The change in method
Less than a month after the publication of hundreds of manuscripts that, according to OpenAI, contained solutions to long-standing mathematical problems, the company announces three new results described as important in the fields of mathematics, computer science, and physics. The difference from the previous occasion, The Verge reports, lies in the involvement of external experts whom OpenAI calls shepherds—that is, guides—for the computer science and physics work. For the mathematics problem, however, the advisers reportedly suggested making the model's output public directly, leaving it to researchers to develop their own explanations.
The company admits that this approach may have problems. The same panel of mathematical advisers convened by OpenAI recommended the previous day against adopting the practice of assigning designated people priority access to the results, citing among the reasons unequal access, borrowed prestige, and biased selection. The panel instead proposes that labs publish on academic repositories, with proofs formalized in Lean and information on how the problems were selected.
The three proofs and who examines them
For mathematics, the model reportedly produced a proof of the local smoothing conjecture in every dimension, thereby also solving the Kakeya conjecture and Stein's restriction conjecture in all dimensions. The material used by the source cites the case of Professor Hong Wang, awarded the Fields Medal a few months ago for solving the Kakeya conjecture in three dimensions.
For computer science, OpenAI claims that the Exponential Time Hypothesis, long believed to be true, is in fact false. Verification would be entrusted to a group of three experts: Russell Impagliazzo and Ramamohan Paturi of the University of California, San Diego, who were part of the group that proposed the hypothesis in 1999, and Ryan Williams of MIT. The group has decided to publish the model's write-up and the Lean proof on GitHub today.
For physics, the content has not been released in full. OpenAI describes it as a mathematically rigorous proof of existence for certain quantum field theories interacting with gauge fields and fermions in four dimensions, including quantum chromodynamics and a unified completion of the Standard Model. David Gross would lead a group with Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov.
The open questions
The computer science group also circulated an open letter to the community to gather input on how to examine the claim and how to establish norms for managing results generated by artificial intelligence. The questions concern early access to results, disclosure of conflicts of interest, recognition of verification and simplification work, and support for students and researchers. The outcome of the independent reviews remains to be verified: at present, the three discoveries are announced by OpenAI and entrusted to groups of experts, and have not yet been validated publicly and fully.
