#Reasoning

AIOpenAI announced last month that it had produced an AI-generated proof for the Navier-Stokes problem, a result the source says is hard even for experts to parse. The source also says LLMs now tackle math problems that have stumped humans for decades, while teachers struggle to keep up with AI-completed homework.

AIAI systems are now solving math problems faster than humans can verify the answers, according to the source's headline. The source text is limited to a brief note that OpenAI's math breakthroughs may trigger an identity crisis for mathematicians.

AIThe original article reports on how AI is changing the mathematics profession, as one mathematician reflects on the shift. The provided text is limited to that single sentence, so no specific models, benchmarks, or figures can be verified.

AIArtificial Analysis reports that generating more output tokens does not necessarily yield a higher score. GPT-6 Astra (max) scored 8.6% using about 81k output tokens per task, while Grok 4.7 (xhigh) used roughly 180k yet scored lower. Three Claude models produced the most output tokens, about 202k to 562k per task, but scored between 2.8% and 6.4%.

AIEthan Mollick notes that some OpenAI proofs have sparked rapid iterative advances from a wide community of collaborators amid debate over their implications for mathematics. A related post reports that a collaborative effort tightened the bound κ from 2⁻¹⁸² to 2⁻¹⁵, a roughly 500-thousand-fold improvement on the previous result.

AILewis Tunstall quotes Kyle Cranmer's post about a paper by Nate Gunnarsson on a non-perturbative approach to chiral fermions in the Standard Model, extending Lüscher's abelian result. The paper's acknowledgments state that OpenAI's GPT-6 Astra model was essential, proposing refinement strategies, writing rewrites of the proof, and carrying out Lean verification.

AIStanford HAI associate directors Risa Wechsler and Russ Altman, speaking at a Stanford orientation, argued that AI agents can deepen scientific research but must be paired with interdisciplinary collaboration. They stressed rigorous, reproducible methods and clearly measured uncertainty, since convincing AI answers are not enough. They also said labs must weigh agent costs and preserve mentorship so that automation supports human participation in research.

AIBoris Power, who owns the OpenAI account posting this, responded to a third update on OpenAI problem #109, integer multiplication. The quoted update reports a tightened bound of κ > 2⁻¹⁸, improved from κ = 2⁻¹⁸², with an exact witness of 4.19 × 10⁻⁶.

AITypeSafe AI released Jev, a "decision model" that returns a floating-point probability rather than text, which can answer yes/no and multiple-choice questions and score content against criteria. The source cites two browser-extension examples: semantic Ctrl+F search and webpage quality scoring. Simon Willison's criticism is that Jev offers no explanation for its numbers.

AIEthereum researcher Justin Drake warned on X that AI-assisted math could, in the worst case, break the signature system used by crypto wallets within months, and urged a "bunker mode" in which users move funds to addresses that have never signed a transaction. Vitalik Buterin agreed but cautioned against moving too fast, saying he has lost more money to botched migrations than to hacks. No one has yet broken the current ECDSA signature scheme in practice.

AIGergely Orosz argues that holding crypto exposes owners to risks from mathematical breakthroughs, key theft, or kidnapping that could drain wallets. He concludes the simplest answer is not to hold crypto at all.

AIScott Aaronson reports, based on his sources, that some AI companies have begun discreetly investigating whether their latest internal models can break important cryptographic protocols and primitives. He notes that cryptography is conspicuously absent from OpenAI's list of 376 papers, and the quoted post adds that the US government has censored academic quantum cryptanalysis results.

AIFrançois Chollet compares AI progress to human learning, noting that 1980s research found programming training improves coding but does not transfer to general reasoning. He argues general intelligence is a fundamental brain property rather than a trainable skill, since domain practice improves only that domain. The post is framed as background for his question whether AI's jagged frontier, driven by math and code via RLVR, reflects general capability or continued human-data bottlenecks.

AIScott Aaronson describes an AI-generated proof of the UGC conjecture that invents an entirely new, bizarre code with a noise test and a crazy recursive construction. He notes that mathematicians increasingly encounter this kind of "alien craziness" and predicts it will become routine.

AIEthan Mollick shares early first-hand accounts from mathematicians grappling with hundreds of AI proofs released by OpenAI. He highlights problems solved in ways no human has yet understood, raising questions about what it means to know something. The linked Scott Aaronson post quotes a researcher, Dana, describing the proofs as unclear and hard to read without AI help, with some possibly verified by a Lean certificate.

AINoam Brown says LLMs have crossed a threshold by surpassing top human experts on some research problems, a jump that makes the recent surge in math results feel sudden. He expects breakthroughs in other domains to follow as models keep improving, though capabilities remain jagged and often still weaker than humans.

AIReplit CEO Amjad Masad argues that mathematics will be the first field AI conquers. He reasons that the purer a field is, the easier it becomes for AI to crack.

AIThe post argues that AI models, lacking any information about SDPO, had to either independently invent something similar or devise another technique with comparable benefits under the same constraints. The post does not identify the specific models or experiment involved.

AIThe post argues that companies are increasingly recognizing business opportunities from reinforcement learning, since many real-world tasks need specialized models, harnesses, and data flywheels rather than AGI. It predicts a new post-training era led by full-stack AI companies, though it provides no concrete figures or raw data to support the claim.

