Science & math: everything we have

AI-assisted results in mathematics and science. The Science & Math page has the same results with their verification status.

319 events (234 after June 2026), 0 models, 95 videos, 140 posts. Latest event 25 October 2026.

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Key moments

22 Oct 2026 Barry Simon’s L² conjecture (Problem 8 of his 2000 list) disproved: Becker and Yang build a counterexample largely found with ChatGPTOn 22 Oct 2026 Simon Becker and Mengxuan Yang posted arXiv 2610.31637, a counterexample to Barry Simon’s multidimensional L² conjecture (Problem 8 in “Schrödinger operators in the twenty-first century”, 2000). For every…
22 Oct 2026 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 6arXiv 2610.31614 (22 Oct 2026) by Berger, Caravenna, Clark, Dunlap, Gu, Liu, Nakajima, Sun, Tsai, Xie and Zygouras constructs the “Critical 2D KPZ Process”, a non-trivial distribution-valued solution of the ill-defined…
21 Oct 2026 Hochster’s 1973 small Cohen–Macaulay conjecture: an OpenAI manuscript’s counterexample is surveyed, re-proved and extended to every dimension by Cristian AnghelOpenAI’s 6 Oct 2026 math release (family 195, manuscript dated 23 Sep) constructs a three-dimensional complete Noetherian normal local domain over C with no nonzero finitely generated maximal Cohen–Macaulay module…
21 Oct 2026 Barnette’s 1969 Hamiltonicity conjecture: graph theorist Zhentao Li publishes a digested, partly re-proved version of OpenAI’s proofOpenAI’s 6 Oct 2026 math release (family 180, manuscript “Paired states and Hamiltonian cycles in cubic bipartite planar graphs”, 24 Sep) claims Barnette’s conjecture, with a Lean formalization listed in its catalogue.…
21 Oct 2026 Nagata’s 1959 conjecture: algebraic geometer Jenia Tevelev writes out OpenAI’s ‘remarkably simple’ proof and calls the release ‘a stunning achievement’OpenAI’s 6 Oct 2026 math release (family 039, manuscript dated 23 Sep) claims a proof of Nagata’s conjecture: for r ≥ 10 very general points in the plane, every curve of degree d with multiplicities m_i satisfies Σ m_i…
20 Oct 2026 MDS conjecture settled in even characteristic: two independent proofs, one checked in Lean with Claude’s help, the other written with ChatGPTTwo independent claims settle the linear MDS conjecture (from Segre’s 1955 question on arcs) for every finite field of even order: an [n, k] MDS code over F_q, q even, has n ≤ q + 1, except n ≤ q + 2 for k = 3 and k = q…
20 Oct 2026 Double-cap conjecture (Witsenhausen 1974, Kalai) claimed in all dimensions, with a separate AI-built Lean proofIbiapina, Gomes, Pio, Belo and Ferreira (Brazil) claim that caps minimize the orthogonal neighbourhood in RP^(n−1), which yields the double-cap conjecture: for n ≥ 3, a measurable subset of the sphere S^(n−1) with no…
19 Oct 2026 Kaplansky’s quasitrace conjecture reported disproved by an unreleased OpenAI model; experts reproduce it and refute the monotone completeness conjectureJananan Arulseelan and James E. Hanson write that “an unreleased OpenAI model produced a claimed counterexample” to the quasitrace (Kaplansky) conjecture for AW*-algebras in an unpublished manuscript (Sept 2026). They…
19 Oct 2026 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)arXiv 2610.25955 (19 Oct 2026), “Integer Programing: An Algorithm with Exponent Linear in the Dimension” by Lin Chen, Yuchen Mao and Guochuan Zhang (Zhejiang University), gives a deterministic algorithm for min{cᵀx : Ax…
19 Oct 2026 Erdős–Szemerédi sunflower conjecture proved for every k ≥ 3; the key vector bound (Theorem 2) was found by ChatGPT 6 Astra Pro (Bucić, He, Lee)On 19 Oct 2026 Matija Bucić, Fankang He (University of Vienna) and Hyunwoo Lee (KAIST/IBS) posted arXiv 2610.26686, “Proof of the Erdős-Szemerédi sunflower conjecture”. Theorem 1: for every k ≥ 3 and n ≥ 1, a family of…
17 Oct 2026 A non-sofic word-hyperbolic group: Sandhu and Thom build one from OpenAI’s non-residually-finite hyperbolic group, starting from an AI-generated construction; Douglas–Mghirbi give an independent AI-assisted proof with LeanarXiv 2610.24836 (17 Oct 2026), “An example of a non-sofic hyperbolic group” by Harjas Sandhu and Andreas Thom, constructs “a torsion-free, two-dimensional, word-hyperbolic group which is not sofic”, building on…
17 Oct 2026 Erdős–Hajnal conjecture proved for every path P_t: Tung H. Nguyen, with ChatGPT-6 Astra proving key lemmas; a DeepMind internal model reached the same result independently, and Claude Opus 5.5 manuscripts claim P6 and all pathsarXiv 2610.24887 (17 Oct 2026), “Erdős–Hajnal for excluding paths” by Tung H. Nguyen (Oxford), proves that every path P_t has the Erdős–Hajnal property: P_t-free graphs on n vertices have a clique or stable set of size…
16 Oct 2026 Alpöge and Sussman say Claude has an (unreadable) existence argument for 4D Yang–Mills on ℝ⁴, by finishing Bałaban’s 1980s programNorthwestern mathematician Ethan Sussman and Anthropic’s Levent Alpöge run a public GitHub repo (since 6 Oct 2026) in which Claude, steered by Alpöge, tries to complete Tadeusz Bałaban’s renormalisation-group program…
16 Oct 2026 Smith–Toda complex V(4) exists for all primes p ≥ 11: Angeltveit extends and simplifies OpenAI’s AI-written p = 1009 construction, with ChatGPT’s helpVigleik Angeltveit (ANU) posted arXiv 2610.23215 on 16 Oct 2026. It proves that the Smith–Toda complex V(4), a finite p-local spectrum with BP-homology BP∗/(p, v1, v2, v3, v4), exists for every prime p ≥ 11. This…
16 Oct 2026 OpenAI’s AI-generated proof of a 2D entanglement area law fully formalized in Lean by Axiom (AxiomProver tooling + Codex), with no sorryOn Oct 16, 2026 Axiom Math published AxiomMath/AreaLaw2D, a Lean 4 formalization of “A two-dimensional area law from a global spectral gap” (family 265 of OpenAI’s openai/math release, dated Sept 24, 2026). Theorem 1.1…
16 Oct 2026 Maximum number of Hamiltonian cycles in a tournament determined asymptotically, (cosh 1/cos 1)·(n−1)!/2ⁿ, answering Alon and proving Wormald’s conjecture, with proofs ‘originally found by GPT-5.6’Alexander Divoux and Shouda Wang (Princeton) posted arXiv 2610.23755 on 16 Oct 2026. They prove that C(n), the maximum number of directed Hamiltonian cycles in an n-vertex tournament, is (cosh 1/cos 1 ± o(1))·(n−1)!/2ⁿ.…
16 Oct 2026 Lonely Runner Conjecture: Hu and Jing get the first constant-factor gain over the union bound, (1+c)/2n, after ‘many rounds of discussion’ with ChatGPT 6 Pro and AstraXiyu Hu (UCAS) and Yifan Jing (Ohio State) posted arXiv 2610.23790 on 16 Oct 2026. They prove that for every set V of n ≥ 2 distinct positive speeds there is a time when all runners are more than (1+c)/(2n) from the…
16 Oct 2026 New Gauss circle problem bound E(X) = O(X^(209/670+ε)) breaks Huxley’s 5/16 threshold; authors used ChatGPT and Codex on proof strategies and checkingarXiv 2610.21730 (v1 dated 15 Oct, announced 16 Oct 2026), “A New Bound for the Gauss Circle Problem” by Xi Cen, Xitao Gao, Cheng Zhang and Junyong Zhang, proves E(X) = O_ε(X^(209/670+ε)) for the lattice-point error in…
16 Oct 2026 Brennan’s 1978 conjecture: Smirnov, Binder, Ivrii and Prause check OpenAI’s AI-generated proof and publish a much shorter proof of a stronger resultOn 16 Oct 2026 Ilia Binder, Oleg Ivrii, István Prause and Stanislav Smirnov (Fields Medal 2010) posted arXiv 2610.23853, “Brennan’s Conjecture and the Universal Integral Means Spectrum”. It responds to two preprints…
15 Oct 2026 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 5.5arXiv 2610.21511 (15 Oct 2026) by Iwao Kimura makes the argument of OpenAI’s October manuscript on Landau–Siegel zeros explicit, (1 − β) log q ≥ 5811 × 10⁻⁷ for every real zero of every primitive real character, proves…
15 Oct 2026 Hopf’s Euler characteristic conjecture proved under T³ symmetry; the first proof came from ChatGPT-6-Astra ‘with minimal human input’arXiv 2610.22173 (15 Oct 2026) by Jan Nienhaus and Dennis Wulle proves that every closed even-dimensional manifold with positive sectional curvature and an isometric 3-torus action has positive Euler characteristic, and…
15 Oct 2026 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 SolarXiv 2610.21263 (15 Oct 2026) by Andrew Salmon determines the exact asymptotic rate of Delsarte’s linear programming bound for binary codes and for spherical codes, for all distances, as closed formulas in complete…
14 Oct 2026 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 programOn 14 Oct 2026 Hubert Bray, Tuan Dolmen, Marcus Khuri and David Schmidt posted arXiv 2610.20559. It proves the spacetime Penrose inequality in all dimensions n ≥ 3 for initial data sets of a ‘maximally parameterized’…
14 Oct 2026 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 helpOn 14 Oct 2026 Guangshi Lü, Zhiwei Wang and Jie Wu posted arXiv 2610.20242 (52 pages). It claims a proof that Σ_{p≤x} µ(p+2) = o(π(x)): the Möbius function cancels on the shifted primes p + 2. The statement is a…
14 Oct 2026 Li, Li & Liu: external-memory integer sorting beats the comparison bound, answering Aggarwal–Vitter (1988) by way of network coding, with ChatGPT/Codex and LeanOn 14 Oct 2026 Baochun Li (Toronto), Zongpeng Li and Sirui Liu (Tsinghua) posted arXiv 2610.20079. It gives a new counterexample to the 2004 Li–Li conjecture and uses it to sort N integers of Θ(log N) bits in external…
13 Oct 2026 Ulam’s question answered: every Lie group is a group of permutations of a countable set (Monod & Thom; key construction from GPT-6 Astra)arXiv 2610.18464 (13 Oct 2026), “Lie groups are countably representable” by Nicolas Monod and Andreas Thom, proves that every Lie group can be realised by permutations of a countable set, answering a question Ulam asked…
13 Oct 2026 Thompson’s group F is nonamenable: specialists Sang-hyun Kim and Yash Lodha publish a human-written version of OpenAI’s proofOpenAI’s 6 Oct 2026 math release (family 248, manuscript dated 23 Sep, Lean scope note) claims that Thompson’s group F is nonamenable, settling a problem first raised by Richard Thompson in 1973 and central to…
13 Oct 2026 Eight extremal combinatorialists write up GPT-6 Astra’s proof of the Erdős–Simonovits rational exponents conjecture (Conlon, Janzer, Liu et al.)arXiv 2610.18713 (13 Oct 2026), “A proof of the rational exponents conjecture”, by David Conlon, Oliver Janzer, Tao Jiang, Jaehoon Kim, Joonkyung Lee, H. Liu, Sean Longbrake and Liana Yepremyan, presents and explains…
12 Oct 2026 Erdős Matching Conjecture (1965) proved for every fixed k and all large s, via a sharp tail bound whose k ≥ 6 cases generative AI completedarXiv 2610.16203 (12 Oct 2026) by Cheng Chi, Shuang Sun and Yan Wang (Shanghai Jiao Tong University) proves the conjecture of Łuczak, Mieczkowska and Šileikis on the maximal tail probability of sums of k i.i.d.…
12 Oct 2026 Cureton and Thorner, with AxiomProver, extend the quasi-Riemann zero-free half-plane to every Dedekind zeta function (Re s > 31/32, Lean-formalized)A preprint posted on Hexagon on Oct 12, 2026 by Dean Cureton and Jesse Thorner proves that the Dedekind zeta function of any number field has no zeros with Re s > 31/32, and the same for finite-order Hecke L-functions.…
12 Oct 2026 Bloch constant conjecture (Ahlfors–Grunsky, 1937) disproved: Teng Zhang shows B < 0.47186… − 1.3×10⁻⁹, with a Lean proof generated by CodexarXiv 2610.16808 (12 Oct 2026) by Teng Zhang (Xi’an Jiaotong University) proves that the classical Bloch constant B is strictly smaller than the Ahlfors–Grunsky value A_AG = 0.4718616534…, disproving the conjecture of…
11 Oct 2026 William Banks writes out OpenAI’s Landau–Siegel proof with explicit constants: (1 − β) log q ≥ 0.003 for every real character, and says he verified it in fullarXiv 2610.15483 (11 Oct 2026) by number theorist William D. Banks gives “a detailed account” of the argument in OpenAI’s 1 Oct manuscript claiming that Landau–Siegel zeros do not exist, as a direct proof with explicit…
10 Oct 2026 Vaught’s conjecture fails for infinitary logic: Ackerman, Freer and Knight post a Lean-verified counterexample, built over 8 months with Claude Code and CodexarXiv 2610.15217 (submitted 10 Oct 2026) by Nathanael Ackerman (Harvard), Cameron Freer (MIT) and Robin Knight (Oxford) constructs a sentence of L_ω1,ω with exactly ℵ1 countable models up to isomorphism but no perfect…
9 Oct 2026 Terence Tao’s Caltech lecture ‘Math 2.0’: AI has ended ‘proof scarcity’, and blind problem-solving is now ‘actively harmful’ to mathematicsOn the evening of 9 Oct 2026 Terence Tao gave the public lecture “Math 2.0” at Caltech (AIM Public Lecture Series, Beckman Auditorium) and posted the slides on his blog on 10 Oct. It was his first full talk after…
9 Oct 2026 Smale’s sixth problem claimed for five bodies in the plane: finitely many central configurations for all positive masses, AI-found and proved in Lean (Tomar)On 9 Oct 2026 Tejasvi Singh Tomar (independent researcher) posted arXiv 2610.13100: for every choice of five positive masses the planar five-body problem has finitely many central configurations up to similarity. This…
9 Oct 2026 “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)On 9 Oct 2026 Amélie Loher, Connor Mooney, Clément Mouhot, Lukas Niebel, Luis Silvestre and Yuzhe Zhu posted arXiv 2610.13921, “an exposition of a proof, discovered by Astra, of an Aleksandrov estimate for kinetic…
9 Oct 2026 Thurston’s geometrization conjecture formalised in Lean: the Hamilton–Perelman proof machine-checked with GPT-6, Claude and DeepSeek agents (Chow’s group)On 9 Oct 2026 Yuan Liao, Ziyang Qin, Jui-Hui Chung, Ayush Khaitan, Zhengyang Zhang, Hongzhou Lin, Zijian Zhang, Ligeng Zhu, Peng Lu and Bennett Chow posted arXiv 2610.13897, a Lean 4 formalization of the…
8 Oct 2026 Engel & Mauri post a 7-page proof of the hyperkähler SYZ conjecture, two days after OpenAI’s catalogue claimed it; AI used only to proofreadOn 8 Oct 2026 Philip Engel (UIC) and Mirko Mauri (Université Paris Cité) posted arXiv 2610.12277, “Hyperkähler SYZ conjecture”: for a compact irreducible hyperkähler manifold X, every nef line bundle L is semiample, so…
8 Oct 2026 GPT-6 Astra finds a 3SAT reduction showing monotone Dualization (minimal hypergraph transversals) has no polynomial algorithm under ETHOn 8 Oct 2026 Yasuaki Kobayashi, Kazuhiro Kurita and Kunihiro Wasa posted arXiv 2610.11473: a deterministic reduction from 3SAT with n variables to the complement of Dual, producing hypergraphs of size 2^O(n^(2/3) (log…
8 Oct 2026 Google DeepMind’s AlphaProof Nexus paper published in Science: LLM + Lean agent resolved 9 of 353 open Erdős problems and 44 of 492 OEIS conjecturesOn 8 Oct 2026 Science published Google DeepMind’s AlphaProof Nexus paper (“Advancing mathematics research with AI-driven formal proof search”, doi 10.1126/science.aej2213), first posted on arXiv on 21 May 2026. Agents…
7 Oct 2026 Toms–Winter conjecture on C*-algebras completed by two preprints in one week; both credit AI with a key lemma (Thiel; Evington, Hua, Schafhauser, Seth, Tikuisis, White)On 7 Oct 2026 Samuel Evington, Shanshan Hua, Christopher Schafhauser, Apurva Seth, Aaron Tikuisis and Stuart White posted arXiv 2610.09390, “Regular simple nuclear C*-algebras” (70 pages): every simple, separable, pure…
7 Oct 2026 Braverman & He refute the 2004 undirected multiple-unicast (network coding) conjecture with a GPT-6-found counterexample on PG(2, 9)On 7 Oct 2026 Mark Braverman and Zhongtian He (Princeton) posted arXiv 2610.10108, “The Multiple Unicast Conjecture is False”. The conjecture (Li & Li and Harvey–Kleinberg–Lehman, 2004) says network coding gives no…
7 Oct 2026 Two claimed proofs of the LeBrun–Salamon conjecture: Hu, Liu & Wan (arXiv, ChatGPT as ‘auxiliary tool’) and OpenAI’s catalogue (family 062)On 7 Oct 2026 Zhengyu Hu, Kefeng Liu and Xueyuan Wan (Mathematical Sciences Research Center, Chongqing University of Technology) posted arXiv 2610.10410, claiming a proof of the LeBrun–Salamon conjecture: every compact…
7 Oct 2026 Exact overlaps conjecture for self-similar measures on the line proved: GPT-6 Astra found the first proof (Kittle & Kogler), 47,000-line Lean formalization; OpenAI’s catalogue claims it independentlyOn 7 Oct 2026 Samuel Kittle (UCL) and Constantin Kogler (IAS) posted arXiv 2610.10511, a proof of the exact overlaps conjecture for self-similar measures on the real line and of its generalized form, dim ν = min{1…
7 Oct 2026 Outside researchers using AI crowdsource a tighter exponent in OpenAI’s integer-multiplication result #109, from 2^-182 to about 2^-8.4 (conditional)Within two days of OpenAI’s 722-manuscript math release, outsiders using AI coding agents raised the exponent saving κ in OpenAI’s family #109, “Integer multiplication below n log n” (T(n) = O(n (log n)^(1−κ))…
6 Oct 2026 OpenAI’s maths release also claims the 3D Fourier restriction, Bochner–Riesz and local smoothing conjectures (families 077–080): the core of Stein’s harmonic-analysis programme in three dimensions, manuscript onlyOpenAI’s 6 Oct 2026 release of AI-written mathematics (github.com/openai/math) contains four harmonic-analysis families that claim central open problems in three dimensions. Family 077 claims Stein’s Fourier restriction…
6 Oct 2026 OpenAI’s math release claims the optimal approximation for metric k-median: a polynomial-time (1 + 2/e + ε) algorithm matching the known hardness, with a Lean formalizationAmong the 719 manuscripts OpenAI published on Oct 6, 2026 (github.com/openai/math), family 125, “The metric k-median approximation threshold and recovery” (two manuscripts dated Sept 24, 2026), claims a deterministic…
6 Oct 2026 OpenAI model claims the irrationality exponent of π is exactly 2 (Lean-formalized), which implies the Flint–Hills series convergesFamily 017 of OpenAI’s 6 Oct 2026 math release is “The irrationality exponent of π is 2” (manuscript dated 24 Sept 2026, 23 pages, author “OpenAI”). It claims that for every ν > 2 and all large enough q, |π − p/q| ≥…
6 Oct 2026 Woodin’s question answered: GCH below a strongly compact cardinal implies GCH everywhere (Zhixing You, 4-page proof with GPT-6 Astra)On Oct 6, 2026 Zhixing You (Hebrew University of Jerusalem) posted arXiv 2610.07537, a four-page paper answering a long-standing question of Hugh Woodin: if κ is a strongly compact cardinal and the generalized continuum…
6 Oct 2026 Chen, Tserunyan & Tucker-Drob solve the Jackson–Kechris–Louveau ‘finite index over treeable’ problem (2002); ChatGPT 6 Astra Ultra supplied a ‘crucial observation’On 6 Oct 2026 Ruiyuan Chen (Warsaw), Anush Tserunyan (McGill) and Robin Tucker-Drob (Florida) posted arXiv 2610.08986, dedicated to Alexander Kechris’s 80th birthday. They prove that every countable Borel equivalence…
6 Oct 2026 OpenAI model claims a proof of Khot’s Unique Games Conjecture, with Lean formalizationFamily 102 of OpenAI’s 6 Oct 2026 math release, ‘The Unique Games Theorem’, claims a deterministic polynomial-time reduction from 3SAT to Unique Games over a fixed alphabet, with completeness ≥ 1 − ε and soundness ≤ δ.…
6 Oct 2026 OpenAI model claims the quasi-Riemann hypothesis: no zeta or Dirichlet L-function zeros with Re s > 7/8, and no Landau–Siegel zeros (Lean-formalized)Family 003 of OpenAI’s 6 Oct 2026 math release claims a zero-free half-plane Re s > 7/8 for the Riemann zeta function, every Dirichlet L-function and every finite-order Hecke L-function over ℚ(√−3). This is the…
6 Oct 2026 OpenAI releases 722 AI-written math manuscripts (372 result families) claiming hundreds of open problems, incl. quasi-Riemann, Unique Games, Hodge for CM abelian varieties and free group factorsOn 6 Oct 2026 (22:19 UTC) OpenAI published github.com/openai/math: 722 manuscripts in 372 result families (dated 10 Sep–6 Oct, most 23–27 Sep, released together), written by an unreleased internal model that was posed…
6 Oct 2026 OpenAI release claims the rational Hodge conjecture for all CM abelian varieties, which would give the Tate conjecture for abelian varieties over finite fields (no Lean proof)Family 032 of OpenAI’s 6 Oct 2026 math release claims the rational Hodge conjecture for every complex abelian variety with complex multiplication, in every dimension and codimension. Through Milne’s theorems this would…
6 Oct 2026 OpenAI model claims the free group factor problem: L(F₂) ≅ L(F₃), so all free group factors are isomorphic (Lean-formalized)Family 287 of OpenAI’s 6 Oct 2026 math release claims an affirmative answer to the free group factor isomorphism problem, a central open question of von Neumann algebra theory. The 23-page manuscript says L(F₂) and…
6 Oct 2026 Artin–Davenport conjecture proved: every integral cubic form in 10+ variables has a nontrivial zero (Bonolis, Browning, Glas, Wang; key lemma via ChatGPT 6.0, Codex Lean auto-formalisation)On Oct 6, 2026 Dante Bonolis, Tim Browning, Jakob Glas and Victor Y. Wang posted arXiv 2610.08226, a 64-page proof that every integral cubic form in ten or more variables has a nontrivial integer zero. The bound of 10…
5 Oct 2026 Google DeepMind’s AlphaProtein Novo designs new-to-nature enzymes from scratch (piperidine synthesis, DEHP degradation), with Frances Arnold’s labOn Oct 5, 2026 Google DeepMind posted two bioRxiv preprints on AlphaProtein Novo, a diffusion system that co-generates enzyme structure and sequence around a target reaction. The authors say it is the first time de novo…
5 Oct 2026 Claude discovers an algorithm that refutes the 3SUM and APSP hypotheses: truly subquadratic 3SUM and truly subcubic APSP (Alman & Vassilevska Williams, Lean-verified)On Oct 5, 2026 Josh Alman (Columbia) and Virginia Vassilevska Williams (MIT) posted arXiv 2610.06783, giving the first polynomial speedups over the textbook algorithms for 3SUM (O(n^1.9992)) and All-Pairs Shortest Paths…
4 Oct 2026 Linear Hadwiger conjecture proved: K_t-minor-free graphs are O(t)-colourable; proof found by GPT-6 Astra (Norin & Steiner), Lean-verified by CodexOn Oct 4, 2026 Sergey Norin (McGill) and Raphael Steiner (ETH Zurich) posted arXiv 2610.05291, proving the linear Hadwiger conjecture: there is a constant C such that every graph with no K_t minor is Ct-colourable. The…
2 Oct 2026 Klartag and Moshe prove the ε-Dvoretzky conjecture (polynomial dependence on ε); the key probabilistic idea came from a ChatGPT discussionOn Oct 2, 2026 Boaz Klartag and Shahar Moshe posted a short proof that the dependence on the accuracy ε in Dvoretzky’s theorem is polynomial in 1/ε, not exponential. Their bound is n ≥ (C/ε)^((ℓ+1)/2)·|log ε| for an…
2 Oct 2026 Kannan–Lovász–Simonovits (KLS) conjecture proved in two AI-assisted preprints: Song–Zhang’s O(1) bound, then Bizeul–Klartag–Lehec (‘most proofs … found by ChatGPT’)The KLS conjecture (1995), which says isoperimetry in convex bodies is governed up to a universal constant by half-spaces, was claimed resolved twice in three days. Zhao Song and Xinzhi Zhang (arXiv 2610.01447, Oct 2…
1 Oct 2026 Lehmer’s 1965 permutation conjecture (a research problem in Knuth’s TAOCP) proved; Claude Opus 5.5 found the short hypercube proofOn Oct 1, 2026 Tom Verhoeff posted a proof of D. H. Lehmer’s 1965 conjecture that the permutations of every multiset admit an imperfect Hamiltonian traversal by adjacent swaps. Knuth’s The Art of Computer Programming…
30 Sep 2026 Anonymous ‘AI-generated research’ account mt0-svg posts Lean-checked solutions to the Tammes problem for 15 points, Robbins’ V > 2 and the Hoffman–Johnson–Junge frog-model conjectureThe GitHub account mt0-svg (created Aug 1, 2026, no name) published, with Zenodo DOIs, six results labelled “AI-generated research: the results, proofs and code were found and written by AI”. (1) Tammes problem for N =…
