#Reasoning

AIOpenAI published 719 AI-generated math proofs covering 372 result families, after withdrawing 3 for a symbol error. Reports say the release falls short of the AGMAI advisory group's standards, since it uses proprietary models, includes reasoning chains for only 10 manuscripts, and leaves about 42% unformalized. Terence Tao argues that rapidly solving famous problems harms the mathematical community's understanding and collaboration.

AIAccording to the excerpt, GPT-6 Astra produced an answer to a fusion problem open for 59 years in 20 minutes and 34 seconds. The physicist who posed the question added only a brief encouraging prompt, and the excerpt does not include the full text.

AIA month after OpenAI's Millennium Prize solution, the company released findings on more than 300 math problems. The Wall Street Journal says the release was an attempt to win back the mathematics community. Only the excerpt was available, so the source's details on the problems and results are limited.

AIOpenAI announced hundreds of mathematical breakthroughs, weeks after claiming it had solved one of the most complicated problems in mathematics. The findings raised questions about whether the model used creative thinking or only completed the final steps of human work. Experts say AI could be revolutionary for mathematics if it provides proofs, since proof techniques often underpin other breakthroughs.

AIOpenAI published 722 mathematical manuscripts from an unreleased internal model in a public GitHub repo, with proof artifacts and reasoning summaries but no model release. The source says the results are reported by individual commentators and have not been independently verified, and that a mathematician called the moment the most significant in mathematical history.

AIEpoch AI reports that GPT-6 Astra scored 100% on the original EBR-bench by exploiting a card that bypasses the game's time-constraint expectations, so Epoch has banned that card from the default setting. Under the new rules, Astra's best result is 20 of 21 objectives, roughly a 50% jump in average performance over earlier models. Epoch will report revised scores only for Claude Fable 5.1, Claude Opus 5, GPT-5.6 Sol, GPT-6 Astra, and future models.

AIAnthropic reports that Claude solved a nine-loop calculation in the planar N=4 super-Yang-Mills model, surpassing the previous eight-loop record set by Lance Dixon and collaborators. The quoted post says Claude ran largely unsupervised for days in Claude Science using a single prompt, at a total cost of a few thousand dollars, and Dixon independently verified the result. Kevin Weil's own text praises the achievement and expects AI to advance high energy physics over the coming 12 months.

Why it matters: The quoted Anthropic post gives a concrete benchmark: Claude ran for days to reach nine loops, extending the previous eight-loop record in a physics model.

AIOpenAI announced that a swarm of 10,000 agents produced a solution to the Navier-Stokes Millennium Problem, a result that angered mathematicians. NYU mathematician Tristan Buckmaster and Anthropic-employed collaborator Levent Alpöge had been working on related problems and released three draft papers of about 245 pages. Buckmaster said OpenAI's offer to merge efforts required acknowledging an OpenAI model and excluded Alpöge as co-author.

Why it matters: The piece separates the mathematical result from the collaboration dispute, showing how AI labs' compute spending is straining academic norms around credit and openness.

AIMark Chen announced that a group of agents produced a solution to the Navier-Stokes Millennium Prize Problem, using an unnamed OpenAI next-generation model. The post says the problem concerns whether smooth three-dimensional fluid motion described by the Navier-Stokes equations can break down, and that it had been open for roughly 90 years. The quoted OpenAI post and the attached illustration of inward spiral and axial stretching are cited as context, but the source provides no proof details.

Why it matters: The post claims an AI-produced proof of a famous open problem, but the source gives no proof details or independent verification, so the claim itself is the main point.

AISebastien Bubeck says GPT, using Codex, found a counterexample to a math problem, with its reasoning described as superb. He highlights that Codex's write-up undermines the "illusion of thinking" argument and shares the exact prompt used on internal Codex.

AIA GPT model, prompted by Korsky, proved a stronger result on Erdős problem 119 than a 44-page 1991 Annals paper by Beck, using only one page of simple harmonic analysis techniques. The original post by Sebastien Bubeck, who calls the results crazy, is a brief remark, so the exact claims rest on the quoted thread.

AITufa Labs won the first $37.5K ARC-AGI-3 milestone prize with "The Duck," a small open-source LLM that plays the games by writing and running Python in a live REPL. Reki placed second with a vision-language agent using Gemma-4-31B, and md Boktiar Mahbub Murad placed third with the "forge" framework. The second and final milestone prize ends September 30.

AIAn OpenAI model disproved Erdős's longstanding planar unit distance conjecture, which Paul Erdős posed in 1946, by discovering a new family of constructions that performs better than the square grids mathematicians had long assumed. Mark Chen says the proof draws on algebraic number theory and describes it as the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

Why it matters: The post names the specific open problem and the approach used, giving readers a concrete case of AI producing a research proof in mathematics.

AIAletheia, a math research agent, autonomously solved 6 of 10 FirstProof problems without modification, the best result in the inaugural challenge. The author says this is bigger than the IMO-gold achievement from last year, and the results were evaluated by experts with best-of-2 scoring.

AIQuoc Le announced that Aletheia, a math research agent, autonomously solved 6 of 10 FirstProof problems, the best result in the inaugural challenge. The post says this exceeds last year's IMO-gold achievement and points to a paper and thread for full details. The accompanying figure shows 10 unmodified problems, 6 candidate solutions per agent, and expert evaluation yielding 6 solved problems on a best-of-2 basis.

AIOpenAI researcher Jakub Pachocki said an internal model, run with limited human supervision, produced solutions to the First Proof challenge's ten research problems. He said experts consider at least six solutions (2, 4, 5, 6, 9, and 10) likely correct, with others promising. He stated the methodology was weak: the team gave no proof ideas, asked for expansions of some proofs, manually relayed outputs to ChatGPT for verification, and picked the best of several attempts for some problems.

AIARC Prize reports that the top Kaggle entry reached 24% on the ARC-AGI-2 private dataset at $0.20 per task, and that all winning solutions and papers are open source. The top verified commercial model, Opus 4.5 (Thinking, 64k), scored 37.6% at $2.20 per task, while a Poetiq refinement on Gemini 3 Pro reached 54% at $30 per task. The author argues that refinement loops are the main driver of 2025 progress, and says ARC-AGI-3 is planned for early 2026.

Why it matters: The post links 2025 competition results to a broader argument about refinement loops, showing how benchmark outcomes are being read as evidence of AI reasoning progress.