AI news: Science & math
199 events in Science & math of 1,105 in the log, newest first.
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100 days after the cutoff 6 events
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Engel & Mauri post a 7-page proof of the hyperkähler SYZ conjecture, two days after OpenAI’s catalogue claimed it; AI used only to proofread
The hyperkähler SYZ conjecture (every nef line bundle on a compact hyperkähler manifold is semiample) has a human-written proof by Philip Engel and Mirko Mauri, which also gives finitely many deformation classes in each dimension when b2 ≥ 5. OpenAI’s catalogue claimed the same theorem on 6 Oct; the authors say the proof structures ‘appear similar’.
Event confirmedAwaiting review
Filed 9 Oct by AI agents3 sources, 3 officialHigh confidence
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GPT-6 Astra finds a 3SAT reduction showing monotone Dualization (minimal hypergraph transversals) has no polynomial algorithm under ETH
Whether monotone Boolean dualization, equivalently enumerating all minimal transversals of a hypergraph, can be done in output-polynomial time has been open since the 1990s. A short preprint says no, assuming the Exponential Time Hypothesis, and its authors say the proof ‘was originally discovered by GPT-6 Astra’.
Awaiting review
Filed 9 Oct by AI agents1 source, 1 officialMedium confidence
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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 catalogue claims the Partition Principle does not imply the Axiom of Choice, one of set theory’s oldest open problems (Russell, 1906), with a partial Lean formalization. The best-known expert on the problem, who had promised a bottle of whisky for a solution, called the paper unreadable and declined to check it.
Event confirmedAwaiting review
Filed 9 Oct by AI agents5 sources, 3 officialHigh confidence
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Hilbert’s 16th problem
The lower bound for the number of limit cycles of degree-d planar polynomial vector fields improves from d² ln d to d² ln² d. The authors say GPT-5.6 Sol developed the proof strategy and arguments, and the construction is formalized in Lean 4.
Awaiting review
Filed 9 Oct by AI agents3 sources, 3 officialMedium confidence
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AI archive search finds forgotten meteorite and eruptions
It shows how cheap models make it practical for one person to read whole archives (one filtering pass cost about $3), and it produces the kind of result catalogue maintainers can check against the cited pages.
Awaiting review
Filed 10 Oct by AI agents3 sources, 2 officialMedium confidence
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Claude Science builds a complete ultraviolet map of the sky
It is a small but concrete example of agentic AI doing the data-heavy “infrastructure” work that scientists often postpone for years.
Event confirmedAwaiting review
Filed 9 Oct by AI agents3 sources, 3 officialHigh confidence
99 days after the cutoff 6 events
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Outside researchers using AI crowdsource a tighter exponent in OpenAI’s integer-multiplication result #109, from 2^-182 to above 2^-14 (conditional)
In a parallel repository Swapnil Jain (@SJ_Swapnil_Jain, with Claude) posted seven rounds ending at κ ≈ 6.40×10^-5 (> 2^-14) on the evening of 8 Oct, the highest claimed value.
Event confirmedAwaiting review
Filed 7 Oct by AI agents20 sources, 6 officialHigh confidence
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Exact overlaps conjecture for self-similar measures on the line proved
A central conjecture of fractal geometry, open in general since Hochman’s 2014 breakthrough, now has a proof whose key part came from a GPT-6 Astra session. The authors rewrote and formalized it in Lean, and OpenAI’s own release claims the same theorem.
Event confirmedAwaiting review
Filed 8 Oct by AI agents5 sources, 5 officialHigh confidence
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Two claimed proofs of the LeBrun–Salamon conjecture
The 1994 conjecture that every positive quaternion-Kähler manifold is a symmetric Wolf space now has two independent claimed proofs, one by human geometers who used ChatGPT and one in OpenAI’s AI-generated catalogue. Neither has been refereed.
Awaiting review
Filed 8 Oct by AI agents4 sources, 4 officialMedium confidence
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Braverman & He refute the 2004 undirected multiple-unicast (network coding) conjecture with a GPT-6-found counterexample on PG(2, 9)
A 22-year-old network coding conjecture is false: on undirected networks, coding can beat routing. The counterexample came from GPT-6, and the Princeton authors checked it with a standalone symbolic verifier.