30 Sep 2026 Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help (July–September catalogue)Between July and September 2026 arXiv saw a steady stream of papers that resolve a named conjecture or open question and disclose that a frontier model (mostly GPT-5.6 Sol/Pro and GPT-6 Astra, also Claude Fable 5/5.1…
29 Sep 2026 List Total Colouring Conjecture (late 1990s) disproved; counterexample found by ChatGPT 6 Astra Ultra ‘with little input’On Sept 29, 2026 Jonathan A. Noel posted a 20-vertex cubic graph whose total chromatic number is 4 but whose list total chromatic number is 5. This disproves the List Total Colouring Conjecture of…
27 Sep 2026 Perelman’s proof of the Poincaré conjecture formalised in Lean, with AI-generated code (Chow, Qin, Liao, Khaitan)On Sept 27, 2026 Ziyang Qin, Yuan Liao, Ayush Khaitan and Ricci-flow expert Bennett Chow posted a Lean 4 formalization of the Hamilton–Perelman proof of the 3D Poincaré conjecture. Via the Moise smoothing theorem it…
27 Sep 2026 Erdős Problem #993 (1987): independent-set sequences of all forests claimed unimodal; a second proof and its Lean 4 formalization are attributed entirely to AI agents (Zhang, Li, Vallier)On 27 Sept 2026 Tong Zhang and Wei Li (Northwestern Polytechnical University, Xi’an) deposited on Zenodo a computer-assisted proof that the independence sequence of every finite forest is unimodal, the 1987 question of…
25 Sep 2026 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 challengeOn Sept 25, 2026 Anthropic published a guest post by physicist-turned-writer Matt von Hippel. In August he had challenged AI companies to compute “N=8 supergravity to seven loops, or N=4 super Yang-Mills to nine loops”.…
23 Sep 2026 Claude agents discover a novel CRISPR-like enzyme system; Anthropic reveals its own biology wet labOn September 23, 2026 Anthropic reported that about 950 Claude agents, running for 21 hours on 210 million tokens over a large DNA-sequence database, found array-associated reverse transcriptases (ARTs). These are a…
22 Sep 2026 Odlyzko–Poonen conjecture (1993) proved unconditionally: ‘The proofs are due to GPT-6 Astra’, which also wrote a 22,000-line Lean formalisationConstantin Kogler posted an unconditional proof of the Odlyzko–Poonen conjecture: a random monic 0/1 polynomial with constant term 1 is irreducible over Q with probability tending to 1 (arXiv 2609.26771, 22 Sep 2026).…
22 Sep 2026 Mathematician posts an unchecked ChatGPT Astra proof of the planar Mumford–Shah conjecture (1989), citing OpenAI’s ‘100 open problems’ claimOn 22 Sep 2026 Francesco Deangelis (University of Münster) posted a claimed proof of the planar Mumford–Shah conjecture (1989), a central open problem in the calculus of variations and image segmentation. He says…
21 Sep 2026 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 & BeiramiThe Courtade–Kumar conjecture (Kumar & Courtade 2013) says that among all Boolean functions f of n uniform bits, a dictator f(x) = x_i maximises the mutual information I(f(X); Y) when Y is X passed through a binary…
21 Sep 2026 Grad’s 1967 conjecture on 3D plasma equilibria falls: two AI-assisted papers give three families of counterexamplesTwo independent arXiv preprints posted a day apart (21 and 22 Sep 2026) construct smooth magnetohydrostatic plasma equilibria with nested toroidal pressure surfaces and non-constant pressure that have none of the…
17 Sep 2026 ζ(5) proved irrational: Aabir Fauzan’s Zenodo preprint, the first such result since Apéry’s ζ(3) in 1978, is formally verified in Lean within a week, one formalization written by ClaudeOn Sept 17, 2026 Aabir Fauzan (Aalto University) posted “ζ(5) is irrational” on Zenodo. It proves that the value ζ(5) is irrational, the first irrationality proof for a specific odd zeta value since Apéry’s ζ(3) (1978).…
16 Sep 2026 Chvátal’s 1972 conjecture proved (Chang–Liu–Liu, ChatGPT-assisted), then a GPT-6 Astra ‘proof from The Book’ and a Codex-built Lean formalizationOn Sept 16, 2026 Fan Chang, Hong Liu and Miao Liu posted a proof of Chvátal’s conjecture (1972): every hereditary family of sets has a largest intersecting subfamily that is a star. It went through a sharp correlation…
15 Sep 2026 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 AstraOn Sept 15, 2026 Purdue’s Jensen Kohlmeyer and Liam Kruer (as “JenW1N”) submitted a Lean 4 proof to the Conjectures.io bounty platform that disproves Erdős Problem #108, the Erdős–Hajnal question from the late 1960s of…
14 Sep 2026 Sylvester’s 1879 conjecture on sums of two cubes is fully proved: Burungale and Tian settle the last case (p ≡ 8 mod 9) after Hongbo Yin’s proof of the 4, 7 cases; both later papers disclose AI useOn Sept 14, 2026 Ashay Burungale (UT Austin) and Ye Tian (AMSS, Chinese Academy of Sciences) posted “A proof of Sylvester’s conjecture” (arXiv 2609.14893). It proves the remaining case p ≡ 8 (mod 9) of Sylvester’s 1879…
14 Sep 2026 The k-server conjecture, the ‘holy grail’ of online algorithms, is proved at Oxford; ChatGPT 6 Astra generalised the authors’ k = 3 proof to all kChristian Coester, Elias Koutsoupias and Marek Zbysiński (Oxford) posted a proof of the k-server conjecture (Manasse–McGeoch–Sleator, 1988): the work function algorithm is k-competitive on every metric space (arXiv…
10 Sep 2026 First Phase III trial of a generative-AI-discovered drug doses first patient (Insilico’s rentosertib)On 2026-09-10 Insilico Medicine dosed the first patients in GENESIS-IPF-3, billed as the world’s first Phase III trial of a drug whose target and molecule were discovered with generative AI: rentosertib, a TNIK…
9 Sep 2026 Pierce–Birkhoff conjecture (1956) disproved by a multi-agent GPT + Claude harness; counterexamples Lean-verifiedOn 9 Sep 2026 Zehua Lai, Lek-Heng Lim and Junyu Ren posted a counterexample to the Pierce–Birkhoff conjecture (Birkhoff and Pierce, 1956). It is a continuous piecewise-quadratic function on R^30 that is not a finite…
8 Sep 2026 OpenAI claims a Millennium Prize problem: 10,000 AI agents prove forced Navier–Stokes blow-up; priority dispute eruptsOn 8 Sep 2026 OpenAI released a 166-page paper and a Lean formalisation proving that the 3D incompressible Navier–Stokes equations with a smooth external force can develop a finite-time singularity from smooth initial…
7 Sep 2026 Pre-release GPT-6 Astra disproves the Köthe conjecture (1930) with a Lean-verified counterexampleDuring an Epoch AI run over the Formal Conjectures collection, pre-release GPT-6 Astra autonomously found an explicit 2×2 matrix counterexample over a nil algebra (Krempa’s matrix form) with a Lean 4 proof, disproving…
6 Sep 2026 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)On 6 Sept 2026 Shengtao Guo, Ethan X. Fang and Junwei Lu posted arXiv 2609.11980, which constructs a smooth metric with strictly positive sectional curvature on S³×S³. Since S³×S³ is even-dimensional with Euler…
6 Sep 2026 Collatz: a positive fraction of integers provably reach 1 in 10.46 ln n steps; AI-agent proof (ProofAtlas + Codex) by Lech Mazur, Lean-formalized and re-formalized by AxiomOn Sept 6, 2026 Lech Mazur posted (X, ~204k views) “Explicit Positive-Density Collatz Convergence in Logarithmic Time”: for explicit c > 0 and X₀, every X ≥ X₀ has at least cX positive integers n < X that reach 1 within…
4 Sep 2026 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)In early September 2026 two preprints settled long-standing problems about Reed–Solomon codes, the most widely used error-correcting codes. Brakensiek, Chen, Putterman, Zhang and Zheng (ECCC TR26-164, 4 Sept; arXiv…
4 Sep 2026 Claude produces the first complete machine-checked proof of Fermat’s Last Theorem in Lean, in 11 daysAnthropic reported that a Claude model (roughly comparable to Claude Fable 5.1), running for 11 days (7–18 Aug 2026) using the Prove2Me multi-agent platform, produced a complete Lean formalisation of Fermat’s Last…
3 Sep 2026 Google DeepMind’s WeatherNext 3 learns from live satellite data: hourly 5 km global forecasts and up to 60% better precipitation skillOn Sept 3, 2026 Google DeepMind and Google Research released WeatherNext 3. It ingests live geostationary satellite mosaics and trains directly on station observations, producing a new global forecast every hour at up…
3 Sep 2026 GPT-6 Astra autonomously disproves Smale’s mean value conjecture (constant 1) in Lean; HKU mathematicians build on it to show Smale’s constant exceeds 1.1018In an Epoch AI LeanOpenProblems evaluation run in September 2026, a pre-release GPT-6 Astra autonomously produced a Lean 4 proof that Smale’s mean value conjecture with constant 1 is false: there is a polynomial p with…
3 Sep 2026 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 runsIn Epoch AI’s FrontierMath Erdős runs (announced 3 Sep 2026), a pre-release GPT-6 Astra autonomously resolved five of 68 hand-picked open Erdős problems with Lean-checked proofs. They include a disproof of Erdős problem…
3 Sep 2026 GPT-6 Astra proves the Erdős–Sós conjecture (1962) with a short counting argument; mathematicians race to simplify and extend itIn Epoch AI’s FrontierMath Erdős runs, a pre-release GPT-6 Astra autonomously proved the Erdős–Sós conjecture (Erdős problem #548): every graph with average degree greater than k−2 contains every tree on k vertices. The…
3 Sep 2026 Claude-written Lean proof claims the dying percolation conjecture θ(p_c)=0 in every dimensionIn early September 2026 a Lean 4 formalization written by Anthropic’s Claude models (directed by Justin Leder, published in anthropics/formal-math) claimed to prove that critical Bernoulli bond percolation on Z^d has no…
30 Aug 2026 GPT-6 Astra lowers the bounded prime gaps record from 246 to 186An OpenAI preprint (30 Aug 2026) claims lim inf (p_{n+1} − p_n) ≤ 186, improving Polymath8b’s bound of 246, which had stood since 2014. It uses ‘triply densely divisible’ conditions feeding a multidimensional Selberg…
28 Aug 2026 Matrix Spencer conjecture proved; authors credit GPT-5.6 Sol Pro with ‘the heavy-lifting’ for the key lemmaEmrullah Akbas and Suvrit Sra posted a proof of the Matrix Spencer conjecture (arXiv 2608.28816, 28 Aug 2026). For symmetric n×n matrices A_1..A_n with operator norm at most 1, one can efficiently find signs x in {±1}^n…
26 Aug 2026 GPT-5.6 improves the Erdős–Rankin / Ford–Green–Konyagin–Maynard–Tao bound for large prime gapsOn 26 Aug 2026 the user “DottedCalculator” posted to erdosproblems.com (problem #4) a proof, generated with GPT-5.6, that there are infinitely many prime gaps larger than C·log n·log log n / log log log log n. This…
23 Aug 2026 Claude-assisted construction claims a complex structure on the 6-sphere, answering Hopf’s 1947 problem (pending verification)On 23 Aug 2026 Anthropic’s Levent Alpöge posted a 100+ page document, produced with an internal Claude model, claiming that the 6-sphere S⁶ admits an integrable complex structure. This would answer Hopf’s 1947 question.…
19 Aug 2026 Peking University preprint claims an AI-found disproof of the Yau–Tian–Donaldson conjecture for constant scalar curvature metricsOn 19 Aug 2026 Jihao Liu (Peking University) posted a 79-page preprint describing a polarized smooth projective fivefold that is K-polystable but has no constant scalar curvature Kähler (cscK) metric. That would…
18 Aug 2026 Claude autonomously designs protein binders that work in the lab against 14 of 15 targetsOn Aug 18, 2026 Anthropic reported that Claude (Mythos Preview and Opus 4.8), running autonomously in Claude Science, designed de novo protein binders against 15 targets and produced confirmed binders for 14 of them in…
13 Aug 2026 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 laterXinbao Lu and Kaiwen Yang posted a proof of Banach’s 1932 isometric conjecture for every odd n (arXiv 2608.13536, 13 Aug 2026). With Gromov’s even-n theorem, this completes the real case: a real Banach space whose…
10 Aug 2026 Claude proves more than two-thirds of Riemann zeta zeros are simple and on the critical line (up from 41.6%)Anthropic reported that an unreleased research version of Claude, running in Claude Code with ~60 subagents, raised the unconditional lower bound on the proportion of Riemann zeta zeros that are simple and on the…
5 Aug 2026 Sendov’s 1958 conjecture on polynomial roots proved with GPT-5.6 Pro; Tao simplifies and formalises itLech Mazur posted a computer-assisted proof, generated with GPT-5.6 Pro, of Sendov’s conjecture for all degrees: if every root of a polynomial lies in the closed unit disk, each root is within distance 1 of a critical…
4 Aug 2026 Alexander Perry disproves the period-index conjecture (Colliot-Thélène, 2001); a flawed ChatGPT example was the starting pointAlexander Perry posted counterexamples to the period-index conjecture for Brauer classes: d-dimensional varieties (d ≥ 3) with a Brauer class of period 2 and index 2^d (arXiv 2608.03684; v1 4 Aug, v2 3 Sep 2026). His AI…
3 Aug 2026 Planar Schiffer and Pompeiu conjectures disproved by two independent groups; one proof has a Lean certificate written by GPT-5.6In August 2026 two groups independently disproved Schiffer’s conjecture (Yau’s Problem 80) and the planar Pompeiu problem (1929). Colbrook and Stepaniants (3 Aug) built one explicit ten-fold symmetric domain with a…
1 Aug 2026 OpenAI’s unreleased ‘Astra’ model claims ten advances in maths and theoretical CS, with Lean proofsOn 1 Aug 2026 OpenAI published ‘Ten advances in mathematics and theoretical computer science’ by an internal model, Astra (released as GPT-6 Astra on 3 Sep). It came with a 249-page manuscript and Lean 4 proofs. The…
27 Jul 2026 Neurosurgery resident uses GPT-5.6 Sol to prove Crouzeix’s conjecture in a 16-hour autonomous runA preprint posted 27 Jul 2026 proves Crouzeix’s conjecture (2004): for every square matrix A and polynomial f, ‖f(A)‖ ≤ 2·max over the numerical range W(A) of |f|. The proof came from one uninterrupted 16-hour…
23 Jul 2026 AI systems score a perfect 42/42 at IMO 2026, officially gradedFor the first time AI achieved full marks at the International Mathematical Olympiad: at IMO 2026 in Shanghai, Huawei’s ‘Celia’ and Xiaohongshu/RedNote’s ‘dots-note-3.0’ each scored 42/42, with solutions graded by IMO…
20 Jul 2026 Claude Fable 5 finds a counterexample to the Jacobian conjecture in dimension 3Anthropic mathematician Levent Alpöge posted an explicit polynomial map F: C³→C³ with constant Jacobian determinant −2 that is not injective, found with Claude Fable 5. This refutes Keller’s 1939 Jacobian conjecture in…
17 Jul 2026 GPT-5.6 Sol Ultra proves the 50-year-old cycle double cover conjectureIn mid-July 2026 OpenAI released a preprint crediting GPT-5.6 Sol Ultra, ‘in less than an hour’, with a proof of the cycle double cover conjecture (Szekeres 1973, Seymour 1979): every bridgeless graph has a collection…
27 May 2026 Erdős–Szemerédi sum-product conjecture shown false over the reals; a GPT-5.5 Pro agent re-disproves it in 7 of 8 runsInspired by the AI disproof of the unit-distance conjecture, Bloom, Sawin, Schildkraut and Zhelezov proved on 27 May 2026 that the Erdős–Szemerédi sum-product conjecture is false over the real numbers. They built sets A…
20 May 2026 OpenAI model disproves Erdős’s 80-year-old unit distance conjectureOn 2026-05-20 OpenAI announced that an internal model found a counterexample to Erdős’s 1946 unit-distance conjecture using algebraic number theory — widely described as the first historically significant proof produced…
3 May 2026 Amateur with GPT-5.4 Pro ‘vibe-maths’ a 60-year-old Erdős conjecture on primitive sets; Tao co-authors the paper23-year-old amateur Liam Price gave GPT-5.4 Pro a single prompt. In about 80 minutes it sketched a proof of Erdős problem #1196, the 1966 Erdős–Sárközy–Szemerédi conjectures on primitive sets and divisibility chains…
1 Mar 2026 Math Inc’s Gauss formalises Viazovska’s sphere-packing proofs in dimensions 8 and 24, fixing errors in the originalsMath Inc’s Gauss agent completed the Lean formalisation of Maryna Viazovska’s Fields-Medal proofs of optimal sphere packing in dimensions 8 (5 days) and 24 (~2 weeks), about 180,000 lines. Along the way it found and…
28 Feb 2026 Donald Knuth’s ‘Claude’s Cycles’: Claude Opus 4.6 solves an open Hamiltonian-cycle problem (‘Shock! Shock!’)Donald Knuth published a note opening ‘Shock! Shock!’ describing how Claude Opus 4.6 found, in about an hour of guided exploration, a general construction decomposing the arcs of a 3D torus digraph on m³ vertices into…
11 Feb 2026 DeepMind’s Aletheia agent and Gemini Deep Think report autonomous Erdős solutions and new physics and CS resultsGoogle DeepMind described Aletheia, a Gemini Deep Think–based maths research agent. It autonomously solved Erdős problems #652, #654 and #1040 and resolved #1051, which led to a peer-reviewed generalisation. A…
6 Jan 2026 Erdős problem #728 solved near-autonomously by GPT-5.2 Pro and Harmonic’s Aristotle, with a Lean proofOn 4–6 Jan 2026 amateur Kevin Barreto relayed an informal argument from GPT-5.2 Pro to Harmonic’s Aristotle, which formalised it in Lean. It was widely accepted as the first Erdős problem solved essentially autonomously…
8 Dec 2025 Genuine AI-assisted solutions to Erdős problems begin: #124 (Aristotle), #1026 (48-hour human–AI collaboration)In Nov–Dec 2025 AI tools produced the first genuinely new (if modest) solutions to Erdős problems. Harmonic’s Aristotle proved a version of #124 in Lean autonomously (29 Nov). Erdős #1026 (posed 1975) was fully solved…
12 Sep 2025 First AI-generated complete genomes: Evo models design viable bacteriophages that kill resistant E. coliBrian Hie’s lab used the Evo 1 and Evo 2 genome language models to generate whole ΦX174-like bacteriophage genomes. Of ~285–300 synthesised designs, 16 were viable. Some rapidly overcame ΦX174-resistant E. coli, and one…
10 Sep 2025 Math Inc’s Gauss agent completes the Strong Prime Number Theorem formalisation in Lean in three weeksMath Inc (Christian Szegedy) announced that its autoformalization agent Gauss completed Terence Tao and Alex Kontorovich’s Strong Prime Number Theorem project in Lean in about 3 weeks, producing ~25,000 lines of Lean…
14 Aug 2025 Generative AI designs new antibiotics that kill drug-resistant gonorrhoea and MRSAMIT’s Collins lab (Cell, Aug 2025) used generative models to design more than 36 million candidate compounds from scratch. Lead NG1 kills multidrug-resistant Neisseria gonorrhoeae and DN1 kills MRSA, clearing skin…
21 Jul 2025 AI systems reach gold-medal level at the International Mathematical OlympiadAt IMO 2025, an advanced Gemini Deep Think model (officially graded) and an experimental OpenAI reasoning model (graded by former medalists) each solved 5 of 6 problems for 35/42 points — gold-medal standard — working…
14 May 2025 AlphaEvolve: Gemini-powered agent discovers new algorithmsGoogle DeepMind’s AlphaEvolve combined Gemini models with evolutionary search and automated evaluation to discover new algorithms, including a way to multiply 4×4 complex matrices with 48 scalar multiplications…
12 Mar 2025 Sakana’s AI Scientist-v2 writes the first fully AI-generated paper to pass peer review (ICLR 2025 workshop)On 12 Mar 2025 Sakana AI reported that a paper generated end-to-end by The AI Scientist-v2 (idea, code, experiments, analysis, writing) scored 6, 7, 6 at an ICLR 2025 workshop, above the acceptance threshold; it was…
25 Feb 2025 AI weather forecasting goes operational: ECMWF’s AIFS (Feb 2025), then NOAA’s AI models (Dec 2025)On 25 Feb 2025 the European Centre for Medium-Range Weather Forecasts made its machine-learned AIFS Single model operational alongside its physics model. It was up to 20% better on tropical-cyclone tracks and used about…
19 Feb 2025 Google’s AI co-scientist independently reproduces an unpublished superbug discovery in 48 hoursGoogle’s Gemini 2.0–based multi-agent ‘AI co-scientist’ (announced 19 Feb 2025) generated hypotheses that were validated in the lab. It proposed AML drug-repurposing candidates, and liver-fibrosis drugs active in human…
25 Jul 2024 AlphaProof and AlphaGeometry 2 reach IMO silver-medal standardGoogle DeepMind’s AlphaProof (RL + Lean formal proofs) and AlphaGeometry 2 solved 4 of 6 problems at the 2024 International Mathematical Olympiad, scoring 28/42 — silver-medal level, one point short of gold.
8 May 2024 AlphaFold 3 predicts structures and interactions of all life’s moleculesAlphaFold 3 extended structure prediction from proteins to complexes with DNA, RNA, ligands and ions, using a diffusion-based architecture, with at least 50% improvement on protein–ligand interactions over prior methods.
14 Dec 2023 FunSearch: an LLM finds new cap-set constructions, the first LLM discovery in open mathsFunSearch (Nature, Dec 2023) paired a code LLM with an automated evaluator in an evolutionary loop. It found a cap set of size 512 in dimension 8 (previous best 496) and better lower bounds on the asymptotic cap-set…
29 Nov 2023 GNoME predicts 2.2 million new crystals, 380,000 stable, but novelty and usefulness are disputedDeepMind’s GNoME (Nature, Nov 2023) used graph neural networks and active learning with DFT to predict 2.2 million new inorganic crystal structures, 380,000 of them computed to be stable. DeepMind called it ‘800 years’…
14 Nov 2023 GraphCast: ML weather model beats the world’s best physics-based 10-day forecast on 90% of targetsGraphCast (Science, Nov 2023), a graph neural network trained on ECMWF reanalysis data, produced 10-day global forecasts in under a minute on one TPU. It beat ECMWF’s HRES, the leading deterministic physics model, on…
11 Jul 2023 RFdiffusion: diffusion models design new proteins that work in the labDavid Baker’s lab (Nature, July 2023) fine-tuned RoseTTAFold as a diffusion model to generate new protein backbones for binders, symmetric assemblies and metal-binding sites. Hundreds of designs were experimentally…
5 Oct 2022 AlphaTensor discovers faster matrix multiplication algorithms, beating Strassen’s 1969 record for 4×4 mod 2DeepMind’s AlphaTensor (Nature, Oct 2022) framed matrix multiplication as a tensor-decomposition game. It found a 4×4 algorithm over GF(2) with 47 multiplications (Strassen-based: 49) and improved 5×5 to 96. Human…
16 Feb 2022 Deep reinforcement learning controls fusion plasma in the TCV tokamakDeepMind and EPFL (Nature, Feb 2022) trained a single deep-RL policy in simulation that commanded all of TCV’s magnetic control coils on the real machine. It produced and held elongated, negative-triangularity and…
30 Nov 2020 AlphaFold 2 solves protein structure prediction at CASP14AlphaFold 2 achieved a median GDT score of 92.4 at CASP14, accuracy competitive with experimental methods, widely seen as solving the 50-year-old protein folding problem for single chains.
20 Feb 2020 Deep learning discovers halicin, a structurally new broad-spectrum antibioticMIT’s Collins and Barzilay labs (Cell, Feb 2020) trained a message-passing neural network on ~2,300 molecules. It identified halicin, a diabetes drug candidate, as a potent antibiotic that killed M. tuberculosis…
2 Dec 2018 AlphaFold (v1) tops the CASP13 protein-structure prediction assessmentDeepMind’s first AlphaFold ranked first in the CASP13 blind assessment of protein structure prediction, an early sign that deep learning could crack the protein folding problem.

