OpenAI announces three big science discoveries and a new way to work with academics

OpenAI has announced three significant discoveries in the fields of mathematics, computer science, and physics, following its previous release of numerous manuscripts that purportedly provided solutions to longstanding mathematical problems. This latest announcement, made less than a month after the earlier release, introduces a new collaborative approach involving external experts, referred to by OpenAI as “shepherds.” These experts will guide the results in the areas of computer science and physics, while for the mathematics discovery, they suggested making the AI-generated output available for researchers to analyze and derive their own explanations.

One of the key findings pertains to the local smoothing for the Euclidean wave equation. The proof presented utilizes an auxiliary partial differential equation to confirm Sogge’s local smoothing for waves across all spatial dimensions of two or greater. This discovery also provides insights into the Kakeya maximal and dimension conjectures as well as Stein’s spherical restriction estimates within the anticipated range. OpenAI plans to release the output from this model directly, similar to the approach taken during the October 6 release.

Another significant development is the assertion that the Exponential Time Hypothesis (ETH) is false. This research introduces a deterministic algorithm capable of accurately counting satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. Specifically, the case of 3-SAT serves to refute the ETH. An independent team of computer scientists, led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams, will investigate and clarify the proof. At the request of this group, OpenAI is making the materials publicly available for broader examination.

Despite the promising nature of this new approach, OpenAI acknowledges potential challenges. The AGMAI panel, composed of mathematical advisors, recently advised against the practice of designating specific individuals for early access to output, citing concerns over unequal access, borrowed reputation, and biased selection processes. They recommend that AI organizations publish their findings in scholarly repositories, including Lean-formalized proofs, details on how problems were selected, funding information for those working to understand the results, and other relevant data.

While full details of the physics discovery have not yet been disclosed, OpenAI describes it as a mathematically rigorous existence proof of certain interacting quantum field theories that incorporate gauge fields and fermions in four dimensions. This includes Quantum Chromodynamics (QCD) and a comprehensive completion of the Standard Model of particle physics. David Gross will lead a team, which includes Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov, to oversee this work.

The collaboration in computer science aims to establish that the ETH, which has been largely accepted as true, is in fact incorrect. OpenAI has formed a verification group comprising experts such as Russell Impagliazzo and Ramamohan Paturi from UC San Diego, who were part of the original proposal for the hypothesis in 1999, along with MIT professor Ryan Williams. The team has opted to publish the AI output write-up and Lean proof on GitHub today.

In conjunction with these releases, OpenAI has issued an open letter to the academic community inviting feedback on how to assess the claim and establish norms for handling AI-generated breakthroughs. The letter poses three broader questions aimed at fostering discussion:

1. What expectations should govern early access to AI-generated results, the disclosure of conflicts of interest, and the use of unpublished material for further research?

2. How should credit be allocated between new discoveries and the accompanying efforts to verify, refine, simplify, explain, and extend these findings?

3. In what ways can we support students and researchers as methodologies and research directions evolve, while ensuring that the critical understanding and judgment necessary for questioning results and fostering new ideas are maintained?

Documentation for the mathematical breakthrough is similarly detailed, indicating that the model produced a proof of the local smoothing conjecture across all dimensions, thereby resolving both the Kakeya conjecture and Stein’s restriction conjecture in every dimension. Notably, just months prior, Hong Wang, a professor at NYU, received a prestigious Fields Medal from the International Mathematical Union for solving the Kakeya conjecture in three dimensions.