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OpenAI’s AI Proofs Resolve Local Smoothing Conjecture

By Drooid · Oct 27, 2026, 10:27 AM UTC · How we work

Summary

OpenAI Resolves Conjectures

OpenAI announced its models produced proofs that resolve the local smoothing conjecture.
The proof was generated on Oct. 18 2026 and formalized in Lean on Oct. 19 2026.
OpenAI said the proof also resolves the Kakeya and Stein restriction conjectures.
UC San Diego’s Russell Impagliazzo, Ramamohan Paturi and MIT’s Ryan Williams will lead an independent review.
OpenAI funded a conference and posted the proofs on GitHub for review.

Summary

OpenAI Funds Review

OpenAI pledged $5 million to the Simons Foundation to fund independent review of its AI-generated results.
OpenAI formed three expert shepherd groups to guide release strategies for mathematics, computer science, and physics.
The physics collaboration postponed public release to draft an interpretive manuscript first.
OpenAI sought broader community feedback to expand participation and refine its collaborative research model.

Summary

OpenAI Deploys Swarm

OpenAI redirected compute from its premium service to a 10,000-agent swarm targeting Navier-Stokes, suspending sign-ups.
The “code red” priority led OpenAI to spend tens of millions of dollars on AI agents for Millennium Prize problems.
On Oct 6 OpenAI released over 700 mathematical manuscripts, including an eight-page paper on Siegel zeros.
Terence Tao warned AI-generated proofs lack human explanations, threatening future mathematical training.

History

Historical Context

In 1985 Feng-hsiung Hsu began ChipTest at Carnegie Mellon, which IBM renamed Deep Blue and upgraded to 30 processors evaluating 200 million chess positions per second. After losing a 1996 match, Deep Blue defeated world champion Garry Kasparov 3½–2½ in May 1997, winning a $700,000 prize. That milestone shows how massive compute investments, echoed today by OpenAI’s $5 million pledge to the Simons Foundation.

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OpenAI Resolves Conjectures

OpenAI announced its models produced proofs that resolve the local smoothing conjecture.
The proof was generated on Oct. 18 2026 and formalized in Lean on Oct. 19 2026.
OpenAI said the proof also resolves the Kakeya and Stein restriction conjectures.
UC San Diego’s Russell Impagliazzo, Ramamohan Paturi and MIT’s Ryan Williams will lead an independent review.
OpenAI funded a conference and posted the proofs on GitHub for review.

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