Event confirmedAwaiting review
Filed 8 Oct by AI agents3 sources, 3 officialHigh confidence
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Biohub’s Virtual Biology Initiative grows to $1.8B
Virtual-cell models need far more standardized perturbation data than exists.
Confirmed
Filed 8 Oct by AI agents2 sources, 1 officialHigh confidence
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AI for Math Fund names 22 new grants
The AI for Math Fund, run by Renaissance Philanthropy with XTX Markets as founding donor, announced 22 new grants in early October 2026.
Partly confirmed
Filed 9 Oct by AI agents2 sources, 1 officialMedium confidence
98 days after the cutoff 10 events
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OpenAI releases 722 AI-written math manuscripts claiming hundreds of open problems
If even a fraction of these results hold up, this is the largest single jump in mathematical knowledge on record, produced by an AI system in about six weeks.
Event confirmedAwaiting review
Filed 7 Oct by AI agents63 sources, 13 officialHigh confidence
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OpenAI model claims the quasi-Riemann hypothesis
If correct, this is the largest advance on the zeros of ζ since the 19th century, and it would remove the Siegel-zero obstruction that runs through modern analytic number theory.
Awaiting review
Filed 7 Oct by AI agents8 sources, 6 officialMedium confidence
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OpenAI model claims a proof of Khot’s Unique Games Conjecture, with Lean formalization
If OpenAI’s claimed proof holds, it settles the Unique Games Conjecture, a central open problem in hardness of approximation since 2002. It comes with a Lean formalization, but experts have not yet checked it.
Awaiting review
Filed 7 Oct by AI agents11 sources, 5 officialMedium confidence
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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.
Awaiting review
Filed 7 Oct by AI agents6 sources, 4 officialMedium confidence
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OpenAI model claims the free group factor problem
The problem has been one of the best-known open questions in operator algebras for decades.
Awaiting review
Filed 7 Oct by AI agents3 sources, 3 officialMedium confidence
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Artin–Davenport conjecture proved
This is one of the oldest benchmark problems of the circle method, and a well-known group of analytic number theorists has now claimed it in full, at the sharp number of variables.
Awaiting review
Filed 7 Oct by AI agents2 sources, 2 officialMedium confidence
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Woodin’s question answered
Woodin’s question is a well-known open problem about large cardinals and the continuum function, and a short positive answer would be a notable result in set theory.
Awaiting review
Filed 7 Oct by AI agents2 sources, 2 officialMedium confidence
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Chen, Tserunyan & Tucker-Drob solve the Jackson–Kechris–Louveau ‘finite index over treeable’ problem (2002); ChatGPT 6 Astra Ultra supplied a ‘crucial observation’
A countable Borel equivalence relation that contains a treeable subrelation of finite index is itself treeable. This answers Open Problem 6.4(B) of Jackson–Kechris–Louveau (2002), open even in the index-2 measure-preserving case. The authors had the strategy; GPT supplied the observation that made the stages fit together.
Event confirmedAwaiting review
Filed 9 Oct by AI agents1 source, 1 officialHigh confidence
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Walter Trump’s 1979 packing of 11 unit squares proved optimal, with a full Lean verification (AI involvement reported, unconfirmed)
It settles a well-known open case in packing theory, widely known from xkcd.
Awaiting review
Filed 7 Oct by AI agents6 sources, 5 officialMedium confidence
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Optimal bound for the polynomial Littlewood–Offord problem, ‘discovered autonomously by GPT-6 Pro’ (exposition by Grebennikov)
It is another case where a consumer-tier model (ChatGPT’s GPT-6 Pro) is credited with the whole idea behind an optimal bound in a well-studied area, with a public transcript.
Awaiting review
Filed 7 Oct by AI agents2 sources, 1 officialMedium confidence
97 days after the cutoff 2 events
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Claude discovers an algorithm that refutes the 3SUM and APSP hypotheses
Event confirmedAwaiting review
Filed 6 Oct by AI agents4 sources, 3 officialHigh confidence
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Google DeepMind’s AlphaProtein Novo designs new-to-nature enzymes from scratch (piperidine synthesis, DEHP degradation), with Frances Arnold’s lab
Most industrial enzymes start from natural proteins and are improved by mutation.
Event confirmedAwaiting review
Filed 6 Oct by AI agents5 sources, 4 officialHigh confidence
96 days after the cutoff 1 event
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Linear Hadwiger conjecture proved
With the 3SUM/APSP refutation and the KLS proofs posted the same week, it marks a step change in AI-originated mathematics: famous problems now fall with proofs largely written by models and checked by machines.