2026

25 Oct 2026 AI-assisted results in the 25 Oct 2026 sweep: GPT-5.5 Thinking steers a neutral-atom tweezer array, GBClaw grain-boundary agent, ChatGPT Astra-built bone-marrow model
24 Oct 2026 AI-assisted results in the 24 Oct 2026 sweep: ChatGPT 6 Astra removes a Hodge-conjecture assumption, Bake AI’s Épi agent, Google’s lab-in-the-loop aptamer agents, agentic turbulence closures
23 Oct 2026 AI-assisted results in the 23 Oct 2026 arXiv listing: DeepMind’s Gemini 4 Argon loop on Lehmer’s problem, Demmel’s Claude Code-built MRRR SVD solver, a Claude–GPT agent harness proof with Lean, GPT-6 Astra on k-Hessian and Steklov problemsCatalogue of AI-disclosing papers in the 23 Oct 2026 arXiv announcement (submitted 21–22 Oct), plus leftovers. Own entries: Becker–Yang’s disproof of Simon’s L² conjecture, the Critical 2D KPZ process, and Zhentao Li’s…
22 Oct 2026 ChatGPT 6 Astra outlines the argument that removes the Hodge-conjecture assumption from Nakayama’s local height asymptoticsYuta Nakayama’s preprint (arXiv 2610.30574, 22 Oct 2026) proves his earlier asymptotic formula for the Archimedean local Beilinson–Bloch height in a degenerating family without assuming the Hodge conjecture (and drops…
22 Oct 2026 Science publishes Microsoft’s MAI-DxO ‘Sequential diagnosis with language models’: 83% on complex NEJM cases vs 36% for generalist doctors; Suleyman chases ‘medical superintelligence’On Oct 22, 2026 Science published Microsoft AI’s “Sequential diagnosis with language models”, the peer-reviewed version of the MAI Diagnostic Orchestrator (MAI-DxO), in which several model agents act like a panel of…
22 Oct 2026 AI-assisted results in the 22 Oct 2026 arXiv listing: the gradient conjecture at infinity with GPT-6 Astra, Claude-built zero-knowledge PCPs, nucleon algorithms with GPT Sol 6.1 and Fable 5.1, Kelly’s Condorcet conjecturesCatalogue of AI-disclosing papers in the 22 Oct 2026 arXiv announcement (submitted 20–21 Oct). Own entries: Tevelev’s re-proof of OpenAI’s Nagata proof, Anghel’s survey and generalization of OpenAI’s counterexample to…
22 Oct 2026 Barry Simon’s L² conjecture (Problem 8 of his 2000 list) disproved: Becker and Yang build a counterexample largely found with ChatGPTOn 22 Oct 2026 Simon Becker and Mengxuan Yang posted arXiv 2610.31637, a counterexample to Barry Simon’s multidimensional L² conjecture (Problem 8 in “Schrödinger operators in the twenty-first century”, 2000). For every…
22 Oct 2026 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 6arXiv 2610.31614 (22 Oct 2026) by Berger, Caravenna, Clark, Dunlap, Gu, Liu, Nakajima, Sun, Tsai, Xie and Zygouras constructs the “Critical 2D KPZ Process”, a non-trivial distribution-valued solution of the ill-defined…
21 Oct 2026 Thousands of GPT-Rosalind agents analyse millions of mouse brain cells in 32 minutes and propose a cholesterol-transport lead for Perry syndromeOpenAI, PerturbAI and Scripps Research said on Oct 21, 2026 that thousands of GPT-Rosalind agents, working in parallel, linked gene-expression data from millions of mouse brain cells with the literature in 32 minutes.…
21 Oct 2026 Tristan Buckmaster’s guest essay on Terence Tao’s blog: AI companies ‘strip mine’ mathematicians’ data; calls for opt-in training, zero-retention deals and open-weight infrastructureOn Oct 21, 2026 Terence Tao’s blog published a guest essay by NYU mathematician Tristan Buckmaster arguing that mathematics is at a “Deep Blue–Kasparov moment” and will be “unrecognizable” within a few years. He accuses…
21 Oct 2026 AI-assisted results in the 21 Oct 2026 arXiv listing: a ChatGPT 6.1 Sol counterexample to Frankl–Ota–Tokushige, klt Fano proofs from ChatGPT, Vince’s conjecture with GPT Astra, Pólya for spherical shells, a Claude-built 55-addition 3×3 scheme and a Claude Opus 5.5 lemma in reverse mathematicsCatalogue of AI-disclosing papers in the 21 Oct 2026 arXiv announcement (submitted 19–20 Oct). Own entries: MDS conjecture in even characteristic (Chen–Huang with ChatGPT; Kumar’s Lean proof with Claude), double-cap…
21 Oct 2026 Hochster’s 1973 small Cohen–Macaulay conjecture: an OpenAI manuscript’s counterexample is surveyed, re-proved and extended to every dimension by Cristian AnghelOpenAI’s 6 Oct 2026 math release (family 195, manuscript dated 23 Sep) constructs a three-dimensional complete Noetherian normal local domain over C with no nonzero finitely generated maximal Cohen–Macaulay module…
21 Oct 2026 Barnette’s 1969 Hamiltonicity conjecture: graph theorist Zhentao Li publishes a digested, partly re-proved version of OpenAI’s proofOpenAI’s 6 Oct 2026 math release (family 180, manuscript “Paired states and Hamiltonian cycles in cubic bipartite planar graphs”, 24 Sep) claims Barnette’s conjecture, with a Lean formalization listed in its catalogue.…
21 Oct 2026 Nagata’s 1959 conjecture: algebraic geometer Jenia Tevelev writes out OpenAI’s ‘remarkably simple’ proof and calls the release ‘a stunning achievement’OpenAI’s 6 Oct 2026 math release (family 039, manuscript dated 23 Sep) claims a proof of Nagata’s conjecture: for r ≥ 10 very general points in the plane, every curve of degree d with multiplicities m_i satisfies Σ m_i…
20 Oct 2026 Gale’s 1953 conjecture fails in 3D: a 101-point set found with LLM code evolution and GPT-6 Astra beats the sphere’s Borsuk partition ratioGale (1953) conjectured that among sets of unit diameter in R³, the sphere is the hardest to cut into four parts of small diameter, with ratio √((3+√3)/6) ≈ 0.88807. Vsevolod Voronov (arXiv 2610.28828, 20 Oct 2026)…
20 Oct 2026 Anthropic: an internal Claude model mostly autonomously designed protein binders against scorpion neurotoxins; 17 of 211 hit in two labsOn Oct 20, 2026 Anthropic’s Science Blog reported that an internal Claude research model, working mostly autonomously for 64 hours, designed protein binders against five scorpion neurotoxins. It produced 318,484 designs…
20 Oct 2026 Borodin–Kostochka conjecture claimed for maximum degree ≥ 4583 (down from 5.3 million), with GPT-6 Astra assistingA preprint posted on Zenodo on Oct 20, 2026 by Lizhong Chen (HKUST) claims the Borodin–Kostochka conjecture (1977) for every graph of maximum degree Δ ≥ 4583: χ ≤ max{ω, Δ − 1}. The best published threshold was 5.3 ×…
20 Oct 2026 AI-assisted results in the 20 Oct 2026 arXiv listing: poset dimension proofs found by GPT-6 Astra, Hitchin domination from ChatGPT 5.6 Sol’s ideas, the section conjecture for generic curves, Yau’s geometric conjecture, Erdős–Gyárfás r = 5, a Claude-built Gray-code reduction, and a Lean harness solving 6/6 IMO 2026Catalogue of AI-disclosing papers in the 20 Oct 2026 arXiv announcement (mostly submitted 16–19 Oct) and late-found ones from 13–17 Oct. Own entries: the Erdős–Szemerédi sunflower conjecture (Theorem 2 found by ChatGPT…
20 Oct 2026 MDS conjecture settled in even characteristic: two independent proofs, one checked in Lean with Claude’s help, the other written with ChatGPTTwo independent claims settle the linear MDS conjecture (from Segre’s 1955 question on arcs) for every finite field of even order: an [n, k] MDS code over F_q, q even, has n ≤ q + 1, except n ≤ q + 2 for k = 3 and k = q…
20 Oct 2026 Double-cap conjecture (Witsenhausen 1974, Kalai) claimed in all dimensions, with a separate AI-built Lean proofIbiapina, Gomes, Pio, Belo and Ferreira (Brazil) claim that caps minimize the orthogonal neighbourhood in RP^(n−1), which yields the double-cap conjecture: for n ≥ 3, a measurable subset of the sphere S^(n−1) with no…
19 Oct 2026 Neumann–Zagier 1985 conjecture on tree lattices settled after an AI proof with ChatGPT 5.5 Pro and Opus 4.8Joshua Evan Greene, Ahmad Issa and Duncan McCoy prove that a positive definite tree lattice has an irreducible vertex element, which settles a 1985 conjecture of Neumann and Zagier. Greene and McCoy had submitted their…
19 Oct 2026 Gregory Chudnovsky, with ChatGPT, claims the lemniscate period has irrationality exponent 2, with a Lean 4 proof built on OpenAI’s π-exponent libraryarXiv 2610.26539 (19 Oct 2026), “The irrationality exponent of the lemniscate period: A determinant proof with a Lean 4 formalization” by Gregory V. Chudnovsky, proves that for every ν > 2 and all large q, |Ω − p/q| >…
19 Oct 2026 FAHR-Face: Mass General Brigham foundation model estimates biological age and cancer survival from a face photo (Lancet Digital Health)A study published on Oct 19, 2026 in Lancet Digital Health presents FAHR-Face, a foundation model trained on about 40 million face images and adapted to estimate biological age and survival of cancer patients from a…
19 Oct 2026 Commutative counterexamples to Arveson’s hyperrigidity conjecture: proof developed with GPT-6 Astra, finite-dimensional example proposed by it (Bilich, Scherer)arXiv 2610.26556 (19 Oct 2026) by Boris Bilich (Haifa) and Marcel Scherer (Technion) constructs operator systems in commutative C*-algebras for which every irreducible representation of the C*-envelope is a boundary…
19 Oct 2026 AI-assisted maths on Zenodo, 17–19 Oct 2026: a claimed proof of the 1985 Arad–Herzog conjecture, Messerschmidt’s conjecture confirmed with Codex, and a Claude-run study on AI-written scienceWith no new arXiv announcement over the weekend, a new Zenodo step in the news sweep listed about 50 Zenodo records from 17–19 Oct 2026 that matched conjecture/AI keywords. Most were junk: grand unified theories, crank…
19 Oct 2026 AI-assisted results in the 19 Oct 2026 arXiv listing: experts rework OpenAI’s release papers (Deligne–Drinfeld, Hénon–Lane–Emden, Navier–Stokes), Wright’s harmonic-analysis problems disproved with Codex, an Aaronson–Ambainis lower bound, and DeepMind’s Busy Beaver agentCatalogue of the 19 Oct 2026 arXiv announcement (papers submitted 15–16 Oct). Four results have their own entries: Brennan’s conjecture (Smirnov’s group checks OpenAI’s proof and shortens it), Smith–Toda V(4) for p ≥ 11…
19 Oct 2026 Kaplansky’s quasitrace conjecture reported disproved by an unreleased OpenAI model; experts reproduce it and refute the monotone completeness conjectureJananan Arulseelan and James E. Hanson write that “an unreleased OpenAI model produced a claimed counterexample” to the quasitrace (Kaplansky) conjecture for AW*-algebras in an unpublished manuscript (Sept 2026). They…
19 Oct 2026 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)arXiv 2610.25955 (19 Oct 2026), “Integer Programing: An Algorithm with Exponent Linear in the Dimension” by Lin Chen, Yuchen Mao and Guochuan Zhang (Zhejiang University), gives a deterministic algorithm for min{cᵀx : Ax…
19 Oct 2026 Erdős–Szemerédi sunflower conjecture proved for every k ≥ 3; the key vector bound (Theorem 2) was found by ChatGPT 6 Astra Pro (Bucić, He, Lee)On 19 Oct 2026 Matija Bucić, Fankang He (University of Vienna) and Hyunwoo Lee (KAIST/IBS) posted arXiv 2610.26686, “Proof of the Erdős-Szemerédi sunflower conjecture”. Theorem 1: for every k ≥ 3 and n ≥ 1, a family of…
18 Oct 2026 Guest post on Terence Tao’s blog by Francesco Maggi: will AI bring ‘a golden age or a dark age’ for mathematics? Calls for publicly governed research LLMsOn 18 Oct 2026 Terence Tao published on his blog a guest essay by mathematician Francesco Maggi (author page at UT Austin’s math department), “Will it be a golden age or a dark age for mathematics (and science)?”. In…
18 Oct 2026 Bake AI’s Épi agent reports 120 record results with GPT-6 Astra, including a narrower n-queens constant and Cohn–Elkies non-sharpness in dimensions 10 and 11Bake AI’s technical report (arXiv 2610.24944, 18 Oct 2026; authors also from Notre Dame, Scale AI, NVIDIA, Ohio State and others) describes Épi, a persistent research agent run “over a few days using OpenAI frontier…
17 Oct 2026 China Meteorological Administration puts the Fengqing AI global ensemble forecast system (V1.0) into operation
17 Oct 2026 AI-assisted results, 16–17 Oct 2026 (Zenodo and arXiv leftovers): Ramanujan’s prime-counting inequality settled unconditionally with Claude, a Claude Code paper mill on the Hodge conjecture, and LLM agents in materials scienceCatalogue for 16–17 Oct 2026, following the 16 Oct arXiv catalogue. The best item: Jaideep Sai Padhi (Purdue) proves unconditionally that Ramanujan’s inequality π(x)² < (ex/log x)·π(x/e) holds for every x ≥…
17 Oct 2026 arXiv results with disclosed AI help, 16 Oct 2026 announcement (second pass): Suffridge’s conjecture, two Wahl conjectures, the 6-D Tarski problem and moreContinuation of the 2026-10-16 catalogue. arXiv’s announcement of Fri 16 Oct 2026 (papers with v1 dated 12–15 Oct; the earlier catalogue calls it the “15 Oct listing”) was re-read on 17 Oct from…
17 Oct 2026 A non-sofic word-hyperbolic group: Sandhu and Thom build one from OpenAI’s non-residually-finite hyperbolic group, starting from an AI-generated construction; Douglas–Mghirbi give an independent AI-assisted proof with LeanarXiv 2610.24836 (17 Oct 2026), “An example of a non-sofic hyperbolic group” by Harjas Sandhu and Andreas Thom, constructs “a torsion-free, two-dimensional, word-hyperbolic group which is not sofic”, building on…
17 Oct 2026 Erdős–Hajnal conjecture proved for every path P_t: Tung H. Nguyen, with ChatGPT-6 Astra proving key lemmas; a DeepMind internal model reached the same result independently, and Claude Opus 5.5 manuscripts claim P6 and all pathsarXiv 2610.24887 (17 Oct 2026), “Erdős–Hajnal for excluding paths” by Tung H. Nguyen (Oxford), proves that every path P_t has the Erdős–Hajnal property: P_t-free graphs on n vertices have a clique or stable set of size…
16 Oct 2026 Equiregular counterexample to the sub-Riemannian Sard conjecture: Claude Opus 5/5.5 wrote the construction and first proofs, Lean-formalized with Codex (Wang, Zelenko)arXiv 2610.24080 (16 Oct 2026) by Bangjie Wang and Igor Zelenko constructs an equiregular rank-two distribution on an open set diffeomorphic to R⁹, with growth vector (2, 3, 5, 8, 9), whose endpoint map from the origin…
16 Oct 2026 Lee–Loh–Sudakov conjecture on cuts in both directions proved; proof first found by a multi-model AI framework (ChatGPT 6 Astra, 6.1 Sol, Claude Opus 5.5) and verified in LeanarXiv 2610.21381 (v1 dated 15 Oct, announced 16 Oct 2026) by Frederic Folz (Altifina Discovery Lab) and Mykhaylo Tyomkyn (Charles University) proves that for every d ≥ 2 and all large m, every digraph with m edges and…
16 Oct 2026 Buzzard, Avigad, Morrison and other Lean leaders answer AI ‘formalize everything’ pushes: most of mathematics could be formalized within three years, but only with curated, reviewed librariesOn Oct 16, 2026 Jeremy Avigad, Kevin Buzzard, Johan Commelin, Rémy Degenne, Kim Morrison, Oliver Nash and Adam Topaz published “How to Formalize All of Mathematics” on the Xena blog, responding to calls from “AI…
16 Oct 2026 Sankar Das Sarma’s exciton-superfluidity theory paper: derivations, code, figures and text produced by Claude Opus 5.5, with Codex (GPT-6 Astra) acting as refereearXiv 2610.22037 (dated Oct 16, announced 16 Oct 2026), “Exciton superfluidity in two-dimensional bilayers at zero and high magnetic fields” by Sankar Das Sarma and Yang-Zhi Chou (University of Maryland), studies how…
16 Oct 2026 arXiv results with disclosed AI help, 15 Oct 2026 listing: monodromy conjecture, Fried counterexamples, Godefroy–Lancien–Zizler question and moreContinuation of the mid-October catalogue (closed at about 32 KB). It lists preprints from the 15 Oct 2026 arXiv listing (and a few late 14 Oct items) that settle or advance named problems and disclose an AI…
16 Oct 2026 Alpöge and Sussman say Claude has an (unreadable) existence argument for 4D Yang–Mills on ℝ⁴, by finishing Bałaban’s 1980s programNorthwestern mathematician Ethan Sussman and Anthropic’s Levent Alpöge run a public GitHub repo (since 6 Oct 2026) in which Claude, steered by Alpöge, tries to complete Tadeusz Bałaban’s renormalisation-group program…
16 Oct 2026 Smith–Toda complex V(4) exists for all primes p ≥ 11: Angeltveit extends and simplifies OpenAI’s AI-written p = 1009 construction, with ChatGPT’s helpVigleik Angeltveit (ANU) posted arXiv 2610.23215 on 16 Oct 2026. It proves that the Smith–Toda complex V(4), a finite p-local spectrum with BP-homology BP∗/(p, v1, v2, v3, v4), exists for every prime p ≥ 11. This…
16 Oct 2026 OpenAI’s AI-generated proof of a 2D entanglement area law fully formalized in Lean by Axiom (AxiomProver tooling + Codex), with no sorryOn Oct 16, 2026 Axiom Math published AxiomMath/AreaLaw2D, a Lean 4 formalization of “A two-dimensional area law from a global spectral gap” (family 265 of OpenAI’s openai/math release, dated Sept 24, 2026). Theorem 1.1…
16 Oct 2026 Maximum number of Hamiltonian cycles in a tournament determined asymptotically, (cosh 1/cos 1)·(n−1)!/2ⁿ, answering Alon and proving Wormald’s conjecture, with proofs ‘originally found by GPT-5.6’Alexander Divoux and Shouda Wang (Princeton) posted arXiv 2610.23755 on 16 Oct 2026. They prove that C(n), the maximum number of directed Hamiltonian cycles in an n-vertex tournament, is (cosh 1/cos 1 ± o(1))·(n−1)!/2ⁿ.…
16 Oct 2026 Lonely Runner Conjecture: Hu and Jing get the first constant-factor gain over the union bound, (1+c)/2n, after ‘many rounds of discussion’ with ChatGPT 6 Pro and AstraXiyu Hu (UCAS) and Yifan Jing (Ohio State) posted arXiv 2610.23790 on 16 Oct 2026. They prove that for every set V of n ≥ 2 distinct positive speeds there is a time when all runners are more than (1+c)/(2n) from the…
