As of: 2026-10-10 14:45 CEST.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code). Human editor: Adam Bicz.
Canonical page: https://postcutoff.com/news/science/

# AI news: Science & math

199 events in Science & math of 1,105 in the log, newest first. Page 1 of 4, 50 events per page, grouped by the day each event happened.

## Thursday 8 October 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 proofread](https://postcutoff.com/e/2026-10-08-hyperkahler-syz-conjecture-engel-mauri/) (Science & math; University of Illinois Chicago, Université Paris Cité, OpenAI; major). 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'. Source: https://arxiv.org/abs/2610.12277
- [GPT-6 Astra finds a 3SAT reduction showing monotone Dualization (minimal hypergraph transversals) has no polynomial algorithm under ETH](https://postcutoff.com/e/2026-10-08-dualization-eth-lower-bound-gpt-6-astra/) (Science & math; Hokkaido University, Okayama University, Hosei University, OpenAI; major). 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'. Source: https://arxiv.org/abs/2610.11473
- [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'](https://postcutoff.com/e/2026-10-08-karagila-openai-partition-principle/) (Science & math; OpenAI). 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. Source: https://github.com/openai/math/blob/main/CONTENTS.md
- [Hilbert's 16th problem](https://postcutoff.com/e/2026-10-08-hilbert-number-lower-bound-gpt-5-6-sol-lean/) (Science & math; Chinese Academy of Sciences, OpenAI). 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. Source: https://arxiv.org/abs/2610.12218
- [AI archive search finds forgotten meteorite and eruptions](https://postcutoff.com/e/2026-10-08-antiquity-ai-archive-search-meteorite-rhinos/) (Science & math; Anthropic, TypeSafe AI). 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. Source: https://jessewaites.com/blog/post/i-pointed-ai-at-400-years-of-archives/
- [Claude Science builds a complete ultraviolet map of the sky](https://postcutoff.com/e/2026-10-08-claude-science-complete-uv-sky-map/) (Science & math; Anthropic, Johns Hopkins University). It is a small but concrete example of agentic AI doing the data-heavy "infrastructure" work that scientists often postpone for years. Source: https://www.anthropic.com/research/the-missing-map-of-the-sky

## Wednesday 7 October 2026

- [Outside researchers using AI crowdsource a tighter exponent in OpenAI's integer-multiplication result #109, from 2^-182 to above 2^-14 (conditional)](https://postcutoff.com/e/2026-10-07-colkitt-codex-integer-multiplication-exponent/) (Science & math; Independent researchers, OpenAI; major). 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. Source: https://github.com/CrocSwap/integer-mult-bounds
- [Exact overlaps conjecture for self-similar measures on the line proved](https://postcutoff.com/e/2026-10-07-exact-overlaps-conjecture-gpt-6-astra/) (Science & math; University College London, Institute for Advanced Study, OpenAI; major). 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. Source: https://arxiv.org/abs/2610.10511
- [Two claimed proofs of the LeBrun–Salamon conjecture](https://postcutoff.com/e/2026-10-07-lebrun-salamon-conjecture-proof/) (Science & math; Chongqing University of Technology, OpenAI; major). 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. Source: https://arxiv.org/abs/2610.10410
- [Braverman & He refute the 2004 undirected multiple-unicast (network coding) conjecture with a GPT-6-found counterexample on PG(2, 9)](https://postcutoff.com/e/2026-10-07-multiple-unicast-conjecture-false-gpt-6/) (Science & math; Princeton University, OpenAI; major). 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. Source: https://arxiv.org/abs/2610.10108
- [Biohub's Virtual Biology Initiative grows to $1.8B](https://postcutoff.com/e/2026-10-07-virtual-biology-initiative-1-8b-doe-nih-deepmind-meta/) (Science & math; Biohub, US Department of Energy, National Institutes of Health, Google DeepMind, Isomorphic Labs, Meta). Virtual-cell models need far more standardized perturbation data than exists. Source: https://biohub.org/news/virtual-biology-initiative-expansion/
- [AI for Math Fund names 22 new grants](https://postcutoff.com/e/2026-10-07-ai-for-math-fund-2026-grants/) (Science & math; Renaissance Philanthropy, XTX Markets). The AI for Math Fund, run by Renaissance Philanthropy with XTX Markets as founding donor, announced 22 new grants in early October 2026. Source: https://renaissancephilanthropy.org/ai-for-math-fund-2026-projects

