OpenAI published full or partial solutions to more than 370 open math problems on Tuesday. The company says its unreleased model averaged about three hours of computing on each, according to Fortune, and mathematicians still dispute the results.
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Mathematicians find OpenAI's Navier-Stokes proof takes a different route from the Spanish program
Mathematicians reading OpenAI's 166-page Navier-Stokes proof say it departs from the Spanish program the company cited, Scientific American reported. That undercuts the stated premise of the public dispute with NYU's Tristan Buckmaster, though the influence question may not be settled.
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The theorem was checked in Lean, more than most capability claims get, but the part that moves a valuation, that very little human input went in, rests on prompt timestamps and a training-data question that went unanswered.
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Three of the 722 mathematics papers OpenAI released on 7 October using an AI model have already been retracted.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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buildConfirmed8 publishers OpenAI's 165-page proof ships with a Lean 4 formalization anyone can download and build, which settles whether the argument follows from its own definitions and leaves whether those definitions state the Clay problem to human readers.
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OpenAI plans to post hundreds of AI-generated math results on GitHub on Tuesday, people familiar with the plans told WIRED. The mathematicians it consulted in August asked for papers they could absorb and use, so a bulk upload leaves that work to every reader.
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Lorraine mathematician confirms Claude's 67.25% bound on Riemann zeta zeros by another route
Youness Lamzouri has independently confirmed Claude's result that at least 67.25% of Riemann zeta zeros lie on the critical line, against 40% known since 1989. The hypothesis itself is still open. The case shows a working split for AI in mathematics, in which a model finds a candidate result and a specialist rebuilds it.
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OpenAI's 10,000 agents propose a Navier-Stokes blowup that needs an external force
OpenAI says about 10,000 AI agents produced a proposed finite-time singularity for the forced 3D Navier-Stokes equations in 88 hours. The construction fits one route the Clay rules allow and leaves unforced smoothness open, while the mathematicians whose forced-Euler work came first ask whether their Codex drafts reached the model.
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A proof checker confirmed the steps of OpenAI's Navier-Stokes result within days. The argument now running through mathematics is over who explains the 166 pages and who gets the credit for them.
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OpenAI says no specific user data was accessed to solve the problem, and that it cannot rule out that de-identified data derived from two mathematicians' use of its products improved its models. A procurement team has to read both sentences.
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buildConfirmed3 publishers 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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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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OpenAI asks nine unpaid mathematicians how to release its 100-plus math results
OpenAI says its new nine-member mathematics advisory group will not advise on the pace of its internal research, and the group's own website says the decisions rest with the AI companies.
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buildConfirmed2 publishers 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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OpenAI now calls it impossible that a Codex user's prompts reached its model
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's 88-hour Navier-Stokes run burned roughly 880,000 agent-hours
OpenAI says the run took 88 hours and cost millions, which tells a small research group more about whether it can compete than the proof itself does, and its wording on user data shows the limit of what any vendor can promise.
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OpenAI spent more than $1m of compute on a prize it says it will not claim
The Navier-Stokes result cost more in compute than the Clay Institute's award, and the interesting line in OpenAI's blog post is the one conceding it cannot rule out that customers' de-identified prompts helped.
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OpenAI puts a machine-checkable Lean proof of finite-time blowup in a public repo
OpenAI says the result resolves statement C of the official Millennium formulation, then says it will not claim the $1M prize. The smooth force applied to its fluid throughout is why that second sentence carries the weight.
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A mathematician kept a year of unpublished drafts in Codex, then asked whether they had been used for training and got silence on that half of the question, which is the half every enterprise rollout treats as settled.
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