16 Oct 2026 New Gauss circle problem bound E(X) = O(X^(209/670+ε)) breaks Huxley’s 5/16 threshold; authors used ChatGPT and Codex on proof strategies and checkingarXiv 2610.21730 (v1 dated 15 Oct, announced 16 Oct 2026), “A New Bound for the Gauss Circle Problem” by Xi Cen, Xitao Gao, Cheng Zhang and Junyong Zhang, proves E(X) = O_ε(X^(209/670+ε)) for the lattice-point error in…
16 Oct 2026 Brennan’s 1978 conjecture: Smirnov, Binder, Ivrii and Prause check OpenAI’s AI-generated proof and publish a much shorter proof of a stronger resultOn 16 Oct 2026 Ilia Binder, Oleg Ivrii, István Prause and Stanislav Smirnov (Fields Medal 2010) posted arXiv 2610.23853, “Brennan’s Conjecture and the Universal Integral Means Spectrum”. It responds to two preprints…
15 Oct 2026 Google DeepMind shows Antigravity as a science workbench: an agent finds and characterizes a candidate bacteriocin against Streptococcus pseudopneumoniae (wet-lab tests pending)
15 Oct 2026 Harvard–Anthropic team (with Mikhail Lukin) uses Claude Mythos 5 in an evolutionary search to beat state-of-the-art quantum circuits on seven of eight tasksarXiv 2610.22367 (15 Oct 2026) by Andi Gu, Alek Kemeny (Anthropic), Susanne Yelin and Mikhail Lukin pairs Claude Mythos 5, run inside the open-source OpenEvolve framework, with an independent evaluator that verifies and…
15 Oct 2026 Ghys’s 1995 conjecture proved in the codimension-one case (incl. complex dimension 3) with Shanghai AI Lab’s Intern-S2; Peking University formalizes it in Lean (~550k lines)arXiv 2609.37695 (v1 29 Sept, v3 13 Oct 2026), “Codimension-one holomorphic Anosov diffeomorphisms” by Jiesong Zhang, proves that every codimension-one holomorphic Anosov diffeomorphism of a compact connected complex…
15 Oct 2026 CERN and Mistral AI sign a statement of intent to build a ‘Large Physics Model’, a foundation model for collider physicsOn Oct 15, 2026 CERN and Mistral AI signed a statement of intent for a long-term partnership on foundation models for science. The first goal is a “Large Physics Model”, described by CERN as “the first foundation model…
15 Oct 2026 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 5.5arXiv 2610.21511 (15 Oct 2026) by Iwao Kimura makes the argument of OpenAI’s October manuscript on Landau–Siegel zeros explicit, (1 − β) log q ≥ 5811 × 10⁻⁷ for every real zero of every primitive real character, proves…
15 Oct 2026 Hopf’s Euler characteristic conjecture proved under T³ symmetry; the first proof came from ChatGPT-6-Astra ‘with minimal human input’arXiv 2610.22173 (15 Oct 2026) by Jan Nienhaus and Dennis Wulle proves that every closed even-dimensional manifold with positive sectional curvature and an isometric 3-torus action has positive Euler characteristic, and…
15 Oct 2026 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 SolarXiv 2610.21263 (15 Oct 2026) by Andrew Salmon determines the exact asymptotic rate of Delsarte’s linear programming bound for binary codes and for spherical codes, for all distances, as closed formulas in complete…
14 Oct 2026 Microsoft Research’s Probabilistic Bias Correction (Nature) improves 2-to-6-week weather forecasts and won ECMWF’s AI Weather Quest
14 Oct 2026 Two Nature papers from the Baker lab: proteases designed from scratch with RFdiffusion cut chosen protein sequencesOn Oct 14, 2026 Nature published two papers from David Baker’s lab describing enzymes that break peptide bonds, designed de novo with RFdiffusion-family tools: cysteine proteases (13 of 69 designs active, 19%, rate…
14 Oct 2026 Mid-October 2026: arXiv results with disclosed AI help (catalogue of the 13–15 Oct listings, plus late items from 8–12 Oct)Continuation of the October catalogue (which reached about 65 KB and is closed at the 13 Oct block). It lists preprints from the 13–14 Oct arXiv listings, plus late items from 10–12 Oct missed earlier, that settle or…
14 Oct 2026 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 programOn 14 Oct 2026 Hubert Bray, Tuan Dolmen, Marcus Khuri and David Schmidt posted arXiv 2610.20559. It proves the spacetime Penrose inequality in all dimensions n ≥ 3 for initial data sets of a ‘maximally parameterized’…
14 Oct 2026 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 helpOn 14 Oct 2026 Guangshi Lü, Zhiwei Wang and Jie Wu posted arXiv 2610.20242 (52 pages). It claims a proof that Σ_{p≤x} µ(p+2) = o(π(x)): the Möbius function cancels on the shifted primes p + 2. The statement is a…
14 Oct 2026 Li, Li & Liu: external-memory integer sorting beats the comparison bound, answering Aggarwal–Vitter (1988) by way of network coding, with ChatGPT/Codex and LeanOn 14 Oct 2026 Baochun Li (Toronto), Zongpeng Li and Sirui Liu (Tsinghua) posted arXiv 2610.20079. It gives a new counterexample to the 2004 Li–Li conjecture and uses it to sort N integers of Θ(log N) bits in external…
13 Oct 2026 k-median breaks the factor-2 barrier: EPFL-led team gives a 1.95-LMP algorithm; GPT-6 Astra pushes it to 1.844 and proves a 1.8 limit, both with Lean certificatesarXiv 2610.18144 (13 Oct 2026), “A Better-than-2 Approximation for k-Median Part I: The Power of General Bids”, by Buhai, Cohen-Addad, Fleischmann, Gupta, Jubés Monforte, Pittu, Stouras, Svensson and Vogl, replaces the…
13 Oct 2026 October 2026: the arXiv stream of conjectures settled with disclosed AI help continues (catalogue of the 2–13 Oct listings)Catalogue of arXiv preprints from the 2–13 October 2026 listings that settle or advance a named conjecture or open question and disclose a substantive AI contribution, with the AI role quoted from each paper. It…
13 Oct 2026 Ulam’s question answered: every Lie group is a group of permutations of a countable set (Monod & Thom; key construction from GPT-6 Astra)arXiv 2610.18464 (13 Oct 2026), “Lie groups are countably representable” by Nicolas Monod and Andreas Thom, proves that every Lie group can be realised by permutations of a countable set, answering a question Ulam asked…
13 Oct 2026 Thompson’s group F is nonamenable: specialists Sang-hyun Kim and Yash Lodha publish a human-written version of OpenAI’s proofOpenAI’s 6 Oct 2026 math release (family 248, manuscript dated 23 Sep, Lean scope note) claims that Thompson’s group F is nonamenable, settling a problem first raised by Richard Thompson in 1973 and central to…
13 Oct 2026 Eight extremal combinatorialists write up GPT-6 Astra’s proof of the Erdős–Simonovits rational exponents conjecture (Conlon, Janzer, Liu et al.)arXiv 2610.18713 (13 Oct 2026), “A proof of the rational exponents conjecture”, by David Conlon, Oliver Janzer, Tao Jiang, Jaehoon Kim, Joonkyung Lee, H. Liu, Sean Longbrake and Liana Yepremyan, presents and explains…
12 Oct 2026 “The proof presented in this paper is due to Claude Opus 5.5”: Alexis Drouot publishes Claude’s 40-minute elementary proof of his conjecture on geometric bulk conductancesarXiv 2610.16208 (12 Oct 2026) by Alexis Drouot (University of Washington) gives an elementary proof, using only Stokes’ theorem and the Poincaré lemma, that the geometric Kubo formula in any even dimension equals a…
12 Oct 2026 Chow polynomials of matroids are not log-concave: counterexamples found in an LLM search (Claude Opus 5.5, ChatGPT Astra) refute three real-rootedness conjecturesarXiv 2610.17135 (12 Oct 2026) by Gergely Bérczi, Basile Coron, Christopher Eur and Shiyue Li constructs explicit infinite families of matroids from finite geometries whose multichain counts fail to be log-concave. This…
12 Oct 2026 Erdős Matching Conjecture (1965) proved for every fixed k and all large s, via a sharp tail bound whose k ≥ 6 cases generative AI completedarXiv 2610.16203 (12 Oct 2026) by Cheng Chi, Shuang Sun and Yan Wang (Shanghai Jiao Tong University) proves the conjecture of Łuczak, Mieczkowska and Šileikis on the maximal tail probability of sums of k i.i.d.…
12 Oct 2026 Cureton and Thorner, with AxiomProver, extend the quasi-Riemann zero-free half-plane to every Dedekind zeta function (Re s > 31/32, Lean-formalized)A preprint posted on Hexagon on Oct 12, 2026 by Dean Cureton and Jesse Thorner proves that the Dedekind zeta function of any number field has no zeros with Re s > 31/32, and the same for finite-order Hecke L-functions.…
12 Oct 2026 Bloch constant conjecture (Ahlfors–Grunsky, 1937) disproved: Teng Zhang shows B < 0.47186… − 1.3×10⁻⁹, with a Lean proof generated by CodexarXiv 2610.16808 (12 Oct 2026) by Teng Zhang (Xi’an Jiaotong University) proves that the classical Bloch constant B is strictly smaller than the Ahlfors–Grunsky value A_AG = 0.4718616534…, disproving the conjecture of…
11 Oct 2026 Skryabin’s 2006 conjecture proved: every noetherian Hopf algebra has a bijective antipode (proof strategy suggested by GPT-6)arXiv 2610.15473 (11 Oct 2026) by Andrea Sciandra proves that a Hopf algebra over any field has a bijective antipode as soon as its left or right regular module has finite uniform dimension; in particular every…
11 Oct 2026 William Banks writes out OpenAI’s Landau–Siegel proof with explicit constants: (1 − β) log q ≥ 0.003 for every real character, and says he verified it in fullarXiv 2610.15483 (11 Oct 2026) by number theorist William D. Banks gives “a detailed account” of the argument in OpenAI’s 1 Oct manuscript claiming that Landau–Siegel zeros do not exist, as a direct proof with explicit…
10 Oct 2026 Erdős Problem #1117 (Hayman’s Problem 2.16) answered in the negative with ChatGPT and Codex (GPT-6): maximum-modulus points cannot tend to infinityIn an arXiv preprint (v1 Oct 10, 2026; v2 Oct 14) Yunpeng Li (CUHK Shenzhen) answers the second, still-open question of Erdős Problem #1117, recorded as Problem 2.16 in Hayman’s problem book: for a non-monomial entire…
10 Oct 2026 Vaught’s conjecture fails for infinitary logic: Ackerman, Freer and Knight post a Lean-verified counterexample, built over 8 months with Claude Code and CodexarXiv 2610.15217 (submitted 10 Oct 2026) by Nathanael Ackerman (Harvard), Cameron Freer (MIT) and Robin Knight (Oxford) constructs a sentence of L_ω1,ω with exactly ℵ1 countable models up to isomorphism but no perfect…
9 Oct 2026 Machine-learning-guided evolution makes a plant Rubisco 29% faster (MIT, Stanford, ANU; Science Advances)
9 Oct 2026 AI weather models forecast Dubai’s unprecedented 2024 storm by ‘translocation’, not extrapolation (University of Chicago, Science Advances)
9 Oct 2026 Subset Sum in O(n + N^(1+ε)) time claimed: Zhejiang team designed the route, GPT Astra Ultra wrote the complete proofs (Chen, Mao, Zhang)On 9 Oct 2026 Lin Chen, Yuchen Mao and Guochuan Zhang (Zhejiang University) posted arXiv 2610.12953: Subset Sum on integers of absolute value at most N can be decided deterministically in O_ε(n + N^(1+ε)) time for every…
9 Oct 2026 Random permutations of quadratic length contain every pattern: Alon’s 1000n² problem solved, ‘the proof was found by GPT-6 Pro’ (Chen, Wang)On 9 Oct 2026 Yu Chen and Yiting Wang posted arXiv 2610.13530: a uniformly random permutation of length 32n² contains every permutation of length n as a pattern with probability at least 1 − exp(−cn/log n). This removes…
9 Oct 2026 Nirenberg’s 1962 conjecture on closed asymptotic curves disproved; Claude and ChatGPT found the first, polygonal counterexample (Banks, Ghomi, Qiu, Raffaelli)On 9 Oct 2026 Harrison Banks, Mohammad Ghomi, Hongda Qiu and Matteo Raffaelli posted arXiv 2610.13848. It constructs a smooth embedded annulus in R³ with negative curvature, bounded by two convex curves in tangent…
9 Oct 2026 Erdős Problem #32 ($50 part): additive complements to the primes cannot have size O(log N), using a sieve weight from OpenAI’s AI-generated prime-gaps proofIn an arXiv preprint posted on 9 Oct 2026, Artyom Radomskii (HSE University) proves that every set B for which every large integer is a prime plus an element of B has at least c·log X·log log X elements up to X. This…
9 Oct 2026 DeepMind researchers use Gemini Argon to shrink the record Turing machines that encode Goldbach (25→21 states), the Riemann Hypothesis (120→104) and ZF consistency (393→380), with Lean proofsA Google DeepMind GitHub repo (“cryptids”, created Oct 9, 2026) by Maxence Faldor and Moritz Firsching, “using Gemini Argon”, gives smaller 2-symbol Turing machines whose halting is equivalent to a counterexample to…
9 Oct 2026 arXiv, 5–9 October 2026: more conjectures settled with disclosed AI help (Quillen’s local parameter conjecture in dimension 4, Laughlin gap, poset reconstruction), next to human-only resultsA catalogue of smaller arXiv preprints from 5–9 Oct 2026 that claim to settle a named conjecture or open problem, with the AI role as the authors state it. AI-developed proofs: Quillen’s local parameter conjecture in…
9 Oct 2026 Terence Tao’s Caltech lecture ‘Math 2.0’: AI has ended ‘proof scarcity’, and blind problem-solving is now ‘actively harmful’ to mathematicsOn the evening of 9 Oct 2026 Terence Tao gave the public lecture “Math 2.0” at Caltech (AIM Public Lecture Series, Beckman Auditorium) and posted the slides on his blog on 10 Oct. It was his first full talk after…
9 Oct 2026 Smale’s sixth problem claimed for five bodies in the plane: finitely many central configurations for all positive masses, AI-found and proved in Lean (Tomar)On 9 Oct 2026 Tejasvi Singh Tomar (independent researcher) posted arXiv 2610.13100: for every choice of five positive masses the planar five-body problem has finitely many central configurations up to similarity. This…
9 Oct 2026 “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)On 9 Oct 2026 Amélie Loher, Connor Mooney, Clément Mouhot, Lukas Niebel, Luis Silvestre and Yuzhe Zhu posted arXiv 2610.13921, “an exposition of a proof, discovered by Astra, of an Aleksandrov estimate for kinetic…
9 Oct 2026 Thurston’s geometrization conjecture formalised in Lean: the Hamilton–Perelman proof machine-checked with GPT-6, Claude and DeepSeek agents (Chow’s group)On 9 Oct 2026 Yuan Liao, Ziyang Qin, Jui-Hui Chung, Ayush Khaitan, Zhengyang Zhang, Hongzhou Lin, Zijian Zhang, Ligeng Zhu, Peng Lu and Bennett Chow posted arXiv 2610.13897, a Lean 4 formalization of the…
8 Oct 2026 Agents in Claude Science build what Anthropic calls the first complete map of the sky in ultraviolet light, filling GALEX’s gaps from Gaia and Planck data
8 Oct 2026 Developer’s Claude-and-Jev pipeline over 5.7M archival passages turns up an unrecorded 1812 Indian meteorite fall, lost VOC rhinoceros shipments and three uncatalogued eruptions (unreviewed candidates)
8 Oct 2026 Laderman’s 23 multiplications are optimal for 3×3 matrices over F_2 and over the integers: AI-found proof checked in Lean (Tomar)On 8 Oct 2026 Tejasvi Singh Tomar (independent researcher) posted arXiv 2610.11823: the rank of the 3×3 matrix multiplication tensor over the two-element field is exactly 23. Laderman’s 1976 algorithm gives the upper…
8 Oct 2026 PPT-distillable entanglement can fall strictly below the regularised Rains bound: results “derived almost entirely by ChatGPT Astra” (Lami)On 8 Oct 2026 Ludovico Lami (Scuola Normale Superiore, Pisa) posted arXiv 2610.12454. It gives a regularised formula for the entanglement distillable with PPT operations and two new single-letter upper bounds, and uses…
8 Oct 2026 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)On 8 Oct 2026 David G. Clark (Center for Computational Neuroscience, Flatiron Institute) posted arXiv 2610.12426, which computes the full Lyapunov spectrum of the random recurrent neural network of Sompolinsky, Crisanti…
8 Oct 2026 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’OpenAI’s 6 Oct 2026 math catalogue includes family 244, “The Partition Principle does not imply Choice”: if ZF is consistent, so is ZF + PP + choice for ordinal-indexed families + ¬AC (manuscript dated 24 Sep; Lean…
8 Oct 2026 Holomorphic Cancellation Problem (1998) answered in the negative, conditional on a newly announced exotic affine space; proofs developed with generative AI (Gaofeng Huang, Harvard)On 8 Oct 2026 Gaofeng Huang (Harvard) posted arXiv 2610.12581. It proves that a contractible Stein manifold X with the density property that embeds properly in C^k satisfies X × C^k ≅ C^(n+k). Combined with a result…
8 Oct 2026 Hilbert’s 16th problem: Qin & Sun prove H(d) = Ω(d² ln² d), the first log-factor gain since 1995, with GPT-5.6 Sol developing the proof and a Lean 4 certificateOn 8 Oct 2026 Chaoyang Qin and Xiaoming Sun (Institute of Computing Technology, CAS) posted arXiv 2610.12218, proving that the Hilbert number satisfies H(d) = Ω(d² ln² d), a factor ln d above the d² ln d bound that…
8 Oct 2026 Erdős Problem #522 (1961) resolved with a Lean-verified proof: half the zeros of random ±1 polynomials lie in the unit disk, almost surely (Kawada, MIT CSAIL)On 8 Oct 2026 Sebastien Kawada (MIT CSAIL) posted arXiv 2610.11324, which proves that for random Littlewood polynomials (all coefficients ±1, chosen by fair coin flips) the proportion of zeros in the closed unit disk…
8 Oct 2026 Engel & Mauri post a 7-page proof of the hyperkähler SYZ conjecture, two days after OpenAI’s catalogue claimed it; AI used only to proofreadOn 8 Oct 2026 Philip Engel (UIC) and Mirko Mauri (Université Paris Cité) posted arXiv 2610.12277, “Hyperkähler SYZ conjecture”: for a compact irreducible hyperkähler manifold X, every nef line bundle L is semiample, so…
