Topic
A method for mathematically proving that software or hardware meets specified properties, using machine-checked proofs rather than testing or simulation.
Mathematician Thomas Bloom stopped tagging Erdős problems as open or solved before OpenAI posted 722 AI-produced manuscripts. A DeepMind paper in Science shows the documented, human-vetted alternative: 9 of 353 open problems solved.
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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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7 publishersReality
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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Ioannis Tsiokos of Automorph announced Chair44, a 3D monotile built from seven-cube chairs that tiles space without ever repeating. Reaction is mixed because he made significant use of generative AI in the proof.
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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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9 publishersReality
OpenAI released 719 manuscripts of claimed solutions to hard math problems this week and included the model's chain of thought for only ten of them. The advisory group of mathematicians OpenAI consulted had set verification standards the lab's release misses on several counts.
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3 publishersReality
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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3 publishersReality
OpenAI posted 719 math papers from an unreleased model on October 6, a week after its IAS-based advisers asked labs to stop such testing. Three mathematicians showed the same day that its machine-checked Navier-Stokes proof proves less than the paper claims, so its results now rest on ordinary peer review.
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Cambridge and King's College London mathematicians say the Lean code for OpenAI's Navier-Stokes proof states a weaker step than the written paper. Both proofs may hold up, but Lean verifies only the code it is given, so a person still has to check that the code matches the text.
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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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6 publishersReality
OpenAI published ten math results from an internal Astra variant, with Lean-formalized proofs and the model's narration of each solution. Astra has no announced API, so what outside teams can take is how the work was split between the model, human authors and a proof checker.
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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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Ramana Kumar used AI to exploit a different bug in each of two Lean kernels, passing off a false Collatz disproof as machine-checked in July. AI labs rely on Lean to vouch for their maths results, so those claims hold only as well as the checker does.
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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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Vitalik Buterin says Ethereum's Hegotá upgrade, planned for 2027, is likely the last fork that someone who knew Ethereum in 2015 would recognize. The work he expects to follow has no dates yet, so ETH holders are pricing a long rebuild of the protocol off a single milestone.
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Anthropic published a 13-million-line Lean 4 proof of Fermat's Last Theorem that dozens of Claude agents wrote in 11 days. For teams weighing agents on correctness-critical code, the kernel checks every step, so what humans still review is the statement being proved.
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An interview with Lean's founder says an AI translated C zlib into Lean and proved compress-then-decompress round-trips in about a week. The remaining work is optimization without breaking the proof.
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Anthropic's own account has dozens of agents writing 13 million machine-checked lines in 11 days, about 7% of them dead ends, and only after a Columbia team built the shared to-do list that stopped them duplicating work.
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Kevin Buzzard holds a five-year grant to do the same job by hand. He compiled Anthropic's 13 million lines himself and says the result teaches mathematicians nothing and anyone running agent fleets quite a lot.
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Trail of Bits' agent-built Lean model of the Miden VM, backed by 95 machine-checked proofs, surfaced a way for a malicious prover to forge Falcon signatures. A dev.to account says the agents built tooling first, so that Miden's stack assembly could be reviewed at all.
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