A Millennium Prize Problem asking whether smooth solutions to the 3D incompressible Navier-Stokes equations always exist or can break down in finite time.
Three of the 722 mathematics papers OpenAI released on 7 October using an AI model have already been retracted. Their value now rests on checking by mathematicians, who have not yet had time to read them all, according to New Scientist.
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OpenAI released hundreds of results on open problems in math and theoretical computer science, many already verified in the Lean programming language. Those are all but certain to be correct, so the months of reading ahead are about whether they hold new ideas.
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OpenAI published 722 math manuscripts across 372 result families, all produced by an internal model it has not released. About 300 come with Lean formalizations a machine can check, Crypto Briefing reported, so the rest wait on human reviewers whom one mathematicians' group is urging to stop working with OpenAI.
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Researchers say AI companies have at least twice in five weeks reached answers to questions they had long been working on, Nature reported. Some now limit their AI use, though one AI-safety scientist expects models to keep getting there first with or without uploaded manuscripts.
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OpenAI posted 372 results from an internal model to GitHub, at about three hours of ChatGPT Pro compute each on average. Finding proofs is now cheap enough that the slow step is mathematicians checking and judging them.
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OpenAI posted 722 model-written math manuscripts in 372 families on GitHub, many with Lean proofs a computer can check. A mathematician citing one has to learn first whether it is a checked proof or a paper still waiting for review.
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OpenAI's new mathematicians' panel must first help release scores more results the company says an unreleased model produced. Researchers call the panel a good first step, though many are unsure how much say it will have over how OpenAI announces what its models find.
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OpenAI's write-up gives the token counts, the agent count and the verification time for its Navier-Stokes result. The verification time is the number that decides whether the method transfers to anyone else's workload.
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Days after Caltech mathematicians called AI "slop mathematics" research misconduct, OpenAI's research lead said the company would stop sponsoring their competition. Organizers say they are talking to other firms.
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With Navier-Stokes claimed and five Millennium problems left, the ordering of what falls next turns on which conjectures a single counterexample would settle. Five million dollars of Clay prize money is still unclaimed.
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Buckmaster was preparing to publish when OpenAI announced it had solved the problem and offered him a share of the credit. A second mathematician, Andreas Thom, then asked the company whether his own ChatGPT conversations had reached its model.
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A week and a half after accusing OpenAI of copying his approach to a problem carrying a $1 million bounty, the NYU mathematician is still running the company's coding agent on his own papers.
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Alex Karp told CNBC that frontier labs are angling for government liability cover because their commercial clients would otherwise sue them. Buyers whose data feeds those models should read their contracts with that in mind.
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The Clay Mathematics Institute has the claimed Navier-Stokes solution under review, and a summer of agent-found bugs in Lean's kernel shows how narrow the guarantee a Lean certificate actually gives.
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Levent Alpoge and Ava Howell used a simple prompt to an internal Claude and got elliptic curves of rank at least 30 and at least 31 in days, in a field where the last single-rank step took more than 18 years.
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Azeem Azhar counted the raised hands himself, in a self-selected room of 250 IT executives at a Las Vegas conference. Every firm in it told him AI spending rises next year. Budgets have to answer for that.
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The declaration lands three days after OpenAI's Navier-Stokes claim, in the middle of a credit dispute where the company and the mathematician at the center give accounts that cannot both be right.
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Tristan Buckmaster used OpenAI's Codex on the Navier-Stokes problem, then asked whether his prompts had fed the system that beat him to a proof, and the company's answer to The Verge got firmer over time.
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OpenAI says tens of thousands of agents solved a 90-year-old problem carrying a $1 million prize. The solution still needs independent verification, and a rival pair of mathematicians has a claim on the credit.
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Tristan Buckmaster told the ABC that the game is up for mathematicians. In the same week, OpenAI described what his Codex prompts did to its models in two incompatible ways, and a customer has no way to pick between them.
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