8 Oct 2026 GPT-6 Astra finds a 3SAT reduction showing monotone Dualization (minimal hypergraph transversals) has no polynomial algorithm under ETHOn 8 Oct 2026 Yasuaki Kobayashi, Kazuhiro Kurita and Kunihiro Wasa posted arXiv 2610.11473: a deterministic reduction from 3SAT with n variables to the complement of Dual, producing hypergraphs of size 2^O(n^(2/3) (log…
8 Oct 2026 Google DeepMind’s AlphaProof Nexus paper published in Science: LLM + Lean agent resolved 9 of 353 open Erdős problems and 44 of 492 OEIS conjecturesOn 8 Oct 2026 Science published Google DeepMind’s AlphaProof Nexus paper (“Advancing mathematics research with AI-driven formal proof search”, doi 10.1126/science.aej2213), first posted on arXiv on 21 May 2026. Agents…
7 Oct 2026 AI for Math Fund (Renaissance Philanthropy, XTX Markets) names 22 new grants; total commitment reported at $35.1M
7 Oct 2026 Biohub’s Virtual Biology Initiative grows to $1.8B: DOE, NIH, Google DeepMind, Isomorphic Labs and Meta join the push for open data to build AI ‘virtual cells’On Oct 7, 2026 Biohub (the Chan Zuckerberg science organization), the US Department of Energy and the NIH expanded the Virtual Biology Initiative to $1.8B in money, data, compute and measurement technology. Google…
7 Oct 2026 Claimed proof of the cyclicity conjecture of Perron–Frobenius theory for positive operators (Dobrick, GPT-5.6 used to simplify arguments)On 7 Oct 2026 Alexander Dobrick posted arXiv 2610.10093, “On the Cyclicity Conjecture”. It claims that the peripheral spectrum of every positive operator on a complex Banach lattice is cyclic, with no growth…
7 Oct 2026 Bolzano (Charles University): open-source multi-agent system run unattended on about 3,800 open problems from research papers; about 200 reported solved, four STOC 2026 questions confirmed by the papers’ authorsOn 7 Oct 2026 Adrián Zámečník, Matěj Kripner, Martin Koutecký, Martin Balko, Jan Grebík, Pavel Hubáček, Robert Šámal and Václav Rozhoň (Charles University, Prague) posted arXiv 2610.09769, accepted at the MATH-AI…
7 Oct 2026 Toms–Winter conjecture on C*-algebras completed by two preprints in one week; both credit AI with a key lemma (Thiel; Evington, Hua, Schafhauser, Seth, Tikuisis, White)On 7 Oct 2026 Samuel Evington, Shanshan Hua, Christopher Schafhauser, Apurva Seth, Aaron Tikuisis and Stuart White posted arXiv 2610.09390, “Regular simple nuclear C*-algebras” (70 pages): every simple, separable, pure…
7 Oct 2026 Braverman & He refute the 2004 undirected multiple-unicast (network coding) conjecture with a GPT-6-found counterexample on PG(2, 9)On 7 Oct 2026 Mark Braverman and Zhongtian He (Princeton) posted arXiv 2610.10108, “The Multiple Unicast Conjecture is False”. The conjecture (Li & Li and Harvey–Kleinberg–Lehman, 2004) says network coding gives no…
7 Oct 2026 Two claimed proofs of the LeBrun–Salamon conjecture: Hu, Liu & Wan (arXiv, ChatGPT as ‘auxiliary tool’) and OpenAI’s catalogue (family 062)On 7 Oct 2026 Zhengyu Hu, Kefeng Liu and Xueyuan Wan (Mathematical Sciences Research Center, Chongqing University of Technology) posted arXiv 2610.10410, claiming a proof of the LeBrun–Salamon conjecture: every compact…
7 Oct 2026 Exact overlaps conjecture for self-similar measures on the line proved: GPT-6 Astra found the first proof (Kittle & Kogler), 47,000-line Lean formalization; OpenAI’s catalogue claims it independentlyOn 7 Oct 2026 Samuel Kittle (UCL) and Constantin Kogler (IAS) posted arXiv 2610.10511, a proof of the exact overlaps conjecture for self-similar measures on the real line and of its generalized form, dim ν = min{1…
7 Oct 2026 Outside researchers using AI crowdsource a tighter exponent in OpenAI’s integer-multiplication result #109, from 2^-182 to about 2^-8.4 (conditional)Within two days of OpenAI’s 722-manuscript math release, outsiders using AI coding agents raised the exponent saving κ in OpenAI’s family #109, “Integer multiplication below n log n” (T(n) = O(n (log n)^(1−κ))…
6 Oct 2026 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’Fedor Vorobyev’s arXiv preprint 2610.10599 (Oct 6, 2026) claims that a random 3-SAT formula with 4.268n clauses is unsatisfiable with high probability. The best earlier rigorous upper bound was 4.4898, and the cavity…
6 Oct 2026 Optimal bound for the polynomial Littlewood–Offord problem, ‘discovered autonomously by GPT-6 Pro’ (exposition by Grebennikov)On Oct 6, 2026 Alexandr Grebennikov posted arXiv 2610.08708, an exposition of a proof he says “was discovered autonomously by GPT-6 Pro”. It shows that a degree-d multilinear polynomial with r disjoint top-degree…
6 Oct 2026 Why SAT solvers fail on multiplication: first exponential resolution lower bound for multiplier associativity; ‘main ideas and the core proof … are due to GPT-5.6-Sol’ (Liew)On 6 Oct 2026 Vincent Liew posted arXiv 2610.08988, “Associativity of Multiplication Is Hard for Resolution”. It shows that general resolution proofs of the associativity of n-bit multiplication need size 2^Ω((n/log…
6 Oct 2026 Explicit tensors of border rank 3n − o(n), past the ‘linear flattening barrier’; proofs obtained with GPT-6 Astra (Benjamin Lovitz)On 6 Oct 2026 Benjamin Lovitz (Concordia University) posted arXiv 2610.08504. It constructs explicit n × n × n tensors of border rank at least 3n − o(n), improving the previous record of (2 + ε)n by Landsberg and…
6 Oct 2026 Walter Trump’s 1979 packing of 11 unit squares proved optimal, with a full Lean verification (AI involvement reported, unconfirmed)On Oct 6, 2026 the GitHub project 11SquaresFormalized reported a complete Lean 4 verification (7,920 modules, zero admissions) that Walter Trump’s 1979 packing of eleven unit squares in a square is optimal, with side…
6 Oct 2026 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)On 6 Oct 2026 doubleAI, the Israeli company founded by Mobileye co-founder Amnon Shashua, published “d-Regular Graphs of Girth 8/5 log_{d−1} n”, authored by its AI system “Double Agent”. For every prime power q it…
6 Oct 2026 OpenAI’s maths release also claims the 3D Fourier restriction, Bochner–Riesz and local smoothing conjectures (families 077–080): the core of Stein’s harmonic-analysis programme in three dimensions, manuscript onlyOpenAI’s 6 Oct 2026 release of AI-written mathematics (github.com/openai/math) contains four harmonic-analysis families that claim central open problems in three dimensions. Family 077 claims Stein’s Fourier restriction…
6 Oct 2026 OpenAI’s math release claims the optimal approximation for metric k-median: a polynomial-time (1 + 2/e + ε) algorithm matching the known hardness, with a Lean formalizationAmong the 719 manuscripts OpenAI published on Oct 6, 2026 (github.com/openai/math), family 125, “The metric k-median approximation threshold and recovery” (two manuscripts dated Sept 24, 2026), claims a deterministic…
6 Oct 2026 OpenAI model claims the irrationality exponent of π is exactly 2 (Lean-formalized), which implies the Flint–Hills series convergesFamily 017 of OpenAI’s 6 Oct 2026 math release is “The irrationality exponent of π is 2” (manuscript dated 24 Sept 2026, 23 pages, author “OpenAI”). It claims that for every ν > 2 and all large enough q, |π − p/q| ≥…
6 Oct 2026 Woodin’s question answered: GCH below a strongly compact cardinal implies GCH everywhere (Zhixing You, 4-page proof with GPT-6 Astra)On Oct 6, 2026 Zhixing You (Hebrew University of Jerusalem) posted arXiv 2610.07537, a four-page paper answering a long-standing question of Hugh Woodin: if κ is a strongly compact cardinal and the generalized continuum…
6 Oct 2026 Chen, Tserunyan & Tucker-Drob solve the Jackson–Kechris–Louveau ‘finite index over treeable’ problem (2002); ChatGPT 6 Astra Ultra supplied a ‘crucial observation’On 6 Oct 2026 Ruiyuan Chen (Warsaw), Anush Tserunyan (McGill) and Robin Tucker-Drob (Florida) posted arXiv 2610.08986, dedicated to Alexander Kechris’s 80th birthday. They prove that every countable Borel equivalence…
6 Oct 2026 OpenAI model claims a proof of Khot’s Unique Games Conjecture, with Lean formalizationFamily 102 of OpenAI’s 6 Oct 2026 math release, ‘The Unique Games Theorem’, claims a deterministic polynomial-time reduction from 3SAT to Unique Games over a fixed alphabet, with completeness ≥ 1 − ε and soundness ≤ δ.…
6 Oct 2026 OpenAI model claims the quasi-Riemann hypothesis: no zeta or Dirichlet L-function zeros with Re s > 7/8, and no Landau–Siegel zeros (Lean-formalized)Family 003 of OpenAI’s 6 Oct 2026 math release claims a zero-free half-plane Re s > 7/8 for the Riemann zeta function, every Dirichlet L-function and every finite-order Hecke L-function over ℚ(√−3). This is the…
6 Oct 2026 OpenAI releases 722 AI-written math manuscripts (372 result families) claiming hundreds of open problems, incl. quasi-Riemann, Unique Games, Hodge for CM abelian varieties and free group factorsOn 6 Oct 2026 (22:19 UTC) OpenAI published github.com/openai/math: 722 manuscripts in 372 result families (dated 10 Sep–6 Oct, most 23–27 Sep, released together), written by an unreleased internal model that was posed…
6 Oct 2026 OpenAI release claims the rational Hodge conjecture for all CM abelian varieties, which would give the Tate conjecture for abelian varieties over finite fields (no Lean proof)Family 032 of OpenAI’s 6 Oct 2026 math release claims the rational Hodge conjecture for every complex abelian variety with complex multiplication, in every dimension and codimension. Through Milne’s theorems this would…
6 Oct 2026 OpenAI model claims the free group factor problem: L(F₂) ≅ L(F₃), so all free group factors are isomorphic (Lean-formalized)Family 287 of OpenAI’s 6 Oct 2026 math release claims an affirmative answer to the free group factor isomorphism problem, a central open question of von Neumann algebra theory. The 23-page manuscript says L(F₂) and…
6 Oct 2026 Artin–Davenport conjecture proved: every integral cubic form in 10+ variables has a nontrivial zero (Bonolis, Browning, Glas, Wang; key lemma via ChatGPT 6.0, Codex Lean auto-formalisation)On Oct 6, 2026 Dante Bonolis, Tim Browning, Jakob Glas and Victor Y. Wang posted arXiv 2610.08226, a 64-page proof that every integral cubic form in ten or more variables has a nontrivial integer zero. The bound of 10…
5 Oct 2026 Decreasing diagrams are complete for confluence: van Oostrom’s 1993 question (RTA open problem 56) settled, machine-checked in Isabelle/HOL and Lean with Claude’s help (Endrullis, Ivanov, van Raamsdonk)
5 Oct 2026 A 15-year-old’s computer-assisted preprint, coded with Claude, claims the rhombicosidodecahedron is not Rupert (Steininger–Yurkevich conjecture)On Oct 5, 2026 Gihyo Jung, described by Korean media as a 15-year-old ninth grader, posted “The rhombicosidodecahedron is not Rupert” on Zenodo with code on GitHub: a computer-assisted proof that this Archimedean solid…
5 Oct 2026 Google DeepMind’s AlphaProtein Novo designs new-to-nature enzymes from scratch (piperidine synthesis, DEHP degradation), with Frances Arnold’s labOn Oct 5, 2026 Google DeepMind posted two bioRxiv preprints on AlphaProtein Novo, a diffusion system that co-generates enzyme structure and sequence around a target reaction. The authors say it is the first time de novo…
5 Oct 2026 Claude discovers an algorithm that refutes the 3SUM and APSP hypotheses: truly subquadratic 3SUM and truly subcubic APSP (Alman & Vassilevska Williams, Lean-verified)On Oct 5, 2026 Josh Alman (Columbia) and Virginia Vassilevska Williams (MIT) posted arXiv 2610.06783, giving the first polynomial speedups over the textbook algorithms for 3SUM (O(n^1.9992)) and All-Pairs Shortest Paths…
4 Oct 2026 Linear Hadwiger conjecture proved: K_t-minor-free graphs are O(t)-colourable; proof found by GPT-6 Astra (Norin & Steiner), Lean-verified by CodexOn Oct 4, 2026 Sergey Norin (McGill) and Raphael Steiner (ETH Zurich) posted arXiv 2610.05291, proving the linear Hadwiger conjecture: there is a constant C such that every graph with no K_t minor is Ct-colourable. The…
2 Oct 2026 ChatGPT Astra finds geometric triangle-free graphs with near-optimal chromatic number, the first improvement on Burling’s 1965 box boundOn Oct 2, 2026 István Tomon (Umeå University) posted geometric constructions of triangle-free and high-girth graphs with rapidly growing chromatic number. The headline result is a triangle-free intersection graph of n…
2 Oct 2026 Meta publishes six maths papers made by mathematicians working with Muse Spark in ordinary meta.ai chat, saying five answer open questionsOn Oct 2, 2026 Meta released six research papers written by mathematicians who used Muse Spark 1.1 and 1.2 in Thinking Mode through the regular meta.ai chat, with no custom scaffold. Results include a sharp threshold…
2 Oct 2026 Klartag and Moshe prove the ε-Dvoretzky conjecture (polynomial dependence on ε); the key probabilistic idea came from a ChatGPT discussionOn Oct 2, 2026 Boaz Klartag and Shahar Moshe posted a short proof that the dependence on the accuracy ε in Dvoretzky’s theorem is polynomial in 1/ε, not exponential. Their bound is n ≥ (C/ε)^((ℓ+1)/2)·|log ε| for an…
2 Oct 2026 Kannan–Lovász–Simonovits (KLS) conjecture proved in two AI-assisted preprints: Song–Zhang’s O(1) bound, then Bizeul–Klartag–Lehec (‘most proofs … found by ChatGPT’)The KLS conjecture (1995), which says isoperimetry in convex bodies is governed up to a universal constant by half-spaces, was claimed resolved twice in three days. Zhao Song and Xinzhi Zhang (arXiv 2610.01447, Oct 2…
1 Oct 2026 Harvard physicist Matthew Schwartz releases BootLoops, an open-source harness that let Claude produce 36 manuscripts in 18 fields in three monthsOn Oct 1, 2026 Anthropic published a guest post, “Claude-Shaped Science”, by Harvard theoretical physicist Matthew Schwartz (a visiting researcher at Anthropic). He released BootLoops 1.0, an open-source toolkit that…
1 Oct 2026 Lehmer’s 1965 permutation conjecture (a research problem in Knuth’s TAOCP) proved; Claude Opus 5.5 found the short hypercube proofOn Oct 1, 2026 Tom Verhoeff posted a proof of D. H. Lehmer’s 1965 conjecture that the permutations of every multiset admit an imperfect Hamiltonian traversal by adjacent swaps. Knuth’s The Art of Computer Programming…
30 Sep 2026 Google’s ERA-built model ranks #1 of 39 in the CDC FluSight 2025–26 flu-hospitalization forecasting challenge
30 Sep 2026 GPT-6 Astra proves Barvinok’s log-concavity question for contingency tables on lines, giving lattice-point bounds for all totally unimodular polytopesJonathan Leake and Maryam Mohammadi Yekta’s Sept 30, 2026 preprint gives a new lower bound on the number of lattice points of every totally unimodular polytope, and with it a deterministic approximate-counting…
30 Sep 2026 Anonymous ‘AI-generated research’ account mt0-svg posts Lean-checked solutions to the Tammes problem for 15 points, Robbins’ V > 2 and the Hoffman–Johnson–Junge frog-model conjectureThe GitHub account mt0-svg (created Aug 1, 2026, no name) published, with Zenodo DOIs, six results labelled “AI-generated research: the results, proofs and code were found and written by AI”. (1) Tammes problem for N =…
30 Sep 2026 Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help (July–September catalogue)Between July and September 2026 arXiv saw a steady stream of papers that resolve a named conjecture or open question and disclose that a frontier model (mostly GPT-5.6 Sol/Pro and GPT-6 Astra, also Claude Fable 5/5.1…
29 Sep 2026 Microsoft Research unveils Quine, a multimodal ‘world model of biology’ validated in pancreatic-cancer screens with the Broad Institute
29 Sep 2026 Lovász conjecture (1969): long paths in vertex-transitive graphs pushed to n^(1−o(1)), with GPT-5.6 Sol supplying key stepsOn Sept 29, 2026 Bowen Li and Abhishek Methuku posted a proof that every connected vertex-transitive graph on n vertices contains a cycle of length n^(1−o(1)). The previous bound was n^(2/3−o(1)), set earlier in 2026.…
29 Sep 2026 EPFL’s LinCodeEvolve (Viazovska, Abbe) finds seven record-breaking binary linear codes with LLM-guided program searchOn Sept 29, 2026 EPFL researchers Amal Seddas, Vladyslav Shashkov, Maryna Viazovska (Fields Medal 2022) and Emmanuel Abbe posted LinCodeEvolve, an LLM-driven evolutionary program search (built on ShinkaEvolve and…
29 Sep 2026 List Total Colouring Conjecture (late 1990s) disproved; counterexample found by ChatGPT 6 Astra Ultra ‘with little input’On Sept 29, 2026 Jonathan A. Noel posted a 20-vertex cubic graph whose total chromatic number is 4 but whose list total chromatic number is 5. This disproves the List Total Colouring Conjecture of…
28 Sep 2026 Caltech ‘Mathathon’ is reworked into ‘Old Problems, New Proofs’ after an open letter from mathematicians
28 Sep 2026 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/SolOn 28 Sep 2026 Jizhou Guo posted what he says are the first counterexamples to the Schiffer and Pompeiu conjectures in dimension three and higher. They are also the first convex counterexamples in any dimension: bounded…
28 Sep 2026 Four-body problem: uniqueness of convex central configurations for all masses claimed (Simó–Yoccoz conjecture), AI-found and formalized in Lean (Tomar)On 28 Sept 2026 Tejasvi Singh Tomar (independent researcher) posted arXiv 2609.35632: for every four positive masses and every cyclic ordering there is exactly one strictly convex planar central configuration up to…
