Computer Scientist Scott Aaronson: OpenAI Model Releases 372 Math Results in a Single Day
Computer scientist Scott Aaronson writes on his blog that OpenAI released 372 mathematical results, including a proof of the Unique Games Conjecture. No human has yet fully understood these proofs, and researchers have begun to examine them.
Theoretical computer scientist Scott Aaronson has written on his blog about what he considers one of the biggest days in the history of mathematics. OpenAI released 372 results at once, on the recommendation of an advisory group that includes Timothy Gowers, Edward Witten and other mathematicians. Among them is reportedly a proof of Subhash Khot's Unique Games Conjecture (UGC), which Aaronson's wife, complexity theorist Dana Moshkovitz, has worked toward proving throughout her career.
Proofs not yet understood
Some of the results come with a Lean certificate, though not all do. According to Aaronson, almost no human has yet understood any of these proofs. Moshkovitz shared her first impressions: the paper is very poorly written, its citations are often irrelevant, and it is hard to read without AI assistance. The proof relies on an entirely new, recursive code construction.
Other results mentioned
Aaronson lists further results: L=BPL, a faster Fourier transform and integer multiplication than O(n log n), a positive solution to the Unitary Synthesis Problem, a proof that parity is not in QAC0, a nearly fourth-power separation between randomized and quantum query complexity, and matrix multiplication in O(n^(9/4)) time. The list also includes partial progress toward the Riemann hypothesis, the Hodge conjecture and the Birch–Swinnerton-Dyer conjecture. P≠NP is not on the list.
Two ways of publishing
Two days earlier, Virginia Williams and Josh Alman posted a preprint on the 3SUM and All-Pairs Shortest Paths problems, built on an idea from an Anthropic model. Unlike OpenAI, Anthropic did not publish raw solutions. In exchange for compensation, it let the researchers write and announce a polished version. Aaronson calls these the two main models of communicating AI breakthroughs and notes the weaknesses of each.
The model and the scale
According to Aaronson, the results came from the latest internal OpenAI model, which could become available to paying customers within a couple of months. On average about three hours of compute were used per problem. The model was tried on roughly 8,000 problems, so it solved about 5% of them.
