Science & Tech · AI · 38 mins ago
OpenAI Shares Three New AI-Generated Math and Physics Claims
OpenAI says its AI models produced results on three major problems in mathematics and physics.
The claims concern the Exponential Time Hypothesis, the Kakeya conjecture and certain quantum field theories, including ones related to QCD and the Standard Model.
These are difficult, long-standing questions, and the claims have not been established as accepted scientific discoveries.
OpenAI says the math results were checked using Lean, a tool designed to verify proofs, but concerns have been raised about whether an earlier Lean-verified result proved what it claimed.
The company plans to share AI-generated work as raw research data and invite outside experts to guide groups of researchers in developing it further.
OpenAI acknowledges that choosing those initial experts could affect who gets involved first.
The physics group is holding back its AI-produced material while it works on writing up the results.
OpenAI says its AI models produced three new claims in mathematics, computer science and physics.
The computer science result claims to disprove the Exponential Time Hypothesis with a subexponential-time algorithm for counting satisfying assignments of fixed-width CNF formulas.
The mathematics result claims a proof of the local smoothing conjecture in every spatial dimension of at least two, with consequences for the Kakeya and Stein conjectures.
The physics claim is a mathematically rigorous existence proof for certain four-dimensional quantum field theories, including Quantum Chromodynamics and a unified completion of the Standard Model.
OpenAI says external experts will guide work on the computer science and physics claims, while it released the math output for researchers to examine.
- Who
- OpenAI says its AI models produced the results. External experts will guide examination of some of the claims.
- What
- OpenAI announced three AI-generated claims in mathematics, computer science and physics.
- When
- October 26, 2026, according to The Verge’s report.
- Where
- The computer science and mathematics materials were posted on GitHub; the physics materials were not released in full.
- Why
- OpenAI says it wants researchers to examine the AI-generated outputs and turn them into scientific understanding.
OpenAI
AGMAI panel of math advisers
Access to results
OpenAI
OpenAI says external experts will guide work on some claims and that the math output was released for researchers to examine.
AGMAI panel of math advisers
The panel recommended that AI companies not give selected people early access, citing unequal access, borrowed reputation and biased selection.
Publication approach
OpenAI
OpenAI describes its outputs as raw research data for researchers to work through.
AGMAI panel of math advisers
The panel recommended scholarly repository releases with Lean-formalized proofs, information about problem selection and support for researchers examining results.
OpenAI released hundreds of AI-generated mathematics results, according to The Verge.
OpenAI announced three further claims in mathematics, computer science and physics.
OpenAI said the computer science materials were being made public on GitHub at the request of the independent working group.
- Number of claims
- 3
- Computer science claim
- The Exponential Time Hypothesis is false
- Math claim
- Local smoothing conjecture proof in every spatial dimension of at least two
- Physics claim
- Existence proof for certain interacting quantum field theories in four dimensions
- Computer science reviewers
- Russell Impagliazzo, Ramamohan Paturi and Ryan Williams
- Physics group leader
- David Gross
3 sources
What people are saying
We are releasing the model output directly, as we did in our October 6 release.
The Exponential Time Hypothesis is False.
best understood as a form of raw research data
we recommend that AI companies do not adopt
Posts on X
We want to support the mathematics community in turning progress in AI into deeper human understanding and new discoveries. To support that goal, we are contributing $5 million to a new Simons Foundation initiative to help mathematicians examine, understand, and build on results