Artificial Intelligence
OpenAI seeks review of AI proofs across three fields
OpenAI said internal models produced proofs in computer science, mathematics and physics, then asked outside specialists to examine them, with separate review arrangements for each result and some proofs translated into Lean.
- OpenAI said its internal models produced proofs for three results in computer science, mathematics and physics, and it described the manuscripts as raw research data that still needed interpretation.
- Ryan Williams, Russell Impagliazzo and Ramamohan Paturi were to review the computer science result, while Impagliazzo and Paturi had originally proposed the Exponential Time Hypothesis with Francis Zane.
- OpenAI said its mathematics result concerned the local smoothing conjecture and would imply the Kakeya conjecture and Stein's restriction conjecture in all dimensions if it held up.
- The company's physics group was to be led by David Gross and also included Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov.
- OpenAI said it had translated the mathematics and computer science proofs into Lean, and had also translated the Yang-Mills proof into Lean.
OpenAI posted three results and said its internal models had generated them. It also translated the mathematics and computer science manuscripts into Lean, a language that can check each proof step, while saying that this still did not settle whether the statements matched the intended problems.
The computer science result concerned the Exponential Time Hypothesis, which says there is no shortcut for worst-case SAT instances. OpenAI said the proof would weaken a large amount of work that depends on that hypothesis, although the underlying results would not automatically become false.
The mathematics result concerned local smoothing, a conjecture on wave behaviour proposed by Christopher Sogge in 1991. OpenAI said the proof covered every dimension and would also resolve the Kakeya and Stein conjectures if it survived review.
For physics, OpenAI said it had shown that certain quantum field theories exist in four dimensions, including a form of Yang-Mills theory, but not the separate mass-gap part of the Millennium problem. David Gross was to lead the review group, and the company said it would handle that result differently from the other two.
Named in this story
People
- Ryan Williams
- will independently check and explain the computer science result
- Russell Impagliazzo
- will independently check the computer science result and had co-proposed the hypothesis
- Ramamohan Paturi
- will independently check the computer science result and had co-proposed the hypothesis
- Francis Zane
- co-proposed the Exponential Time Hypothesis with Impagliazzo and Paturi
- Christopher Sogge
- proposed the local smoothing conjecture in 1991
- David Gross
- will lead the physics review group and won the 2004 Nobel Prize in Physics
- Michael Douglas
- is on the physics review group
- Arthur Jaffe
- is on the physics review group and helped write the Yang-Mills problem
- Igor Klebanov
- is on the physics review group
- Nikita Nekrasov
- is on the physics review group
Companies
- OpenAI
- said its models produced the proofs and arranged outside review
Organisations
- UC San Diego
- is the affiliation of Impagliazzo and Paturi
- Clay Mathematics Institute
- offers the million-dollar prize attached to the Yang-Mills problem
- Simons Foundation
- will receive OpenAI funding for workshops and conferences
Products and systems
- Lean
- was the language OpenAI used to check parts of the proofs
How the source tells it
The piece was mostly measured and explanatory, but it repeatedly stressed the scale of the claims and the need for independent checking.
- high stakes it frames the possible consequences as broad academic fallout if the computer science proof survives review
- caution it keeps qualifying the claims with proof checking, outside review and explicit notes that participation is not an endorsement