OpenAI says its internal AI models have produced major research results spanning pure mathematics, theoretical computer science and physics. The company published manuscripts containing solutions or progress on 372 mathematical problems on October 26, but the work is being presented as raw research material rather than as a set of settled findings.
The manuscripts are public on GitHub, and OpenAI says the proofs were formalized and checked with Lean, software designed to verify mathematical proofs. The company is also involving outside specialists to assess and explain the results.
Three high-profile claims
- A proof of the local smoothing conjecture proposed by Christopher Sogge in 1991. In simplified terms, the result concerns limits on how strongly waves can remain concentrated over time. OpenAI says it has proved the statement in every spatial dimension, with implications for the Kakeya and Stein conjectures.
- A result that would disprove the Exponential Time Hypothesis, an assumption about the difficulty of solving certain logical satisfiability problems. If upheld, it could alter theoretical complexity limits, although it would not automatically translate into faster software.
- A claimed rigorous mathematical construction of four-dimensional quantum field theories, including quantum chromodynamics, the theory describing interactions between quarks and gluons.
The physics claim is still being reviewed by a group led by Nobel laureate David Gross, and the underlying materials have not yet been published in full. It also does not amount to a solution of the Yang–Mills Millennium Prize Problem: establishing the existence of the theory is only one part of that challenge, which also requires proving a positive mass gap between the vacuum and excited states.
The release has also prompted criticism from researchers working on related AI-assisted mathematics. Anthropic researcher Levent Alpöge and mathematician Ethan Sussman had been publicly developing a related approach using Claude to advance the mathematical program of Tadeusz Bałaban. Alpöge objected to OpenAI announcing its result separately rather than collaborating with their effort.
Alpöge and Sussman have also cautioned that their own largely AI-generated research materials are works in progress with claims that still need checking. For OpenAI’s headline results, independent expert verification—particularly of the unpublished quantum-field-theory work—remains the key next step.