## Tuesday 6 October 2026

- [OpenAI releases 722 AI-written math manuscripts claiming hundreds of open problems](https://postcutoff.com/e/2026-10-06-openai-math-release-722-manuscripts/) (Science & math; OpenAI; historic). 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. Source: https://x.com/OpenAI/status/2107596713791767021
- [OpenAI model claims the quasi-Riemann hypothesis](https://postcutoff.com/e/2026-10-06-quasi-riemann-hypothesis-openai/) (Science & math; OpenAI; historic). 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. Source: https://github.com/davegoldblatt/openai-zeta-proof-check
- [OpenAI model claims a proof of Khot's Unique Games Conjecture, with Lean formalization](https://postcutoff.com/e/2026-10-06-unique-games-conjecture-openai/) (Science & math; OpenAI; historic). 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. Source: https://github.com/openai/math/blob/main/preprints/The-Unique-Games-Theorem-September-23-2026/paper.pdf
- [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)](https://postcutoff.com/e/2026-10-06-hodge-conjecture-cm-abelian-varieties-openai/) (Science & math; OpenAI; historic). 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. Source: https://github.com/openai/math/blob/main/history.md
- [OpenAI model claims the free group factor problem](https://postcutoff.com/e/2026-10-06-free-group-factors-isomorphism-openai/) (Science & math; OpenAI; historic). The problem has been one of the best-known open questions in operator algebras for decades. Source: https://github.com/openai/math/blob/main/preprints/An-isomorphism-of-the-free-group-factors-September-23-2026/An-isomorphism-of-the-free-group-factors-September-23-2026.pdf
- [Artin–Davenport conjecture proved](https://postcutoff.com/e/2026-10-06-artin-davenport-cubic-forms-ten-variables/) (Science & math; TU Graz, ISTA, Imperial College London, Leibniz Universität Hannover, Academia Sinica, OpenAI; historic). 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. Source: https://arxiv.org/abs/2610.08226
- [Woodin's question answered](https://postcutoff.com/e/2026-10-06-gch-above-strongly-compact-woodin-question/) (Science & math; Hebrew University of Jerusalem, OpenAI; major). 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. Source: https://arxiv.org/abs/2610.07537
- [Chen, Tserunyan & Tucker-Drob solve the Jackson–Kechris–Louveau 'finite index over treeable' problem (2002); ChatGPT 6 Astra Ultra supplied a 'crucial observation'](https://postcutoff.com/e/2026-10-06-finite-index-over-treeable-jkl-problem/) (Science & math; University of Warsaw, McGill University, University of Florida, OpenAI; major). 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. Source: https://arxiv.org/abs/2610.08986
- [Walter Trump's 1979 packing of 11 unit squares proved optimal, with a full Lean verification (AI involvement reported, unconfirmed)](https://postcutoff.com/e/2026-10-06-eleven-square-packing-optimality-lean/) (Science & math; Open-source community). It settles a well-known open case in packing theory, widely known from xkcd. Source: https://github.com/Queuingtheorydotcom/11SquaresFormalized
- [Optimal bound for the polynomial Littlewood–Offord problem, 'discovered autonomously by GPT-6 Pro' (exposition by Grebennikov)](https://postcutoff.com/e/2026-10-06-polynomial-littlewood-offord-gpt-6-pro/) (Science & math; OpenAI). 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. Source: https://arxiv.org/abs/2610.08708

## Monday 5 October 2026

- [Claude discovers an algorithm that refutes the 3SUM and APSP hypotheses](https://postcutoff.com/e/2026-10-05-claude-refutes-3sum-apsp-hypotheses/) (Science & math; Anthropic, Columbia University, MIT; historic). Source: https://arxiv.org/abs/2610.10153
- [Google DeepMind's AlphaProtein Novo designs new-to-nature enzymes from scratch (piperidine synthesis, DEHP degradation), with Frances Arnold's lab](https://postcutoff.com/e/2026-10-05-deepmind-alphaprotein-novo-enzyme-design/) (Science & math; Google DeepMind, Caltech, University of Pittsburgh; major). Most industrial enzymes start from natural proteins and are improved by mutation. Source: https://www.biorxiv.org/content/10.64898/2026.10.01.756017v1

## Sunday 4 October 2026

- [Linear Hadwiger conjecture proved](https://postcutoff.com/e/2026-10-04-linear-hadwiger-conjecture-proved-gpt-6-astra/) (Science & math; OpenAI, McGill University, ETH Zurich; historic). 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. Source: https://arxiv.org/abs/2610.05291

