OpenAI releases hundreds of math solutions

OpenAI released hundreds of claimed solutions to some of the world's hardest math problems this week, saying it had consulted an advisory group of elite mathematicians to avoid past controversy.

The advisory group sets standards

The Advisory Group on Mathematics and Artificial Intelligence, hosted by Princeton University's Institute for Advanced Studies, released guidelines at the end of September for frontier labs solving math problems.

OpenAI ignored a key recommendation

The advisory group's first request was to stop testing advanced mathematical problems on proprietary models. OpenAI's release explicitly says it is evaluating its proprietary models using open research problems in mathematics.

“to stop testing advanced mathematical problems on proprietary models”

Most proofs lack chain of thought

OpenAI released 719 manuscripts, but just ten of them included releases of the model's chain of thought, showing how the models reached their conclusions.

Formalization gap is significant

The advisory group suggested proofs should be formalized, but just forty-two percent of the proofs released by OpenAI had undergone this process, leaving most unverified by formal methods.

Terence Tao criticizes the approach

Prominent mathematician Terence Tao wrote on social media that AI prompters solving problems have no interest in the broader field and do not understand the AI output well enough to answer questions or give talks.

“Problems are being solved autonomously by AI prompters who have no interest in the broader field itself once their initial target is 'solved'”

Translation errors found in proofs

Mathematicians at the University of Cambridge and King's College in London found at least two discrepancies between OpenAI's natural language proof and its Lean code for a problem derived from the Navier-Stokes equations.

Peer review needed for AI proofs

The Cambridge and King's College paper concludes that natural language proofs and autoformalised Lean proofs should not be trusted without the same peer review process and scrutiny that other proofs receive.

“the NL proof by OpenAI and other autoformalised Lean proofs should not prima facie be trusted without the same peer review process and scrutiny that other proofs are subjected to”

Human mathematicians must engage

Harvard mathematics professor Melanie Wood told TechCrunch that when a model spits out a solution, there is not human understanding of it at the point of release, and now the work begins.

“there is not human understanding of them at the point of release, and now the work begins”