Overview of Scientific Breakthroughs
Less than a month after its mass release of hundreds of manuscripts containing solutions to long-standing mathematics questions, OpenAI has announced three more major discoveries in math, computer science, and physics. The company chose to have external experts guide the results in computer science and physics, while for the math problem, it released the AI output directly for researchers to examine.
OpenAI Announces Three Big Science Discoveries and a New Way to Work with Academics
This time OpenAI says it is taking new advice from scientists on how to release the results.
Specific Results Across Disciplines
Local smoothing for the Euclidean wave equation. The proof uses an auxiliary partial differential equation to establish Sogge’s local smoothing for waves in every spatial dimension at least two. It also yields the Kakeya maximal and dimension conjectures and Stein’s spherical restriction estimates throughout the interior of the conjectured range. The Exponential Time Hypothesis is False. The paper gives a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. The case of 3-SAT refutes the Exponential Time Hypothesis. An independent working group of computer scientists led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams will examine and explain the proof. At the group’s request, we are making the materials public immediately so others can examine them as well.
Academic Feedback and Collaboration
This approach could have its own issues, the company admits, and the AGMAI panel of math advisers OpenAI assembled recommended that AI companies avoid designating certain people to receive outputs first, citing unequal access, borrowed reputation, and biased selection. Instead, they recommended that AI labs release output on scholarly repositories, with Lean-formalized proofs, info on how the problems were chosen, and funding for researchers working on understanding the results.
The physics information has not been released in full, but is described as a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics and a unified completion of the Standard Model of particle physics. David Gross will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov to shepherd this work.
The computer science collaboration is said to prove that the Exponential Time Hypothesis, which has been widely believed to be true, is actually false. OpenAI says verification of the result will be guided by a group of three experts that includes UC San Diego’s Russell Impagliazzo and Ramamohan Paturi, with the group deciding to release the AI output writeup and Lean proof on GitHub.
There is similar documentation for the math breakthrough, where its model produced a proof of the local smoothing conjecture in every dimension and therefore also resolved the Kakeya conjecture and Stein’s restriction conjecture in all dimensions.
