What exactly did OpenAI's AI prove?

OpenAI says its models proved the Exponential Time Hypothesis false, proved the local smoothing conjecture in every dimension, and proved that certain quantum field theories exist in four dimensions.

Who is checking the computer science proof?

MIT professor Ryan Williams, Russell Impagliazzo, and Ramamohan Paturi of UC San Diego are independently checking the result. They have no nondisclosure agreements, are working unpaid, and plan to share interim findings.

Will the physics proof solve the Millennium Prize Problem?

No. OpenAI explicitly says it has solved only the existence part of the Yang-Mills theory problem, not the mass gap part, so the Millennium Problem would not be fully solved.

Large Language ModelsAI Safety & AlignmentTHE DECODER2h agoOct 27, 2026, 22:01 JST

OpenAI asks David Gross to vet AI proofs on three open problems

Send on LINE

3 Key Points

What happened
OpenAI says its models proved the Exponential Time Hypothesis false, proved the local smoothing conjecture in every dimension, and proved certain quantum field theories exist in four dimensions. It translated the math and computer science proofs into Lean.
Why it matters
If the proofs hold, hundreds of papers in graph theory, computational biology, databases, and computational geometry lose their foundation, and complexity theory would need rethinking, according to OpenAI and outside experts.

WHO IT HITSResearchers in complexity theory, graph theory, computational biology, and database algorithms may need to revisit results that assumed the Exponential Time Hypothesis. Mathematicians working on harmonic analysis and physicists studying quantum field theory face similar re-examination, pending independent review.

Not sure about something? Ask the AI

Questions and answers are published on this page.

Summaries like this, every morning.

Get these free every morning

Context & Analysis

OpenAI's decision to hand the proofs to outside experts follows criticism over a previous PR incident involving Navier-Stokes, and the company now says it is not claiming scientific credit for the discoveries. The review process itself comes with trade-offs: OpenAI admits that whoever picks the first shepherds helps decide who gets involved first, and some people end up knowing more sooner than others. The three fields are being handled differently. The computer science group, led by Ryan Williams with Russell Impagliazzo and Ramamohan Paturi—two of the original proposers of the Exponential Time Hypothesis—is working unpaid and without nondisclosure agreements, and OpenAI is publishing all raw data at their request. The math result has no dedicated shepherd; OpenAI published the proof and Lean proof directly on an outside expert's advice. The physics group, led by David Gross, is holding back the AI's materials for now and plans to write up the result itself. OpenAI has also pledged $5 million to the Simons Foundation to fund workshops and conferences on AI results.

FAQ

What exactly did OpenAI's AI prove?: OpenAI says its models proved the Exponential Time Hypothesis false, proved the local smoothing conjecture in every dimension, and proved that certain quantum field theories exist in four dimensions.
Who is checking the computer science proof?: MIT professor Ryan Williams, Russell Impagliazzo, and Ramamohan Paturi of UC San Diego are independently checking the result. They have no nondisclosure agreements, are working unpaid, and plan to share interim findings.
Will the physics proof solve the Millennium Prize Problem?: No. OpenAI explicitly says it has solved only the existence part of the Yang-Mills theory problem, not the mass gap part, so the Millennium Problem would not be fully solved.

THE DECODERRead Original Article

Send on LINE

AI news that matters for your work, delivered every morning.

Pick your industry and the AI tools you use, and get news related to your work every day.

Get it free

Free · 30 seconds with Google · unsubscribe anytimeWhat is AIToday? →

Ask AI

Ask AI anything about this article. The AI reads this article, earlier AIToday articles, and Wikipedia, and cites its sources. Q&As are published on this page for other readers too.