27 Sep 2026 Perelman’s proof of the Poincaré conjecture formalised in Lean, with AI-generated code (Chow, Qin, Liao, Khaitan)On Sept 27, 2026 Ziyang Qin, Yuan Liao, Ayush Khaitan and Ricci-flow expert Bennett Chow posted a Lean 4 formalization of the Hamilton–Perelman proof of the 3D Poincaré conjecture. Via the Moise smoothing theorem it…
27 Sep 2026 Erdős Problem #993 (1987): independent-set sequences of all forests claimed unimodal; a second proof and its Lean 4 formalization are attributed entirely to AI agents (Zhang, Li, Vallier)On 27 Sept 2026 Tong Zhang and Wei Li (Northwestern Polytechnical University, Xi’an) deposited on Zenodo a computer-assisted proof that the independence sequence of every finite forest is unimodal, the 1987 question of…
26 Sep 2026 GPT-6 Astra finds a proof improving the Kővári–Sós–Turán bound: diagonal bipartite Ramsey numbers b(t,t) = O(2^t) (Mubayi)On Sept 26, 2026 Dhruv Mubayi posted a proof that every bipartite graph with N vertices per side and at least N²/2 edges contains K_{t,t} once N ≥ c·2^t. That improves the classical Kővári–Sós–Turán requirement of order…
25 Sep 2026 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 paperOn Sept 25, 2026 Jonathan Kleid published a machine-checked Lean 4 proof that the irrationality measure of ζ(2) = π²/6 is at most 5.0495243, improving Zudilin’s 2014 record of 5.095412. Kleid found the parameters…
25 Sep 2026 Lila Sciences’ AI-run lab screens 2,942 catalysts and finds iridium- and ruthenium-free palladium oxides for green hydrogenOn 25 Sept 2026 Lila Sciences reported that its AI-directed autonomous lab proposed, synthesized and screened 2,942 oxide catalysts (53 material systems, 26 elements) for the acidic oxygen evolution reaction used in PEM…
25 Sep 2026 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’Between Sept 15 and Sept 25, 2026, Conjectures.io paid bounties for machine-checked Lean proofs of seven formalised open problems. The platform runs on Bittensor subnet 66, publishes open problems as pinned Lean…
25 Sep 2026 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 challengeOn Sept 25, 2026 Anthropic published a guest post by physicist-turned-writer Matt von Hippel. In August he had challenged AI companies to compute “N=8 supergravity to seven loops, or N=4 super Yang-Mills to nine loops”.…
24 Sep 2026 DeepMind, EMBL-EBI, NVIDIA and CEPI add predicted protein-complex structures for 2,800+ viruses to the AlphaFold DatabaseOn Sept 24, 2026 a consortium of Google DeepMind, EMBL-EBI, NVIDIA, CEPI and universities in Korea, Switzerland and the UK released predicted viral protein-complex structures for more than 2,800 viruses in the AlphaFold…
23 Sep 2026 Claude agents discover a novel CRISPR-like enzyme system; Anthropic reveals its own biology wet labOn September 23, 2026 Anthropic reported that about 950 Claude agents, running for 21 hours on 210 million tokens over a large DNA-sequence database, found array-associated reverse transcriptases (ARTs). These are a…
22 Sep 2026 Odlyzko–Poonen conjecture (1993) proved unconditionally: ‘The proofs are due to GPT-6 Astra’, which also wrote a 22,000-line Lean formalisationConstantin Kogler posted an unconditional proof of the Odlyzko–Poonen conjecture: a random monic 0/1 polynomial with constant term 1 is irreducible over Q with probability tending to 1 (arXiv 2609.26771, 22 Sep 2026).…
22 Sep 2026 Mathematician posts an unchecked ChatGPT Astra proof of the planar Mumford–Shah conjecture (1989), citing OpenAI’s ‘100 open problems’ claimOn 22 Sep 2026 Francesco Deangelis (University of Münster) posted a claimed proof of the planar Mumford–Shah conjecture (1989), a central open problem in the calculus of variations and image segmentation. He says…
21 Sep 2026 OpenAI says an internal model resolved 100+ long-standing open problems in 24 days of training (list released 6 Oct: 722 manuscripts)On 21 Sep 2026 OpenAI said an unnamed internal model had resolved more than 100 long-standing open problems during about 24 days of training (28 Aug – 21 Sep). It released no list and no proofs, and did not define…
21 Sep 2026 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 & BeiramiThe Courtade–Kumar conjecture (Kumar & Courtade 2013) says that among all Boolean functions f of n uniform bits, a dictator f(x) = x_i maximises the mutual information I(f(X); Y) when Y is X passed through a binary…
21 Sep 2026 Grad’s 1967 conjecture on 3D plasma equilibria falls: two AI-assisted papers give three families of counterexamplesTwo independent arXiv preprints posted a day apart (21 and 22 Sep 2026) construct smooth magnetohydrostatic plasma equilibria with nested toroidal pressure surfaces and non-constant pressure that have none of the…
19 Sep 2026 FutureHouse and Edison Scientific publish twelve ‘Millennium Problems for Biology’, pitched as the ‘last reasonable eval’ for AI in biologyOn Sept 19, 2026, citing AI’s progress in mathematics, FutureHouse and Edison Scientific (Sam Rodriques, Michaela Hinks) published twelve “Millennium Problems for Biology”: very hard to solve but easy to validate in a…
17 Sep 2026 Science: Stanford’s ‘Virtual Biotech’ of 37,000 AI agents mines ~50,000 clinical trials and designs a lung-cancer ADC later matched by pharmaOn Sept 17, 2026 James Zou’s Stanford group (lead author Harrison Zhang) published the “Virtual Biotech” in Science (aeg6779): about 37,000 specialized AI agents organized like a biotech company under a…
17 Sep 2026 Claude speeds up 30+ open-source biology models about 4x and folds 10,000+ token complexes on one GPU nodeOn Sept 17, 2026 Anthropic reported that Claude, working in Claude Science, optimized more than 30 open-source biomolecular models (structure prediction, protein design, genomics, protein language models) in under four…
17 Sep 2026 ζ(5) proved irrational: Aabir Fauzan’s Zenodo preprint, the first such result since Apéry’s ζ(3) in 1978, is formally verified in Lean within a week, one formalization written by ClaudeOn Sept 17, 2026 Aabir Fauzan (Aalto University) posted “ζ(5) is irrational” on Zenodo. It proves that the value ζ(5) is irrational, the first irrationality proof for a specific odd zeta value since Apéry’s ζ(3) (1978).…
16 Sep 2026 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
16 Sep 2026 Chvátal’s 1972 conjecture proved (Chang–Liu–Liu, ChatGPT-assisted), then a GPT-6 Astra ‘proof from The Book’ and a Codex-built Lean formalizationOn Sept 16, 2026 Fan Chang, Hong Liu and Miao Liu posted a proof of Chvátal’s conjecture (1972): every hereditary family of sets has a largest intersecting subfamily that is a star. It went through a sharp correlation…
15 Sep 2026 Periodic Labs introduces Periodic Neon, a 1T-parameter lab-trained model that beats GPT-6 Astra at X-ray diffraction analysisOn Sept 15, 2026 Periodic Labs, the materials-science startup of Liam Fedus and Ekin Dogus Cubuk, published its first research. It introduced Periodic Neon, a 1-trillion-parameter model built by mid-training and…
15 Sep 2026 OpenAI Foundation launches Public Data for Health with $125M+ in grants for open biomedical datasetsOn Sept 15, 2026 the OpenAI Foundation, the nonprofit that controls OpenAI, launched Public Data for Health. It is its second science program, after AI for Alzheimer’s in April, and starts with more than $125M in grants…
15 Sep 2026 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 AstraOn Sept 15, 2026 Purdue’s Jensen Kohlmeyer and Liam Kruer (as “JenW1N”) submitted a Lean 4 proof to the Conjectures.io bounty platform that disproves Erdős Problem #108, the Erdős–Hajnal question from the late 1960s of…
14 Sep 2026 FDA grants priority review to Takeda’s zasocitinib, a computationally designed TYK2 inhibitor, with a decision due Q1 2027Takeda said on 14 Sept 2026 that the FDA had accepted, with priority review, its new drug application for zasocitinib (TAK-279), an oral TYK2 inhibitor for moderate-to-severe plaque psoriasis. The target action date is…
14 Sep 2026 Friedgut’s 2004 influential-coalitions conjecture resolved (Chattopadhyay–Gurumukhani, ChatGPT Pro used extensively); Friedgut then has GPT-6 Astra simplify the proofOn Sept 14, 2026 Eshan Chattopadhyay and Mohit Gurumukhani (Cornell) posted a proof (arXiv 2609.16401) of Ehud Friedgut’s 2004 conjecture: every monotone Boolean function on the continuous cube [0,1]^n has a coalition…
14 Sep 2026 Sylvester’s 1879 conjecture on sums of two cubes is fully proved: Burungale and Tian settle the last case (p ≡ 8 mod 9) after Hongbo Yin’s proof of the 4, 7 cases; both later papers disclose AI useOn Sept 14, 2026 Ashay Burungale (UT Austin) and Ye Tian (AMSS, Chinese Academy of Sciences) posted “A proof of Sylvester’s conjecture” (arXiv 2609.14893). It proves the remaining case p ≡ 8 (mod 9) of Sylvester’s 1879…
14 Sep 2026 The k-server conjecture, the ‘holy grail’ of online algorithms, is proved at Oxford; ChatGPT 6 Astra generalised the authors’ k = 3 proof to all kChristian Coester, Elias Koutsoupias and Marek Zbysiński (Oxford) posted a proof of the k-server conjecture (Manasse–McGeoch–Sleator, 1988): the work function algorithm is k-competitive on every metric space (arXiv…
11 Sep 2026 Medvedev’s logic of finite problems (1962) shown undecidable; key idea from ChatGPT Sol 5.6, central argument checked in Lean by Claude Opus 5Rodrigo Nicolau Almeida and Søren Brinck Knudstorp proved that Medvedev’s logic of finite problems, a well-known superintuitionistic logic, is undecidable, which settles what they call a longstanding open problem (arXiv…
11 Sep 2026 Fields Medallists’ open letter ‘A Severe Misalignment of AI in Mathematics’ criticises labs’ race for famous problemsOn 11 Sep 2026 about 25 Fields Medallists, including Terence Tao, Peter Scholze, Maryna Viazovska and Pierre Deligne, published an open letter criticising AI labs for treating famous open problems as marketing targets.…
10 Sep 2026 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 2On 10 Sep 2026 Yufei Bai posted arXiv 2609.11276, proving that the irrationality measure of π is below 7.101862832357, down from the 7.103205334137 of Zeilberger and Zudilin (arXiv 1912.06345), by introducing two…
10 Sep 2026 SAIR’s IGP24 challenge: all 25,000 transitive groups of degree 24 realized as Galois groups; Klüners and Malle win without AI against mostly AI-assisted teamsThe third SAIR Foundation competition, IGP24 (announced by Terence Tao on 16 June 2026, run with the LMFDB), asked for explicit degree-24 polynomials realizing each of the ~25,000 transitive permutation groups of degree…
10 Sep 2026 GPT-6 Astra’s Epoch AI run adds more Lean-checked results: Dittert conjecture proved, Ibragimov–Iosifescu and eternal-domination conjectures disprovedAfter the Köthe disproof, the same September 2026 Epoch AI run of pre-release GPT-6 Astra over the Formal Conjectures collection produced more machine-written Lean results, published by Tom Adamczewski: a proof of the…
10 Sep 2026 First Phase III trial of a generative-AI-discovered drug doses first patient (Insilico’s rentosertib)On 2026-09-10 Insilico Medicine dosed the first patients in GENESIS-IPF-3, billed as the world’s first Phase III trial of a drug whose target and molecule were discovered with generative AI: rentosertib, a TNIK…
9 Sep 2026 Google and NASA JPL release MAPL-EMIT, an AI model that maps methane plumes worldwide from the EMIT space instrument (PNAS)On Sept 9, 2026 Google Research and NASA’s Jet Propulsion Laboratory published MAPL-EMIT (Methane Analysis and Plume Localization with EMIT) in PNAS. The deep-learning model detects, quantifies and localizes methane…
9 Sep 2026 Pierce–Birkhoff conjecture (1956) disproved by a multi-agent GPT + Claude harness; counterexamples Lean-verifiedOn 9 Sep 2026 Zehua Lai, Lek-Heng Lim and Junyu Ren posted a counterexample to the Pierce–Birkhoff conjecture (Birkhoff and Pierce, 1956). It is a continuous piecewise-quadratic function on R^30 that is not a finite…
8 Sep 2026 AlphaGenome Atlas predicts the effect of all ~9 billion possible single-letter human DNA variantsOn 8 Sep 2026 DeepMind released AlphaGenome Atlas: predictions for all ~9 billion possible single-nucleotide variants in the human genome (~1 PB of data). A new variant-impact score reportedly ‘more than doubles’…
8 Sep 2026 OpenAI claims a Millennium Prize problem: 10,000 AI agents prove forced Navier–Stokes blow-up; priority dispute eruptsOn 8 Sep 2026 OpenAI released a 166-page paper and a Lean formalisation proving that the 3D incompressible Navier–Stokes equations with a smooth external force can develop a finite-time singularity from smooth initial…
7 Sep 2026 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 conjecturesOn Sept 7, 2026 an anonymous author posted “Almost everywhere monotone additive functions” on Zenodo. It claims a proof of Erdős’s 1946 conjecture (Erdős problem #1122) that an additive function which decreases only on…
7 Sep 2026 Caltech team (Anandkumar) reports a stable self-similar singularity candidate for the unforced 3D Euler equations on R³, found with PINNs and LLM helpOn 7 Sep 2026, the evening before OpenAI’s Navier–Stokes announcement, Anima Anandkumar’s Caltech group posted a self-similar singular profile for the unforced incompressible 3D Euler equations on all of R³.…
7 Sep 2026 Pre-release GPT-6 Astra disproves the Köthe conjecture (1930) with a Lean-verified counterexampleDuring an Epoch AI run over the Formal Conjectures collection, pre-release GPT-6 Astra autonomously found an explicit 2×2 matrix counterexample over a nil algebra (Krempa’s matrix form) with a Lean 4 proof, disproving…
6 Sep 2026 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)On 6 Sept 2026 Shengtao Guo, Ethan X. Fang and Junwei Lu posted arXiv 2609.11980, which constructs a smooth metric with strictly positive sectional curvature on S³×S³. Since S³×S³ is even-dimensional with Euler…
6 Sep 2026 Collatz: a positive fraction of integers provably reach 1 in 10.46 ln n steps; AI-agent proof (ProofAtlas + Codex) by Lech Mazur, Lean-formalized and re-formalized by AxiomOn Sept 6, 2026 Lech Mazur posted (X, ~204k views) “Explicit Positive-Density Collatz Convergence in Logarithmic Time”: for explicit c > 0 and X₀, every X ≥ X₀ has at least cX positive integers n < X that reach 1 within…
5 Sep 2026 The I3322 Bell inequality needs infinite dimensions: Pál–Vértesi conjecture (2010) proved from an approximate proof by GPT-5.5 ProAndrea Coladangelo (University of Washington) proved the Pál–Vértesi conjecture that no finite-dimensional quantum strategy reaches the maximal violation of the I3322 Bell inequality, while an infinite-dimensional one…
4 Sep 2026 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)In early September 2026 two preprints settled long-standing problems about Reed–Solomon codes, the most widely used error-correcting codes. Brakensiek, Chen, Putterman, Zhang and Zheng (ECCC TR26-164, 4 Sept; arXiv…
4 Sep 2026 Claude produces the first complete machine-checked proof of Fermat’s Last Theorem in Lean, in 11 daysAnthropic reported that a Claude model (roughly comparable to Claude Fable 5.1), running for 11 days (7–18 Aug 2026) using the Prove2Me multi-agent platform, produced a complete Lean formalisation of Fermat’s Last…
3 Sep 2026 PPPL’s PACMAN framework lets multiple AI models control a tokamak in ~20 ms, preventing a tearing mode
3 Sep 2026 Complete male fruit fly nervous-system connectome (166,000 neurons), reconstructed with Google AI, published in CellOn Sept 3, 2026 Google Research, HHMI Janelia and Cambridge (MRC LMB) announced peer-reviewed publication in Cell of the first complete connectome of an adult male fruit fly’s central nervous system (brain plus ventral…
3 Sep 2026 Google DeepMind’s WeatherNext 3 learns from live satellite data: hourly 5 km global forecasts and up to 60% better precipitation skillOn Sept 3, 2026 Google DeepMind and Google Research released WeatherNext 3. It ingests live geostationary satellite mosaics and trains directly on station observations, producing a new global forecast every hour at up…
3 Sep 2026 GPT-6 Astra autonomously disproves Smale’s mean value conjecture (constant 1) in Lean; HKU mathematicians build on it to show Smale’s constant exceeds 1.1018In an Epoch AI LeanOpenProblems evaluation run in September 2026, a pre-release GPT-6 Astra autonomously produced a Lean 4 proof that Smale’s mean value conjecture with constant 1 is false: there is a polynomial p with…
3 Sep 2026 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 runsIn Epoch AI’s FrontierMath Erdős runs (announced 3 Sep 2026), a pre-release GPT-6 Astra autonomously resolved five of 68 hand-picked open Erdős problems with Lean-checked proofs. They include a disproof of Erdős problem…
3 Sep 2026 GPT-6 Astra proves the Erdős–Sós conjecture (1962) with a short counting argument; mathematicians race to simplify and extend itIn Epoch AI’s FrontierMath Erdős runs, a pre-release GPT-6 Astra autonomously proved the Erdős–Sós conjecture (Erdős problem #548): every graph with average degree greater than k−2 contains every tree on k vertices. The…
3 Sep 2026 Claude-written Lean proof claims the dying percolation conjecture θ(p_c)=0 in every dimensionIn early September 2026 a Lean 4 formalization written by Anthropic’s Claude models (directed by Justin Leder, published in anthropics/formal-math) claimed to prove that critical Bernoulli bond percolation on Z^d has no…