## Friday 2 October 2026

- [Kannan–Lovász–Simonovits conjecture proved in two AI-assisted preprints](https://postcutoff.com/e/2026-10-02-kls-conjecture-proved-ai-assisted/) (Science & math; Microsoft Research, Weizmann Institute of Science, OpenAI, Anthropic; historic). KLS was among the best-known open problems in high-dimensional geometry, with consequences for sampling algorithms on convex bodies. Source: https://arxiv.org/abs/2610.01447
- [Klartag and Moshe prove the ε-Dvoretzky conjecture](https://postcutoff.com/e/2026-10-02-epsilon-dvoretzky-conjecture-klartag-moshe/) (Science & math; Tel Aviv University, Weizmann Institute of Science, OpenAI; major). 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. Source: https://arxiv.org/abs/2610.03204
- [Meta publishes six maths papers made by mathematicians working with Muse Spark in ordinary meta.ai chat, saying five answer open questions](https://postcutoff.com/e/2026-10-02-meta-muse-spark-six-math-papers/) (Science & math; Meta). 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. Source: https://research.meta.ai/blog/solving-open-research-problems-together
- [ChatGPT Astra finds geometric triangle-free graphs with near-optimal chromatic number, the first improvement on Burling's 1965 box bound](https://postcutoff.com/e/2026-10-02-tomon-triangle-free-box-graphs-astra/) (Science & math; Umeå University, OpenAI). 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. Source: https://arxiv.org/abs/2610.03517

## Thursday 1 October 2026

- [Lehmer's 1965 permutation conjecture proved](https://postcutoff.com/e/2026-10-01-lehmer-permutation-conjecture-opus-5-5/) (Science & math; Eindhoven University of Technology, Anthropic, Harmonic; major). 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. Source: https://arxiv.org/abs/2610.01240
- [Harvard physicist Matthew Schwartz releases BootLoops, an open-source harness that let Claude produce 36 manuscripts in 18 fields in three months](https://postcutoff.com/e/2026-10-01-bootloops-claude-shaped-science/) (Science & math; Harvard University, Anthropic). 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. Source: https://www.anthropic.com/research/claude-shaped-science

## Wednesday 30 September 2026

- [Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help](https://postcutoff.com/e/2026-09-30-ai-assisted-conjecture-wave-summer-2026/) (Science & math; OpenAI, Anthropic, Google DeepMind, various mathematicians; major). This entry catalogues about 50 of them, with the AI role as the authors state it. Source: https://arxiv.org/abs/2608.24961
- [GPT-6 Astra proves Barvinok's log-concavity question for contingency tables on lines, giving lattice-point bounds for all totally unimodular polytopes](https://postcutoff.com/e/2026-09-30-barvinok-log-concavity-totally-unimodular-astra/) (Science & math; OpenAI). It is a named question in a central area of combinatorial counting, with the core proof credited to the model. Source: https://arxiv.org/abs/2609.39917
- [Google's ERA-built model ranks #1 of 39 in the CDC FluSight 2025–26 flu-hospitalization forecasting challenge](https://postcutoff.com/e/2026-09-30-google-era-flusight-flu-forecasting/) (Science & math; Google Research). It is a real-world, prospectively scored test of AI-generated scientific software, not a retrospective benchmark. Source: https://blog.google/innovation-and-ai/models-and-research/google-research/google-science-ai-flu-forecasts/

## Tuesday 29 September 2026

- [List Total Colouring Conjecture (late 1990s) disproved](https://postcutoff.com/e/2026-09-29-list-total-colouring-conjecture-false-astra/) (Science & math; OpenAI, University of Victoria; major). 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. Source: https://arxiv.org/abs/2609.38417
- [GPT-5.6 Sol supplies key steps in a nearly linear bound for the Lovász path conjecture](https://postcutoff.com/e/2026-09-29-lovasz-conjecture-nearly-linear-bound-gpt-5-6-sol/) (Science & math; OpenAI). This is a large quantitative step on a famous 57-year-old problem in graph theory. Source: https://arxiv.org/abs/2609.38135
- [EPFL's LinCodeEvolve (Viazovska, Abbe) finds seven record-breaking binary linear codes with LLM-guided program search](https://postcutoff.com/e/2026-09-29-lincodeevolve-record-binary-codes/) (Science & math; EPFL). Viazovska, who solved sphere packing in dimensions 8 and 24, is now co-authoring LLM-search papers. Source: https://arxiv.org/abs/2609.37056
- [Microsoft Research unveils Quine, a multimodal 'world model of biology' validated in pancreatic-cancer screens with the Broad Institute](https://postcutoff.com/e/2026-09-29-microsoft-quine-biology-world-model/) (Science & math; Microsoft Research, 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. Source: https://www.microsoft.com/en-us/research/blog/introducing-quine-an-ai-research-system-designed-for-the-complexity-of-biology/

