makes a plant Rubisco 29% faster (MIT, Stanford, ANU. Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-10-09-ml-assisted-directed-evolution-plant-rubisco/
- 2026-10-05: Google DeepMind's AlphaProtein Novo designs new-to-nature enzymes from scratch (piperidine synthesis, DEHP degradation), with Frances Arnold's lab. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-05-deepmind-alphaprotein-novo-enzyme-design/
- 2026-09-29: Microsoft Research unveils Quine, a multimodal 'world model of biology' validated in pancreatic-cancer screens with the Broad Institute. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-09-29-microsoft-quine-biology-world-model/
- 2026-09-24: DeepMind, EMBL-EBI, NVIDIA and CEPI add predicted protein-complex structures for 2,800+ viruses to the AlphaFold Database. Result confirmed; Unverified claim. https://postcutoff.com/e/2026-09-24-viral-protein-complex-structures-alphafold-db/
- 2026-09-23: Claude agents discover a novel CRISPR-like enzyme system. Disputed; Preprint only. https://postcutoff.com/e/2026-09-23-claude-discovers-novel-enzyme-system/
- 2026-09-19: FutureHouse and Edison Scientific publish twelve 'Millennium Problems for Biology', pitched as the 'last reasonable eval' for AI in biology. Event confirmed, Awaiting review; Unverified claim. https://postcutoff.com/e/2026-09-19-millennium-problems-for-biology/
- 2026-09-17: Science: Stanford's 'Virtual Biotech' of 37,000 AI agents mines ~50,000 clinical trials and designs a lung-cancer ADC later matched by pharma. Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-09-17-stanford-virtual-biotech-37000-agents/
- 2026-09-03: Complete male fruit fly nervous-system connectome (166,000 neurons), reconstructed with Google AI, published in Cell. Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-09-03-male-fruit-fly-connectome/
- 2026-08-18: Claude autonomously designs protein binders that work in the lab against 14 of 15 targets. Result confirmed; Expert-checked. https://postcutoff.com/e/2026-08-18-claude-protein-binders-wet-lab/

### Materials (3)

- 2026-10-04: Claude agents propose room-temperature magnetic semiconductors. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-10-04-vals-claude-agents-luttinger-compensated-magnetic-semiconductors/
- 2026-09-25: Lila Sciences' AI-run lab screens 2,942 catalysts and finds iridium- and ruthenium-free palladium oxides for green hydrogen. Awaiting review; Preprint only. https://postcutoff.com/e/2026-09-25-lila-ai-lab-palladium-oer-catalysts/
- 2026-09-15: Periodic Labs introduces Periodic Neon, a 1T-parameter lab-trained model that beats GPT-6 Astra at X-ray diffraction analysis. Event confirmed, Awaiting review; Unverified claim. https://postcutoff.com/e/2026-09-15-periodic-labs-neon/

### Medicine (7)

- 2026-10-22: Microsoft MAI-DxO diagnosis paper in Science. Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-10-22-microsoft-mai-dxo-science-sequential-diagnosis/
- 2026-10-19: FAHR-Face: Mass General Brigham foundation model estimates biological age and cancer survival from a face photo (Lancet Digital Health). Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-10-19-fahr-face-cancer-survival-face-photos/
- 2026-09-30: Google's ERA-built model ranks #1 of 39 in the CDC FluSight 2025–26 flu-hospitalization forecasting challenge. Result confirmed; Unverified claim. https://postcutoff.com/e/2026-09-30-google-era-flusight-flu-forecasting/
- 2026-09-15: OpenAI Foundation launches Public Data for Health with $125M+ in grants for open biomedical datasets. Event confirmed, Awaiting review; Unverified claim. https://postcutoff.com/e/2026-09-15-openai-foundation-public-data-for-health/
- 2026-09-14: FDA grants priority review to Takeda's zasocitinib, a computationally designed TYK2 inhibitor, with a decision due Q1 2027. Event confirmed, Awaiting review; Unverified claim. https://postcutoff.com/e/2026-09-14-takeda-zasocitinib-fda-priority-review/
- 2026-09-10: First Phase III trial of a generative-AI-discovered drug doses first patient. Event confirmed, Awaiting review; Peer-reviewed. https://postcutoff.com/e/2026-09-10-insilico-rentosertib-phase-3/
- 2026-09-08: AlphaGenome Atlas predicts the effect of all ~9 billion possible single-letter human DNA variants. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-09-08-alphagenome-atlas/

### Climate and weather (6)

- 2026-10-17: China's Fengqing AI ensemble weather forecast goes operational. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-10-17-cma-fengqing-ai-ensemble-forecast-operational/
- 2026-10-14: Microsoft PBC improves sub-seasonal weather forecasts (Nature). Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-10-14-microsoft-probabilistic-bias-correction-subseasonal-forecasts/
- 2026-10-09: AI weather models forecast Dubai's unprecedented 2024 storm by 'translocation', not extrapolation (University of Chicago, Science Advances). Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-10-09-ai-weather-models-gray-swan-dubai-2024/
- 2026-09-09: Google and NASA JPL release MAPL-EMIT, an AI model that maps methane plumes worldwide. Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-09-09-google-nasa-jpl-mapl-emit-methane/
- 2026-09-03: Google DeepMind's WeatherNext 3 learns from live satellite data. Result confirmed; Expert-checked. https://postcutoff.com/e/2026-09-03-weathernext-3/
- 2026-08-06: DeepMind open-sources WeatherNext 2 and WeatherNext Cyclones with a Nature paper showing ~1 extra day of hurricane warning. Result confirmed; Peer-reviewed. https://postcutoff.com/e/2026-08-06-weathernext-open-source/

### Astronomy (1)

- 2026-10-08: Claude Science builds a complete ultraviolet map of the sky. Event confirmed, Awaiting review; Unverified claim. https://postcutoff.com/e/2026-10-08-claude-science-complete-uv-sky-map/

### Other fields (3)

- 2026-11-10: Viral claim that AI agents found an unmapped Maya site turns out to be a rediscovery of a site published in 2025. Disputed; Unverified claim. https://postcutoff.com/e/2026-11-10-ai-agents-maya-site-claim-rediscovered/
- 2026-10-08: AI archive search finds forgotten meteorite and eruptions. Awaiting review; Unverified claim. https://postcutoff.com/e/2026-10-08-antiquity-ai-archive-search-meteorite-rhinos/
- 2026-10-01: Harvard physicist Matthew Schwartz releases BootLoops, an open-source harness that let Claude produce 36 manuscripts in 18 fields in three months. Event confirmed, Awaiting review; Preprint only. https://postcutoff.com/e/2026-10-01-bootloops-claude-shaped-science/

## Credits

We cross-check VibeMathed (https://vibemathed.com/), Terence Tao’s Erdős wiki (https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems, frozen since 2026-06-30) and Epoch AI’s data on AI use in mathematics (https://epoch.ai/data/arxiv).