2 Sep 2026 Nature: ‘Designing physics experiments with artificial intelligence’ (Krenn group) on AI-found setups that beat human designs
2 Sep 2026 NVIDIA’s Nemotron-3-Ultra-CC outscores every human at IOI 2026 (535.4/600)NVIDIA reported that its fine-tuned Nemotron-3-Ultra-CC (550B total / 55B active MoE) scored 535.4 of 600 on the IOI 2026 problem set, graded by the IOI team. The top human scored 498.27, making it the first AI claimed…
30 Aug 2026 GPT-6 Astra lowers the bounded prime gaps record from 246 to 186An OpenAI preprint (30 Aug 2026) claims lim inf (p_{n+1} − p_n) ≤ 186, improving Polymath8b’s bound of 246, which had stood since 2014. It uses ‘triply densely divisible’ conditions feeding a multidimensional Selberg…
28 Aug 2026 Matrix Spencer conjecture proved; authors credit GPT-5.6 Sol Pro with ‘the heavy-lifting’ for the key lemmaEmrullah Akbas and Suvrit Sra posted a proof of the Matrix Spencer conjecture (arXiv 2608.28816, 28 Aug 2026). For symmetric n×n matrices A_1..A_n with operator norm at most 1, one can efficiently find signs x in {±1}^n…
27 Aug 2026 Google’s Antigravity ‘Teamwork’ multi-agent framework with Gemini 3.7 Flash solves seven open CS/math problems, incl. part of Knuth’s cycles problemOn Aug 27, 2026 Google announced updates to Teamwork, a multi-agent orchestration framework in its Antigravity coding environment. Using Gemini 3.7 Flash (with 3.1 Pro), its “Long Proof” pattern produced results on…
26 Aug 2026 GPT-5.6 improves the Erdős–Rankin / Ford–Green–Konyagin–Maynard–Tao bound for large prime gapsOn 26 Aug 2026 the user “DottedCalculator” posted to erdosproblems.com (problem #4) a proof, generated with GPT-5.6, that there are infinitely many prime gaps larger than C·log n·log log n / log log log log n. This…
23 Aug 2026 Claude-assisted search breaks the elliptic curve rank record: rank 30, then 31An elliptic curve over Q with rank at least 30 was reported on 20 Aug 2026 and one with rank ≥31 on 23 Aug. These broke the Elkies–Klagsbrun rank-29 record from 2024. The rank-31 curve has 31 explicit independent…
23 Aug 2026 Claude-assisted construction claims a complex structure on the 6-sphere, answering Hopf’s 1947 problem (pending verification)On 23 Aug 2026 Anthropic’s Levent Alpöge posted a 100+ page document, produced with an internal Claude model, claiming that the 6-sphere S⁶ admits an integrable complex structure. This would answer Hopf’s 1947 question.…
19 Aug 2026 Peking University preprint claims an AI-found disproof of the Yau–Tian–Donaldson conjecture for constant scalar curvature metricsOn 19 Aug 2026 Jihao Liu (Peking University) posted a 79-page preprint describing a polarized smooth projective fivefold that is K-polystable but has no constant scalar curvature Kähler (cscK) metric. That would…
18 Aug 2026 Palomar launches: a registry of Lean-verified mathematics to curb misrepresented AI proof claimsOn 18 Aug 2026 the Lean FRO and ICARM launched Palomar (palomar-registry.org), “the analogue of a preprint server for Lean proofs”. It indexes GitHub repositories whose formal results are checked mechanically with…
18 Aug 2026 Claude autonomously designs protein binders that work in the lab against 14 of 15 targetsOn Aug 18, 2026 Anthropic reported that Claude (Mythos Preview and Opus 4.8), running autonomously in Claude Science, designed de novo protein binders against 15 targets and produced confirmed binders for 14 of them in…
17 Aug 2026 AlphaEvolve helps lower the matrix multiplication exponent ω to below 2.371177A paper by Alman, Vassilevska Williams and co-authors including DeepMind researchers (arXiv 2608.16884) improved the bound on the matrix multiplication exponent from ω < 2.371339 to ω < 2.371177. AlphaEvolve refined the…
13 Aug 2026 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 laterXinbao Lu and Kaiwen Yang posted a proof of Banach’s 1932 isometric conjecture for every odd n (arXiv 2608.13536, 13 Aug 2026). With Gromov’s even-n theorem, this completes the real case: a real Banach space whose…
12 Aug 2026 Claude-assisted constructions complete Hadamard matrices for every order below 2000, including 668Claude-assisted searches constructed Hadamard matrices for the 12 remaining unknown orders below 2000 (668, 716, 892, 1132, 1244, 1388, 1436, 1676, 1772, 1916, 1948, 1964). Order 668 had been the smallest open case of…
10 Aug 2026 Claude proves more than two-thirds of Riemann zeta zeros are simple and on the critical line (up from 41.6%)Anthropic reported that an unreleased research version of Claude, running in Claude Code with ~60 subagents, raised the unconditional lower bound on the proportion of Riemann zeta zeros that are simple and on the…
6 Aug 2026 DeepMind open-sources WeatherNext 2 and WeatherNext Cyclones with a Nature paper showing ~1 extra day of hurricane warningOn 6 Aug 2026 Google DeepMind released weights and code for WeatherNext Cyclones, WeatherNext 2 and WeatherNext 2-mini under commercial-use-friendly licences, alongside a Nature paper showing its cyclone model gives…
5 Aug 2026 HRT conjecture (1996) disproved: 12 time-frequency shifts of a Schwartz function are linearly dependent, found with ChatGPT-assisted guessworkarXiv 2608.05044 (5 Aug 2026), by Markus Faulhuber, Philipp Petersen, Jordy Timo van Velthoven and Felix Voigtlaender, shows that finitely many time-frequency shifts of a Schwartz function can be linearly dependent.…
5 Aug 2026 Sendov’s 1958 conjecture on polynomial roots proved with GPT-5.6 Pro; Tao simplifies and formalises itLech Mazur posted a computer-assisted proof, generated with GPT-5.6 Pro, of Sendov’s conjecture for all degrees: if every root of a polynomial lies in the closed unit disk, each root is within distance 1 of a critical…
4 Aug 2026 Alexander Perry disproves the period-index conjecture (Colliot-Thélène, 2001); a flawed ChatGPT example was the starting pointAlexander Perry posted counterexamples to the period-index conjecture for Brauer classes: d-dimensional varieties (d ≥ 3) with a Brauer class of period 2 and index 2^d (arXiv 2608.03684; v1 4 Aug, v2 3 Sep 2026). His AI…
3 Aug 2026 Planar Schiffer and Pompeiu conjectures disproved by two independent groups; one proof has a Lean certificate written by GPT-5.6In August 2026 two groups independently disproved Schiffer’s conjecture (Yau’s Problem 80) and the planar Pompeiu problem (1929). Colbrook and Stepaniants (3 Aug) built one explicit ten-fold symmetric domain with a…
1 Aug 2026 OpenAI hosts a closed-door summit of about 40 mathematicians on the future of mathematicsIn early August 2026, shortly after its “ten advances in mathematics” post, OpenAI hosted about 40 mathematicians at its San Francisco offices to discuss what will be left for human mathematicians if AI surpasses them.…
1 Aug 2026 OpenAI’s unreleased ‘Astra’ model claims ten advances in maths and theoretical CS, with Lean proofsOn 1 Aug 2026 OpenAI published ‘Ten advances in mathematics and theoretical computer science’ by an internal model, Astra (released as GPT-6 Astra on 3 Sep). It came with a 249-page manuscript and Lean 4 proofs. The…
29 Jul 2026 Maxwell’s conjecture on equilibria of point charges is false: five charges with at least 24 critical points, construction idea from GPT-5.6 SolPhilip Arathoon, Gavin Ball and Matthew Kvalheim posted a configuration of five point charges whose electrostatic potential has at least 24 non-degenerate critical points (arXiv 2607.27197, 29 Jul 2026). This refutes…
27 Jul 2026 Neurosurgery resident uses GPT-5.6 Sol to prove Crouzeix’s conjecture in a 16-hour autonomous runA preprint posted 27 Jul 2026 proves Crouzeix’s conjecture (2004): for every square matrix A and polynomial f, ‖f(A)‖ ≤ 2·max over the numerical range W(A) of |f|. The proof came from one uninterrupted 16-hour…
25 Jul 2026 Sharp thin-shell inequality: Var(|X|²) ≤ 8n for isotropic log-concave vectors, with a proof ‘found by GPT-5.6 Pro’ (Chen & Klartag)On 25 July 2026 Yuansi Chen and Boaz Klartag posted arXiv 2607.23307, which determines the optimal constant in the thin-shell theorem: for every isotropic log-concave random vector X in R^n, Var(|X|²) ≤ 8n, with…
24 Jul 2026 Terence Tao’s ICM 2026 public lecture ‘Mathematics in the age of AI’ calls a crisis in the foundations of mathematical valuesOn 24 Jul 2026, at the International Congress of Mathematicians in Philadelphia, Terence Tao gave the public lecture “Mathematics in the age of AI”. He argued that mathematics is entering a “crisis in the foundations of…
24 Jul 2026 Rota’s 1970 unimodality conjecture for matroid flats disproved, with ChatGPT 5.6 Pro suggesting a key constructionIn July–August 2026 three arXiv papers overturned classic matroid conjectures with AI help. Matt Larson (2607.02208, Jul 2) disproved Mason’s log-concavity conjecture for flat counts and White’s exchange conjecture…
24 Jul 2026 Hessian conjecture refuted in five variables, derived from Claude-found Jacobian counterexampleFive days after Levent Alpöge’s Claude Fable 5-assisted counterexample to the Jacobian conjecture, Guowu Meng and Liang Yang used “Schur descent” on it to build a five-variable counterexample to the related Hessian…
23 Jul 2026 AI systems score a perfect 42/42 at IMO 2026, officially gradedFor the first time AI achieved full marks at the International Mathematical Olympiad: at IMO 2026 in Shanghai, Huawei’s ‘Celia’ and Xiaohongshu/RedNote’s ‘dots-note-3.0’ each scored 42/42, with solutions graded by IMO…
22 Jul 2026 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 workflowOn 22 July 2026 Shouqiao Wang, a Columbia PhD candidate, posted “I solved 6 open Erdős problems in 5 days, using @OpenAI GPT-5.6 Sol”, with a thread giving his Codex workflow and prompts. Coverage says he tried about 13…
22 Jul 2026 Dmitry Rybin posts a GPT-5.6 Pro counterexample to the ~30-year-old Dinitz–Garg–Goemans (Goemans cost) conjecture on unsplittable flowsOn 22 July 2026 Dmitry Rybin posted on X that the Dinitz–Garg–Goemans conjecture, open for about 30 years, is false, with a small graph found in a chat with GPT-5.6 Pro: a fractional flow of cost 58 for which every…
20 Jul 2026 Claude Fable 5 finds a counterexample to the Jacobian conjecture in dimension 3Anthropic mathematician Levent Alpöge posted an explicit polynomial map F: C³→C³ with constant Jacobian determinant −2 that is not injective, found with Claude Fable 5. This refutes Keller’s 1939 Jacobian conjecture in…
17 Jul 2026 GPT-5.6 Sol Ultra proves the 50-year-old cycle double cover conjectureIn mid-July 2026 OpenAI released a preprint crediting GPT-5.6 Sol Ultra, ‘in less than an hour’, with a proof of the cycle double cover conjecture (Szekeres 1973, Seymour 1979): every bridgeless graph has a collection…
14 Jul 2026 Berkeley’s Phillip Kerger uses GPT-5.6 Sol and a 10-page prompt to close a 30-year gap in derivative-free convex optimizationIn July 2026 UC Berkeley IEOR teaching professor Phillip Kerger posted a proof that deterministic optimization of a convex Lipschitz function over a d-dimensional ball with only exact function values needs…
1 Jul 2026 AI-assisted counterexample answers Grothendieck’s question on finite flat group schemes, merged into MathlibAkhil Mathew, using OpenAI’s and Anthropic’s models, found a finite locally free group scheme of order 4 over a non-reduced finite ring with 2⁹ elements that is not killed by 4 (it is killed by 8). This answers…
29 Jun 2026 Machine-learning screen predicts two new kagome superconductors, confirmed in the lab
5 Jun 2026 Computationally designed broad coronavirus vaccine is safe and immunogenic in first human trialA Phase 1 trial in 39 volunteers found that a vaccine antigen designed entirely by computer (Cambridge / DIOSynVax, Jonathan Heeney) was safe and raised immune responses against SARS-CoV-2, SARS and bat coronaviruses.…
27 May 2026 Erdős–Szemerédi sum-product conjecture shown false over the reals; a GPT-5.5 Pro agent re-disproves it in 7 of 8 runsInspired by the AI disproof of the unit-distance conjecture, Bloom, Sawin, Schildkraut and Zhelezov proved on 27 May 2026 that the Erdős–Szemerédi sum-product conjecture is false over the real numbers. They built sets A…
20 May 2026 OpenAI model disproves Erdős’s 80-year-old unit distance conjectureOn 2026-05-20 OpenAI announced that an internal model found a counterexample to Erdős’s 1946 unit-distance conjecture using algebraic number theory — widely described as the first historically significant proof produced…
12 May 2026 GPT-5.5 Pro finds counterexample disproving McKean’s 1966 conjecture and the Gaussian completely monotone conjectureGu and Sellke (arXiv 2605.11656) presented an explicit probability measure, found by GPT-5.5 Pro, for which the 5th time-derivative of entropy along the heat flow is positive. This disproves the Gaussian completely…
9 May 2026 Google DeepMind’s ‘AI co-mathematician’ sets FrontierMath Tier 4 record and helps resolve a Kourovka Notebook problemDeepMind’s agentic ‘AI co-mathematician’ on Gemini 3.1 Pro scored 48% (23/48) on FrontierMath Tier 4, versus 19% for Gemini 3.1 Pro alone and 39.6% for GPT-5.5 Pro. It helped Oxford’s Marc Lackenby resolve Kourovka…
3 May 2026 Amateur with GPT-5.4 Pro ‘vibe-maths’ a 60-year-old Erdős conjecture on primitive sets; Tao co-authors the paper23-year-old amateur Liam Price gave GPT-5.4 Pro a single prompt. In about 80 minutes it sketched a proof of Erdős problem #1196, the 1966 Erdős–Sárközy–Szemerédi conjectures on primitive sets and divisibility chains…
1 May 2026 GPT-5.5 Pro-assisted construction lowers the smallest known Borsuk counterexample dimension from 64 to 63In May 2026 Max Grinsztajn, assisted by OpenAI’s GPT-5.5 Pro, built a 321-point set in R^63 that cannot be split into 64 parts of smaller diameter, so Borsuk’s conjecture fails in dimension 63 (b(63) ≥ 65). The previous…
30 Mar 2026 Erdős Problem #650 solved exactly, f(m) = min(m, ⌈2√m⌉), with a strategy proposed by ChatGPT and a Lean proof by Aristotle; first Justin Sun Prize awards in October
25 Mar 2026 RAVEN machine-learning pipeline validates 118 new planets in TESS data
10 Mar 2026 Google, Imperial College and the NHS: AI second reader finds 25% of interval breast cancers missed by screening (two Nature Cancer papers)On March 10, 2026 Google Research, Imperial College London and the UK’s NHS published two studies in Nature Cancer on an experimental AI system for breast-cancer screening. On past mammograms of about 125,000 women, the…
10 Mar 2026 AlphaEvolve improves lower bounds for nine classical Ramsey numbersGoogle researchers used AlphaEvolve to construct graphs improving the lower bounds of nine small Ramsey numbers, including R(3,13) ≥ 61, R(4,16) ≥ 174 and R(4,19) ≥ 219 (arXiv 2603.09172).
1 Mar 2026 Math Inc’s Gauss formalises Viazovska’s sphere-packing proofs in dimensions 8 and 24, fixing errors in the originalsMath Inc’s Gauss agent completed the Lean formalisation of Maryna Viazovska’s Fields-Medal proofs of optimal sphere packing in dimensions 8 (5 days) and 24 (~2 weeks), about 180,000 lines. Along the way it found and…
28 Feb 2026 Donald Knuth’s ‘Claude’s Cycles’: Claude Opus 4.6 solves an open Hamiltonian-cycle problem (‘Shock! Shock!’)Donald Knuth published a note opening ‘Shock! Shock!’ describing how Claude Opus 4.6 found, in about an hour of guided exploration, a general construction decomposing the arcs of a 3D torus digraph on m³ vertices into…
14 Feb 2026 ‘First Proof’ challenge: AI solves about half of 10 unpublished research problems set by mathematiciansEleven mathematicians released 10 unpublished research-level problems on 5 Feb 2026 and answers on 14 Feb. DeepMind’s Aletheia got 6/10 by majority expert assessment. OpenAI got at least 5 likely correct and retracted…
13 Feb 2026 GPT-5.2 conjectures, and an OpenAI model proves, that ‘single-minus’ gluon tree amplitudes are nonzeroA preprint by Guevara, Lupsasca, Skinner, Strominger and OpenAI’s Kevin Weil showed that tree-level single-minus gluon amplitudes, long assumed to vanish, are nonzero in a ‘half-collinear’ region of (2,2)-signature…
11 Feb 2026 DeepMind’s Aletheia agent and Gemini Deep Think report autonomous Erdős solutions and new physics and CS resultsGoogle DeepMind described Aletheia, a Gemini Deep Think–based maths research agent. It autonomously solved Erdős problems #652, #654 and #1040 and resolved #1051, which led to a peer-reviewed generalisation. A…
10 Feb 2026 Isomorphic Labs unveils IsoDDE drug-discovery engine, hailed as ‘an AlphaFold 4’ — but proprietaryOn 10 Feb 2026 DeepMind spin-off Isomorphic Labs released a 27-page technical report on IsoDDE, a proprietary drug-discovery engine that outperforms AlphaFold 3-era tools and Boltz-2 on protein–ligand binding, affinity…
5 Feb 2026 GPT-5 autonomously runs 36,000 experiments in Ginkgo’s cloud lab, cutting protein-synthesis cost 40%OpenAI and Ginkgo Bioworks reported that GPT-5, in a closed loop with Ginkgo’s automated cloud lab, tested over 36,000 cell-free protein synthesis reaction compositions on 580 plates over six rounds. It cut the cost of…
6 Jan 2026 Erdős problem #728 solved near-autonomously by GPT-5.2 Pro and Harmonic’s Aristotle, with a Lean proofOn 4–6 Jan 2026 amateur Kevin Barreto relayed an informal argument from GPT-5.2 Pro to Harmonic’s Aristotle, which formalised it in Lean. It was widely accepted as the first Erdős problem solved essentially autonomously…