## Monday 28 September 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/Sol](https://postcutoff.com/e/2026-09-28-schiffer-pompeiu-convex-higher-dimensions/) (Science & math; Jizhou Guo). 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. Source: https://arxiv.org/abs/2609.35419
- [Caltech 'Mathathon' is reworked into 'Old Problems, New Proofs' after an open letter from mathematicians](https://postcutoff.com/e/2026-09-28-mathathon-joint-statement/) (Science & math; Caltech, XTX Markets, SAIR). 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. Source: https://terrytao.wordpress.com/2026/09/28/joint-statement-about-mathathon/

## Sunday 27 September 2026

- [Perelman's proof of the Poincaré conjecture formalised in Lean, with AI-generated code](https://postcutoff.com/e/2026-09-27-poincare-conjecture-lean-formalization/) (Science & math; UC San Diego, Cornell University, Princeton University; major). After Fermat's Last Theorem (Claude, Sept 2026), this is the second landmark formalization of a famous proof in a month. Source: https://arxiv.org/abs/2609.33842

## Saturday 26 September 2026

- [GPT-6 Astra finds a proof improving the Kővári–Sós–Turán bound](https://postcutoff.com/e/2026-09-26-mubayi-zarankiewicz-astra/) (Science & math; University of Illinois Chicago, OpenAI). It is a quantitative improvement on a classical bound in a central area, credited outright to a model in the abstract. Source: https://arxiv.org/abs/2609.32937

## Friday 25 September 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 challenge](https://postcutoff.com/e/2026-09-25-claude-nine-loop-amplitude-n4-sym/) (Science & math; Anthropic; major). It is a frontier-level computation in theoretical physics done almost autonomously by an AI agent on a modest budget. Source: https://zenodo.org/records/22800071
- [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'](https://postcutoff.com/e/2026-09-25-conjectures-io-erdos-green-bounty-solves/) (Science & math; Conjectures.io, OpenAI). A crypto-funded bounty market is now paying for formal proofs of open problems, and AI-assisted solvers are collecting the payouts in days. Source: https://conjectures.io/results
- [Lila Sciences' AI-run lab screens 2,942 catalysts and finds iridium- and ruthenium-free palladium oxides for green hydrogen](https://postcutoff.com/e/2026-09-25-lila-ai-lab-palladium-oer-catalysts/) (Science & math; Lila Sciences). It is one of the first concrete, data-backed discovery claims from the heavily funded "scientific superintelligence" startups. Source: https://www.lila.ai/news/how-an-ai-run-lab-cracked-open-green-hydrogens-catalyst-problem
- [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](https://postcutoff.com/e/2026-09-25-zeta2-irrationality-measure-claude-lean/) (Science & math; Anthropic). 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. Source: https://github.com/qedbook/zeta2-irrationality-measure

## Thursday 24 September 2026

- [DeepMind, EMBL-EBI, NVIDIA and CEPI add predicted protein-complex structures for 2,800+ viruses to the AlphaFold Database](https://postcutoff.com/e/2026-09-24-viral-protein-complex-structures-alphafold-db/) (Science & math; Google DeepMind, EMBL-EBI, NVIDIA, CEPI). It gives vaccine and antiviral researchers structural hypotheses for thousands of viruses at once. Source: https://blogs.nvidia.com/blog/open-protein-dataset/

## Wednesday 23 September 2026

- [Claude agents discover a novel CRISPR-like enzyme system](https://postcutoff.com/e/2026-09-23-claude-discovers-novel-enzyme-system/) (Science & math; Anthropic; major). It is an example of massively parallel agent search yielding a biologically novel finding endorsed by a leading domain expert. Source: https://www.anthropic.com/news/claude-discovers-novel-enzyme-system

## Tuesday 22 September 2026

- [Odlyzko–Poonen conjecture (1993) proved unconditionally](https://postcutoff.com/e/2026-09-22-odlyzko-poonen-conjecture-proved/) (Science & math; Constantin Kogler, OpenAI; major). The unconditional case had stayed open after Breuillard and Varjú's conditional proof in 2019. Source: https://arxiv.org/abs/2609.26771
- [Mathematician posts an unchecked ChatGPT Astra proof of the planar Mumford–Shah conjecture (1989), citing OpenAI's '100 open problems' claim](https://postcutoff.com/e/2026-09-22-mumford-shah-conjecture-astra-claim/) (Science & math; Francesco Deangelis, University of Münster, OpenAI; major). If correct, it would settle one of the best-known open problems in the calculus of variations. Source: https://arxiv.org/abs/2609.26732

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