OpenAI Claims AI Solved Three Major Scientific Problems in Math, CS, and Physics

OpenAI says its AI systems generated proofs addressing three major open problems across mathematics, computer science and physics. OpenAI is involving outside experts to assess the results. Independent researchers must still establish whether the proofs are valid and determine the significance of the findings for each field.

OpenAI said its models proved the local smoothing conjecture, a decades-old mathematical problem concerning the propagation and concentration of waves. The conjecture predicts that averaging waves over time reduces their intensity compared with their most extreme moments. The result would also settle the longstanding Kakeya conjecture and Stein's restriction conjecture. The Kakeya conjecture concerns the minimum size of a shape containing a line segment oriented in every direction. Stein's restriction conjecture concerns the behavior of functions' mathematical frequencies along curved surfaces. OpenAI said the models generated the result on October 18. OpenAI said the result was formalized the next day using Lean, a language for verifying proofs. OpenAI said a natural-language explanation and a formal proof were published on GitHub.

OpenAI said its computer science system generated a disproof of the Exponential Time Hypothesis. The hypothesis supports conditional computational-hardness results concerning satisfiability problems and related questions in computational complexity. OpenAI said the natural-language disproof was generated on October 16. OpenAI said the disproof was formalized using Lean on October 17. A team headed by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams is examining the result. OpenAI pledged funding for a conference examining the result's possible implications.

An external physics group headed by David Gross will evaluate a result that OpenAI describes as a rigorous existence proof for interacting quantum field theories in four dimensions. The claimed proof covers quantum chromodynamics (QCD) and a grand unified extension of the Standard Model. Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov are also involved in the assessment. Unlike the mathematics and computer science projects, the physics group has chosen to withhold the AI-generated materials from public release for now. The group's members will instead concentrate on writing their own account of the work.

OpenAI said the company is testing three methods of sharing AI-generated research with the scientific community. The methods involve immediate publication, release together with external collaborators, or giving an outside team control over when materials are made public. OpenAI is requesting feedback to determine which approach best serves researchers. The collaborations prohibit nondisclosure agreements and claims of academic credit for the discoveries themselves. The collaborations recognize researchers who create explanations and supporting materials. Participation is voluntary and unpaid, and collaborators will represent only their own views.

The claims could have substantial consequences if independent scrutiny confirms the results, particularly the claimed disproof of the Exponential Time Hypothesis. The hypothesis supports much of modern computational complexity theory. The initiative also raises questions about making potentially major AI-generated discoveries transparent, reproducible and credible to scientists.