AIGary Marcus argues that OpenAI's math announcement omits the procedure, the model architecture, and the failure rate, so its generalizability cannot be assessed. He says it could be a step toward AGI or a Lean-based verification trick in a verifiable domain, and the initial report cannot distinguish the two. The post includes a quoted Terence Tao post that shares a satirical press release about a fictional film-endings repository.

AIMark Chen says the Navier-Stokes achievement matters more for the figure it shows than for the problem itself, representing a decade of mathematical progress in a single week. He says he is eager to apply these tools to life sciences, the building of OpenAI's next models, and alignment research.

AIDeedy argues LLMs have made substantial progress on four of the seven Millennium Prize problems, including a claimed Navier-Stokes result, conditional on verification. He says OpenAI's results averaged only 3 hours of thinking compute on unreleased models. He concludes that by most definitions of AGI, we have already achieved it.

AISantiago argues prompt engineering was never a real discipline and will vanish as models improve. He predicts future models will understand natural communication, so the skill will simply become communication skills.

AIOpenAI has released a document with over 300 math solutions, many of potentially historic importance, at varying stages of verification. The author argues that the results leave human mathematicians as spectators, with AI now doing the discovery work.

AIOpenAI released 722 mathematical manuscripts in 372 families, produced by an unreleased frontier model, with the average result taking the equivalent of three hours of ChatGPT Pro thinking. The author notes many results are verified in Lean but not all, and suggests mathematics could divide into vast machine-verified work and a compressed human 'effective theory' that people can actually understand.

AILLMs have many dimensions that can be scaled. But OpenAI's recent underperformance tells us that verifier scaling currently appears to be the most boring, slowest, and worst-experience way to scale.

AIJake Boggan, a Hacker News commenter, reacted to reports that Barnette's Conjecture, a graph theory problem he spent years studying, has been proven, as listed in openai/math problem 180. He said he had spent thousands of hours on the problem and had briefly believed he solved it last summer. He described the news as bittersweet.

AIYuchen Jin notes that in 2024 GPT-4o famously got "Is 9.9 > 9.11?" wrong, while AI now appears poised to solve the hardest math problems. He describes the pace of progress as a wild time to be living through.

AIAndrew Curran argues that the approach generalizes to everything and continues to scale. The post builds on Christian Szegedy's claim that mathematical reasoning will transfer to other complex, reasoning-heavy domains, filling data gaps with high sample efficiency.

AILewis Tunstall says Chinese open models are strong but token-inefficient, citing a plot from the Beam release at IMO. The background post from @reflection_ai says Beam is 3-4x more efficient than GLM 5.2 and over 4x more efficient than leading Western open models in inference. He hopes future open models will compete on this efficiency axis.

AIMike Knoop argues AI can now automate conceptual search, transformation, and verification toward new science. He says AI can tell whether an open problem needs new ideas or whether the answer is already latent in existing knowledge. He calls this the most significant change in the philosophy of science since writing was invented about 6,000 years ago.

AIA breakdown of OpenAI's released internal-model math results shows about 73 disproofs and counterexamples, roughly 20% of the total. The author argues this counters claims that recent math breakthroughs are concentrated in counterexamples because models are only good at brute-force search.

AIWill Depue, an OpenAI-affiliated account, says he is surprised that AI lab math results have so far contained no profound errors or real bugs, which he notes is unlike typical human work. He expects at least a couple of today's results will not survive scrutiny.

AIFrançois Chollet asks whether the jagged frontier of AI capability is mainly math and code, which can be pushed far with RLVR. He questions whether steady gains in non-verifiable areas come from higher generalization driven by RLVR or only from continued injection of new human data.

AIKevin Weil, OpenAI's account owner, called today's OpenAI release an incredible step for AI in mathematics. He said models of similar caliber are still needed in the physical sciences, and that he expects to get there.

AIOpenAI has published a repository called Openai/math, which the author reads as a sign that math problems, or any verifiable problems, are being solved. The author says OpenAI's tools exhausted their Pro token allowance on subagent tests unrelated to their main task, concluding that the work was aimed at verification for its own sake.

AIEthan Mollick sarcastically says AI commentators routinely claim deep number theory expertise when opining on the latest math breakthroughs. The post offers no specific breakthrough, model, or figure, so its point is a skeptical observation about AI-community commentary.

AIRoon notes that in 2023 GPT-4 was confused by elementary school story problems, a limitation younger users may not remember. The post offers a brief reminder of how quickly model capabilities have advanced since then.

AIA post by Will DePue titled "Fable 5.1's list" presents 100 mathematical results and says 59% were released today, 87% AI and 13% human. The list includes items attributed to OpenAI, Anthropic, Google DeepMind and human mathematicians, each marked by a colored indicator, and it describes many entries as formalized in Lean or as openai/math family numbers. The post supplies no independent verification of these claims.

AIMicrosoft Research podcast host Chad Atalla interviews Jennifer Neville, a partner research manager at Microsoft, about her path into AI and her work on how evaluation exposes surprising failures in models tested beyond traditional benchmarks. The conversation also covers practical guidance for working with current AI systems and why examining underlying data matters when results defy expectations.