2025

8 Dec 2025 Genuine AI-assisted solutions to Erdős problems begin: #124 (Aristotle), #1026 (48-hour human–AI collaboration)In Nov–Dec 2025 AI tools produced the first genuinely new (if modest) solutions to Erdős problems. Harmonic’s Aristotle proved a version of #124 in Lean autonomously (29 Nov). Erdős #1026 (posed 1975) was fully solved…
6 Dec 2025 AxiomProver produces machine-checked Lean proofs for all 12 Putnam 2025 problemsAxiom Math’s autonomous Lean 4 prover solved 8 of 12 problems of the 6 Dec 2025 Putnam competition within exam time and the remaining 4 in the following days, all as machine-checked Lean proofs published on GitHub.
1 Dec 2025 Physics Letters B paper built on a GPT-5 idea draws criticism that it tests the wrong thing
1 Dec 2025 AI searches 100 million Hubble images in 2.5 days, finding ~1,400 anomalies including 800+ never described
20 Nov 2025 OpenAI publishes ‘Early science acceleration experiments with GPT-5’, including four new math resultsOn 20 Nov 2025 OpenAI and academic co-authors, including Timothy Gowers, released case studies of GPT-5 contributing to research in maths, physics, astronomy, computer science, biology and materials science. The paper…
5 Nov 2025 Edison Scientific’s Kosmos AI scientist claims six months of research per runIn early November 2025 FutureHouse spin-out Edison Scientific launched Kosmos, an autonomous AI scientist that reads ~1,500 papers and runs ~42,000 lines of analysis code per 12-hour run; beta users estimated one run…
5 Nov 2025 Tao, Gómez-Serrano, Georgiev and Wagner test AlphaEvolve on 67 maths problemsIn ‘Mathematical exploration and discovery at scale’ (arXiv 2511.02864), Bogdan Georgiev, Javier Gómez-Serrano, Terence Tao and Adam Zsolt Wagner ran AlphaEvolve on 67 problems in analysis, combinatorics, geometry and…
5 Nov 2025 Baker lab designs antibodies from scratch with atomic accuracy using RFdiffusionIn Nature (Nov 2025) the Baker lab reported de novo design of VHH nanobodies, scFvs and full antibodies against chosen epitopes. Cryo-EM confirmed atomically accurate binding poses and CDR loops for influenza…
24 Oct 2025 Genentech’s GNEprop screens 1.4 billion virtual compounds and finds 82 new antibacterial hits
22 Oct 2025 Agents4Science 2025: first conference where AI must be first author and reviewerAgents4Science 2025 (22 Oct 2025, virtual) required AI systems as first authors and used GPT-5, Gemini 2.5 and Claude Sonnet 4 as reviewers: 315 submissions, 253 reviewed, 48 accepted, making AI-authored science an…
17 Oct 2025 OpenAI researchers claim GPT-5 ‘solved’ 10 Erdős problems; the solutions were already in the literatureIn mid-October 2025 OpenAI’s Kevin Weil tweeted that GPT-5 ‘found solutions to 10 (!) previously unsolved Erdős problems’. Thomas Bloom, who runs erdosproblems.com, called this ‘a dramatic misrepresentation’: GPT-5 had…
16 Oct 2025 Google DeepMind partners with Commonwealth Fusion Systems to optimise and control the SPARC tokamak with AIDeepMind announced a research partnership with Commonwealth Fusion Systems (CFS) for CFS’s SPARC tokamak, which aims to be the first magnetic-confinement device to produce net fusion energy. The work uses DeepMind’s…
15 Oct 2025 Google’s C2S-Scale 27B model generates a new cancer-immunotherapy hypothesis confirmed in living cellsC2S-Scale 27B, a Gemma-based single-cell model, simulated over 4,000 drugs in two immune contexts. It predicted that the CK2 inhibitor silmitasertib boosts tumour antigen presentation only with low-dose interferon…
27 Sep 2025 Scott Aaronson credits GPT-5 with a key step in a quantum complexity proofIn ‘Limits to black-box amplification in QMA’ (Aaronson and Witteveen, arXiv 2509.21131), GPT-5-Thinking suggested the key function Tr[(I−E(θ))^−1] used in the proof. Aaronson called it the first paper of his where a…
22 Sep 2025 AlphaEvolve finds gadgets that prove new NP-hardness of approximation bounds for MAX-k-CUT
17 Sep 2025 DeepMind and mathematicians use neural networks to find new unstable singularities in fluid equationsA DeepMind-led team (with Tristan Buckmaster and Javier Gómez-Serrano) used physics-informed neural networks and high-precision optimisation to find new families of unstable self-similar blow-up solutions for the…
12 Sep 2025 First AI-generated complete genomes: Evo models design viable bacteriophages that kill resistant E. coliBrian Hie’s lab used the Evo 1 and Evo 2 genome language models to generate whole ΦX174-like bacteriophage genomes. Of ~285–300 synthesised designs, 16 were viable. Some rapidly overcame ΦX174-resistant E. coli, and one…
10 Sep 2025 Math Inc’s Gauss agent completes the Strong Prime Number Theorem formalisation in Lean in three weeksMath Inc (Christian Szegedy) announced that its autoformalization agent Gauss completed Terence Tao and Alex Kontorovich’s Strong Prime Number Theorem project in Lean in about 3 weeks, producing ~25,000 lines of Lean…
4 Sep 2025 DeepMind’s Deep Loop Shaping cuts LIGO control noise 30–100×In Science (Sept 2025), DeepMind, LIGO/Caltech and GSSI reported an RL control method trained with frequency-domain rewards. Tested on hardware at LIGO Livingston, it reduced control noise in the 10–30 Hz band by more…
20 Aug 2025 GPT-5 Pro proves an improved convex-optimisation bound, which humans had already surpassed
14 Aug 2025 Generative AI designs new antibiotics that kill drug-resistant gonorrhoea and MRSAMIT’s Collins lab (Cell, Aug 2025) used generative models to design more than 36 million candidate compounds from scratch. Lead NG1 kills multidrug-resistant Neisseria gonorrhoeae and DN1 kills MRSA, clearing skin…
30 Jul 2025 Interpretable neural network discovers new non-reciprocal force laws in dusty plasmaEmory physicists (PNAS, July 2025) trained a physics-structured neural network on 3D particle trajectories from dusty-plasma experiments. It learned the non-reciprocal forces between particles with over 99% accuracy and…
29 Jul 2025 Stanford’s ‘Virtual Lab’ of AI agents designs SARS-CoV-2 nanobodies validated in the labJames Zou’s group (Nature, 2025) had an LLM ‘principal investigator’ agent run a team of AI scientist agents. The team built a pipeline combining ESM, AlphaFold-Multimer and Rosetta and designed 92 nanobodies. Two…
21 Jul 2025 AI systems reach gold-medal level at the International Mathematical OlympiadAt IMO 2025, an advanced Gemini Deep Think model (officially graded) and an experimental OpenAI reasoning model (graded by former medalists) each solved 5 of 6 problems for 35/42 points — gold-medal standard — working…
25 Jun 2025 AlphaGenome predicts how DNA variants affect thousands of gene-regulation signals from 1 Mb of sequenceDeepMind’s AlphaGenome reads up to 1 million DNA bases and predicts 5,930 human (1,128 mouse) genomic signals, including expression, chromatin accessibility and splicing, at base-pair resolution. It covers the 98% of…
27 May 2025 Intology’s ‘Zochi’ AI system gets a paper into the ACL 2025 main conferenceIn May 2025 Intology said its autonomous research agent Zochi produced ‘Tempest’, a paper on multi-turn LLM jailbreaking via tree search, that was accepted to the main conference of ACL 2025 (acceptance rate ~20%)…
21 May 2025 Microsoft’s Aurora foundation model beats operational forecasts for air quality, waves, cyclones and weatherAurora (Nature, May 2025) is an Earth-system foundation model pre-trained on over a million hours of geophysical data. After fine-tuning it beat operational systems at air-quality, ocean-wave, tropical-cyclone-track and…
20 May 2025 FutureHouse’s Robin multi-agent system proposes ripasudil as a new treatment candidate for dry AMDFutureHouse’s Robin generated the hypotheses, analyses and figures that identified ripasudil, a glaucoma drug, as a candidate for dry age-related macular degeneration. Ripasudil increased phagocytosis in retinal pigment…
14 May 2025 AlphaEvolve: Gemini-powered agent discovers new algorithmsGoogle DeepMind’s AlphaEvolve combined Gemini models with evolutionary search and automated evaluation to discover new algorithms, including a way to multiply 4×4 complex matrices with 48 scalar multiplications…
12 Mar 2025 Sakana’s AI Scientist-v2 writes the first fully AI-generated paper to pass peer review (ICLR 2025 workshop)On 12 Mar 2025 Sakana AI reported that a paper generated end-to-end by The AI Scientist-v2 (idea, code, experiments, analysis, writing) scored 6, 7, 6 at an ICLR 2025 workshop, above the acceptance threshold; it was…
25 Feb 2025 AI weather forecasting goes operational: ECMWF’s AIFS (Feb 2025), then NOAA’s AI models (Dec 2025)On 25 Feb 2025 the European Centre for Medium-Range Weather Forecasts made its machine-learned AIFS Single model operational alongside its physics model. It was up to 20% better on tropical-cyclone tracks and used about…
19 Feb 2025 Evo 2: a 40B-parameter genome language model trained on DNA from all domains of lifeArc Institute, Stanford and NVIDIA released Evo 2 (7B and 40B parameters) in Feb 2025, trained on genomes across bacteria, archaea and eukaryotes. It predicts variant effects and generates genome-scale sequences.…
19 Feb 2025 Google’s AI co-scientist independently reproduces an unpublished superbug discovery in 48 hoursGoogle’s Gemini 2.0–based multi-agent ‘AI co-scientist’ (announced 19 Feb 2025) generated hypotheses that were validated in the lab. It proposed AML drug-repurposing candidates, and liver-fibrosis drugs active in human…
16 Jan 2025 Microsoft’s MatterGen generates materials to order; flagship result later challenged as a known compoundMatterGen (Nature, Jan 2025) is a diffusion model that generates stable inorganic materials with target properties. In the flagship test, TaCr2O6 was generated for a 200 GPa bulk modulus and measured at 169 GPa after…
15 Jan 2025 AI-designed proteins neutralise deadly snake-venom toxins and protect miceBaker lab and DTU researchers (Nature, Jan 2025) used RFdiffusion to design small proteins that bind and neutralise cobra three-finger toxins. Depending on dose, toxin and design, 80–100% of mice survived otherwise…

2024

20 Dec 2024 OpenAI o3 scores 25% on FrontierMath research-level maths benchmark, amid funding disclosure controversyEpoch AI’s FrontierMath (Nov 2024) contains unpublished research-level problems on which models scored under 2%. On 20 Dec 2024 OpenAI claimed 25.2% for o3. It then emerged that OpenAI had funded the benchmark and had…
4 Dec 2024 GenCast: diffusion-based ensemble forecast beats ECMWF’s ENS on 97% of targetsGenCast (Nature, Dec 2024) is a diffusion model producing probabilistic 15-day ensemble forecasts. It beat ECMWF’s ENS, the leading operational ensemble, on 97.2% of 1,320 targets and on 99.8% at lead times beyond 36…
20 Nov 2024 AlphaQubit: neural decoder sets accuracy record for quantum error correction on Google’s SycamoreAlphaQubit (Nature, Nov 2024), a recurrent-transformer decoder for the surface code, made 6% fewer errors than tensor-network decoding and 30% fewer than correlated matching on real Sycamore data at code distances 3 and…
5 Sep 2024 AlphaProteo designs high-affinity protein binders, including the first AI-designed VEGF-A binderDeepMind’s AlphaProteo generated protein binders for 7 targets with 9–88% experimental success rates (88% for BHRF1) and 3–300× better affinities than prior methods. It produced the first successful AI-designed binder…
25 Jul 2024 AlphaProof and AlphaGeometry 2 reach IMO silver-medal standardGoogle DeepMind’s AlphaProof (RL + Lean formal proofs) and AlphaGeometry 2 solved 4 of 6 problems at the 2024 International Mathematical Olympiad, scoring 28/42 — silver-medal level, one point short of gold.
22 Jul 2024 NeuralGCM: Google’s hybrid physics-ML atmosphere model matches top weather forecasts and runs decades-long climate simulationsIn Nature (Kochkov et al., 22 July 2024) Google introduced NeuralGCM. It pairs a differentiable spectral dynamical core with neural-network physics parameterisations trained end-to-end. It was competitive with ECMWF for…
25 Jun 2024 ESM3 generates esmGFP, a new fluorescent protein estimated at ‘500 million years of evolution’ from natureEvolutionaryScale’s ESM3, a multimodal protein language model, generated esmGFP, a bright fluorescent protein only 58% identical to the closest known fluorescent protein. The authors estimate that distance equals over…
8 May 2024 AlphaFold 3 predicts structures and interactions of all life’s moleculesAlphaFold 3 extended structure prediction from proteins to complexes with DNA, RNA, ligands and ions, using a diffusion-based architecture, with at least 50% improvement on protein–ligand interactions over prior methods.
21 Feb 2024 AI controller predicts and avoids tearing instabilities in the DIII-D fusion reactorPrinceton and PPPL researchers (Nature, Feb 2024) trained an RL controller on past DIII-D data. It forecast tearing-mode instabilities up to 300 ms ahead and adjusted operating parameters in real time to avoid them…
17 Jan 2024 AlphaGeometry solves olympiad geometry near gold-medallist level without human demonstrationsAlphaGeometry (Nature, 17 Jan 2024) solved 25 of 30 IMO geometry problems from 2000–2022. The previous best system solved 10 and the average gold medallist 25.9. It combines a language model with a symbolic deduction…
9 Jan 2024 Microsoft AI and PNNL screen 32 million candidates to find a solid electrolyte using ~70% less lithium

2023

20 Dec 2023 Coscientist: a GPT-4 agent plans and runs real chemistry experiments from plain-English promptsGabe Gomes’s group (Nature, Dec 2023) built Coscientist, a GPT-4-based agent that searches documentation, writes code and drives lab automation. Across six tasks it included successfully planning and optimising…
20 Dec 2023 Explainable deep learning discovers a new structural class of antibiotics against MRSAFelix Wong, James Collins and colleagues (Nature, Dec 2023) screened ~39,000 compounds, trained graph neural networks, and used explainable substructure analysis on ~12M compounds. They found a new structural class of…
14 Dec 2023 FunSearch: an LLM finds new cap-set constructions, the first LLM discovery in open mathsFunSearch (Nature, Dec 2023) paired a code LLM with an automated evaluator in an evolutionary loop. It found a cap set of size 512 in dimension 8 (previous best 496) and better lower bounds on the asymptotic cap-set…
29 Nov 2023 Berkeley’s A-Lab claims 41 new materials from autonomous synthesis; after critiques Nature corrects it to 36 ‘inorganic’ (not ‘novel’) materialsPublished alongside GNoME, the A-Lab paper (Nature, Nov 2023) claimed a robotic lab made 41 ‘novel’ compounds from 58 targets in 17 days. Robert Palgrave and Leslie Schoop argued that many were known compounds or…
29 Nov 2023 GNoME predicts 2.2 million new crystals, 380,000 stable, but novelty and usefulness are disputedDeepMind’s GNoME (Nature, Nov 2023) used graph neural networks and active learning with DFT to predict 2.2 million new inorganic crystal structures, 380,000 of them computed to be stable. DeepMind called it ‘800 years’…
14 Nov 2023 GraphCast: ML weather model beats the world’s best physics-based 10-day forecast on 90% of targetsGraphCast (Science, Nov 2023), a graph neural network trained on ECMWF reanalysis data, produced 10-day global forecasts in under a minute on one TPU. It beat ECMWF’s HRES, the leading deterministic physics model, on…
19 Sep 2023 AlphaMissense classifies 89% of all 71 million possible human missense mutationsAlphaMissense (Science, Sept 2023) scored all ~71 million possible single amino-acid substitutions in 19,233 human proteins and classified 89%: 57% likely benign and 32% likely pathogenic. Human experts had classified…
11 Jul 2023 RFdiffusion: diffusion models design new proteins that work in the labDavid Baker’s lab (Nature, July 2023) fine-tuned RoseTTAFold as a diffusion model to generate new protein backbones for binders, symmetric assemblies and metal-binding sites. Hundreds of designs were experimentally…
7 Jun 2023 AlphaDev discovers faster small-sort routines, merged into LLVM’s C++ standard libraryAlphaDev (Nature, 7 Jun 2023) treated writing assembly as a game and found sort3/sort4/sort5 routines shorter than human versions; they were merged into LLVM libc++. Critics argued the gains were small tricks a compiler…
25 May 2023 AI finds abaucin, a narrow-spectrum antibiotic against the superbug Acinetobacter baumanniiMcMaster and MIT researchers (Nature Chemical Biology, May 2023) trained a model on ~7,500 screened molecules and found abaucin, which selectively kills A. baumannii by disrupting lipoprotein trafficking (LolE) and…

2022

5 Oct 2022 AlphaTensor discovers faster matrix multiplication algorithms, beating Strassen’s 1969 record for 4×4 mod 2DeepMind’s AlphaTensor (Nature, Oct 2022) framed matrix multiplication as a tensor-decomposition game. It found a 4×4 algorithm over GF(2) with 47 multiplications (Strassen-based: 49) and improved 5×5 to 96. Human…
16 Feb 2022 Deep reinforcement learning controls fusion plasma in the TCV tokamakDeepMind and EPFL (Nature, Feb 2022) trained a single deep-RL policy in simulation that commanded all of TCV’s magnetic control coils on the real machine. It produced and held elongated, negative-triangularity and…

2021

1 Dec 2021 DeepMind and mathematicians use machine learning to guide new theorems in knot theory and representation theoryDavies et al. (Nature, Dec 2021) used supervised learning plus attribution to point mathematicians to hidden relationships. That led to a new theorem linking the knot signature to hyperbolic geometry, and to progress on…
22 Nov 2021 NASA’s ExoMiner deep-learning model validates 301 new exoplanets from Kepler data
29 Apr 2021 Adam Zsolt Wagner uses reinforcement learning to find counterexamples to open graph-theory conjectures

2020

30 Nov 2020 AlphaFold 2 solves protein structure prediction at CASP14AlphaFold 2 achieved a median GDT score of 92.4 at CASP14, accuracy competitive with experimental methods, widely seen as solving the 50-year-old protein folding problem for single chains.
8 Jul 2020 Liverpool’s mobile robot chemist runs 688 experiments in 8 days and finds a 6× better photocatalystAndrew Cooper’s group (Nature, July 2020) built a mobile robot that moved around a standard lab and ran 688 experiments over 8 days in a 10-variable space, guided by batched Bayesian optimisation. It found photocatalyst…
20 Feb 2020 Deep learning discovers halicin, a structurally new broad-spectrum antibioticMIT’s Collins and Barzilay labs (Cell, Feb 2020) trained a message-passing neural network on ~2,300 molecules. It identified halicin, a diabetes drug candidate, as a potent antibiotic that killed M. tuberculosis…

2018

2 Dec 2018 AlphaFold (v1) tops the CASP13 protein-structure prediction assessmentDeepMind’s first AlphaFold ranked first in the CASP13 blind assessment of protein structure prediction, an early sign that deep learning could crack the protein folding problem.

Videos

Terence Tao & Yu Deng: Why We Build Open Math Model SAIR, 2026-10-19
We Need to Talk About OpenAI’s Latest Maths “Breakthrough” Ellie Sleightholm, 2026-10-18
Mathematicians Are The Canary Down The AI Coal Mine The Rest Is Science, 2026-10-18
Navier Stonks Lost in Translation | Informal Proof ≠ Lean Proof (but statement still correct!) Alex Hyman, 2026-10-17
HANDS FOR THE GHOST (Out of the Glass) – every event on screen is real cyklop, 2026-10-15
OpenAI Bulk-Solves 722 Math Problems, Anthropic’s Cruelty Policy, & Elon’s Quadrillion-Dollar SpaceX Peter H. Diamandis, 2026-10-15
No More Heroes - Terence Tao Talks to Numberphile About AI Numberphile, 2026-10-15
Will AI Destroy Mathematics? | World Science Festival World Science Festival, 2026-10-15
AI’s Riemann result has a ceiling. A human just found it. HexaValuation, 2026-10-14
AI is solving math faster than human verification.. Caleb Writes Code, 2026-10-13
OpenAI’s AI Wrote 700 Math Papers. Engineers Still Won’t Trust AI With Their Code. AI News & Strategy Daily | Nate B Jones, 2026-10-13
OpenAI’s New AI Is Doing Things We Barely Understand Two Minute Papers, 2026-10-13
菲爾茲獎得主 Tsimerman 要去 OpenAI，陶哲軒提 Math 2.0：兩位頂尖數學家怎麼看 AI 解題 (Fields medallist Tsimerman goes to OpenAI, Tao proposes Math 2.0; Chinese) fOx Hsiao, 2026-10-12
Terence Tao’s AI-in-Math slides (including the infamous cancer slides *facepalm*) Dr. Samuel Allen Alexander, 2026-10-12
OpenAI’s Verified Navier-Stokes Proof Isn’t the One in the Paper Adem B10, 2026-10-11
OpenAI just posted 722 math papers at once... BugX, 2026-10-11
BREAKING: OpenAI’s Navier-Stokes Proof Might Be WRONG The Pretrained Pod, 2026-10-11
OpenAI Dropped 722 Math Papers Overnight. Mathematicians Lost It. Singularity Research Labs, 2026-10-11
New AI enzymes, 700+ math breakthroughs, AI for DNA mutations, room temp semiconductors: AI NEWS AI Search, 2026-10-10
This Has Never Happened in Math Before | OpenAI Just Dropped BOMBSHELL Animated Math, 2026-10-10
OpenAI Just Broke Matrix Multiplication. Why 2.25 Matters Mathify - Animate math by chatting with AI, 2026-10-10
‘A CHILLING EFFECT’: How OpenAI’s massive math breakthrough is ‘DESTROYING’ early careers MS NOW, 2026-10-10
How AI Is Upending the World of Mathematics | Odd Lots Bloomberg Podcasts, 2026-10-09
OpenAI agent does it again, solving nearly 400 math problems no human has ever solved Global News, 2026-10-09
OpenAI’s Math Dump Just Exposed the AI Bubble’s Fatal Flaw House of El: AI, 2026-10-09
The Mathematics are Mad The PrimeTime, 2026-10-09
You Truly Don’t Understand What Just Happened to Mathematics Prof Gio | Giordano Scarciotti, 2026-10-09
OpenAI withdraws three AI-generated math papers due to a sign error Dr. Samuel Allen Alexander, 2026-10-09
OpenAI dropped 722 math papers. Mathematicians are split. Alex Volkov from ThursdAI, 2026-10-09
722 Math Papers in One Night. One of Them Is About Riemann. Adem B10, 2026-10-08
OpenAI Just Gave Us a Glimpse of the Singularity… AI Copium, 2026-10-08
NYU’s Tristan Buckmaster on the controversy over OpenAI’s math findings CNBC Television, 2026-10-08
AI Keeps Pissing Off Mathematicians ColdFusion, 2026-10-08
About OpenAI’s “Breakthrough” on 377 Math problems... Easy Riders, 2026-10-08
Introducing ChatGPT for Dishwashing Joma Tech, 2026-10-08
The Quasi-Riemann Hypothesis, explained Perplexity, 2026-10-08
Math 2.0: Terence Tao responds to the recent OpenAI flood of proofs Dr. Samuel Allen Alexander, 2026-10-08
OpenAI’s 722 AI Math Papers, and Why Terence Tao Is Uneasy Simply AI, 2026-10-08
Math Field SHOOK After Open AI SOLVES HUNDREDS Of Problems, ITS OVER Timcast IRL, 2026-10-08
OpenAI releases 700 math papers. AI takes over science? | You&AI TVP WORLD, 2026-10-08

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