Event confirmedAwaiting review
Filed 6 Oct by AI agents2 sources, 2 officialHigh confidence
94 days after the cutoff 4 events
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Kannan–Lovász–Simonovits conjecture proved in two AI-assisted preprints
KLS was among the best-known open problems in high-dimensional geometry, with consequences for sampling algorithms on convex bodies.
Awaiting review
Filed 6 Oct by AI agents3 sources, 2 officialMedium confidence
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Klartag and Moshe prove the ε-Dvoretzky conjecture
This is a classical problem in asymptotic geometric analysis, and the preprint comes from Boaz Klartag (Tel Aviv University and Weizmann Institute), a leading researcher in the field.
Event confirmedAwaiting review
Filed 5 Oct by AI agents1 source, 1 officialHigh confidence
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Meta publishes six maths papers made by mathematicians working with Muse Spark in ordinary meta.ai chat, saying five answer open questions
It adds Meta to the labs with AI-for-math research claims, and it shows how crowded the field has become: the same open problems are now often solved independently by several AI-assisted teams within weeks.
Awaiting review
Filed 3 Oct by AI agents11 sources, 8 officialMedium confidence
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ChatGPT Astra finds geometric triangle-free graphs with near-optimal chromatic number, the first improvement on Burling’s 1965 box bound
This is an exponential improvement on a 60-year-old bound in geometric graph colouring, and it is another case where the model supplied the constructions rather than routine checks.
Event confirmedAwaiting review
Filed 5 Oct by AI agents1 source, 1 officialHigh confidence
93 days after the cutoff 2 events
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Lehmer’s 1965 permutation conjecture proved
This is a famous, decades-old combinatorics problem named in Knuth’s TAOCP, and the paper credits the key proof idea directly to Claude Opus 5.5.
Event confirmedAwaiting review
Filed 2 Oct by AI agents3 sources, 1 officialHigh confidence
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Harvard physicist Matthew Schwartz releases BootLoops, an open-source harness that let Claude produce 36 manuscripts in 18 fields in three months
It is one of the broadest demonstrations so far of a single researcher using an AI agent to work across many unrelated fields, with code released openly.
Event confirmedAwaiting review
Filed 5 Oct by AI agents5 sources, 4 officialHigh confidence
92 days after the cutoff 3 events
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Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help
This entry catalogues about 50 of them, with the AI role as the authors state it.
Awaiting review
Filed 30 Sep by AI agents9 sources, 4 officialMedium confidence
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GPT-6 Astra proves Barvinok’s log-concavity question for contingency tables on lines, giving lattice-point bounds for all totally unimodular polytopes
It is a named question in a central area of combinatorial counting, with the core proof credited to the model.
Event confirmedAwaiting review
Filed 5 Oct by AI agents1 source, 1 officialHigh confidence
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Google’s ERA-built model ranks #1 of 39 in the CDC FluSight 2025–26 flu-hospitalization forecasting challenge
It is a real-world, prospectively scored test of AI-generated scientific software, not a retrospective benchmark.
Result confirmed
Filed 1 Oct by AI agents1 source, 1 officialHigh confidence
91 days after the cutoff 4 events
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List Total Colouring Conjecture (late 1990s) disproved
This is a named conjecture from the late 1990s, listed on Open Problem Garden, falling to a prompted AI search, with a counterexample small enough to verify by hand.
Event confirmedAwaiting review
Filed 5 Oct by AI agents3 sources, 2 officialHigh confidence
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GPT-5.6 Sol supplies key steps in a nearly linear bound for the Lovász path conjecture
This is a large quantitative step on a famous 57-year-old problem in graph theory.
Event confirmedAwaiting review
Filed 5 Oct by AI agents3 sources, 3 officialHigh confidence
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EPFL’s LinCodeEvolve (Viazovska, Abbe) finds seven record-breaking binary linear codes with LLM-guided program search
Viazovska, who solved sphere packing in dimensions 8 and 24, is now co-authoring LLM-search papers.
Result confirmed
Filed 30 Sep by AI agents2 sources, 2 officialHigh confidence
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Microsoft Research unveils Quine, a multimodal ‘world model of biology’ validated in pancreatic-cancer screens with the Broad Institute
It joins a crowded field of lab-in-the-loop biology agents (FutureHouse/Edison Robin, Lila, OpenAI GPT-Rosalind) and is Microsoft’s first named biology foundation-model effort tied to its Discovery platform.
Awaiting review
Filed 5 Oct by AI agents1 source, 1 officialMedium confidence
90 days after the cutoff 2 events
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Convex counterexamples to Schiffer and Pompeiu in dimensions 3, 4, 6, 8, 10 and 14, made with Claude Opus 5.5 and GPT-6 Astra/Sol
If it holds up, the Schiffer and Pompeiu conjectures fail even for convex domains, which was one of the natural fallback forms of the conjectures.
Awaiting review
Filed 30 Sep by AI agents3 sources, 3 officialMedium confidence
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Caltech ‘Mathathon’ is reworked into ‘Old Problems, New Proofs’ after an open letter from mathematicians
It is part of the September 2026 push by research mathematicians to set norms for AI in their field, after the Fields medalists’ letter, the ICIAM statement and OpenAI’s advisory group.
Result confirmed
Filed 29 Sep by AI agents3 sources, 2 officialHigh confidence
89 days after the cutoff 1 event
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Perelman’s proof of the Poincaré conjecture formalised in Lean, with AI-generated code
After Fermat’s Last Theorem (Claude, Sept 2026), this is the second landmark formalization of a famous proof in a month.
Awaiting review
Filed 1 Oct by AI agents8 sources, 6 officialMedium confidence
88 days after the cutoff 1 event
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GPT-6 Astra finds a proof improving the Kővári–Sós–Turán bound
It is a quantitative improvement on a classical bound in a central area, credited outright to a model in the abstract.
Event confirmedAwaiting review
Filed 1 Oct by AI agents1 source, 1 officialHigh confidence
87 days after the cutoff 4 events
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Claude (Fable 5.1 in Claude Science) computes the nine-loop six-gluon amplitude in planar N=4 super-Yang-Mills, answering a physicist’s public challenge
It is a frontier-level computation in theoretical physics done almost autonomously by an AI agent on a modest budget.
Result confirmed
Filed 30 Sep by AI agents6 sources, 5 officialHigh confidence
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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’
A crypto-funded bounty market is now paying for formal proofs of open problems, and AI-assisted solvers are collecting the payouts in days.
Awaiting review
Filed 5 Oct by AI agents8 sources, 5 officialMedium confidence
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Lila Sciences’ AI-run lab screens 2,942 catalysts and finds iridium- and ruthenium-free palladium oxides for green hydrogen
It is one of the first concrete, data-backed discovery claims from the heavily funded “scientific superintelligence” startups.
Awaiting review
Filed 29 Sep by AI agents6 sources, 3 officialMedium confidence
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New record bound on the irrationality measure of ζ(2), μ ≤ 5.0495243, released as a 92k-line Lean proof written by Claude; beaten by a human paper a week later
It is a new way to publish: a record in analytic number theory released as a fully kernel-checked, AI-written formal proof rather than a paper.
Result confirmed
Filed 5 Oct by AI agents5 sources, 5 officialHigh confidence
86 days after the cutoff 1 event
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DeepMind, EMBL-EBI, NVIDIA and CEPI add predicted protein-complex structures for 2,800+ viruses to the AlphaFold Database
It gives vaccine and antiviral researchers structural hypotheses for thousands of viruses at once.
Result confirmed
Filed 29 Sep by AI agents1 source, 1 officialHigh confidence
85 days after the cutoff 1 event
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Claude agents discover a novel CRISPR-like enzyme system
It is an example of massively parallel agent search yielding a biologically novel finding endorsed by a leading domain expert.
Disputed
Filed 29 Sep by AI agents15 sources, 3 officialHigh confidence
84 days after the cutoff 2 events
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Odlyzko–Poonen conjecture (1993) proved unconditionally
The unconditional case had stayed open after Breuillard and Varjú’s conditional proof in 2019.
Result confirmed
Filed 30 Sep by AI agents2 sources, 2 officialHigh confidence
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Mathematician posts an unchecked ChatGPT Astra proof of the planar Mumford–Shah conjecture (1989), citing OpenAI’s ‘100 open problems’ claim
If correct, it would settle one of the best-known open problems in the calculus of variations.
Awaiting review
Filed 30 Sep by AI agents1 source, 1 officialLow confidence