OpenAI's math proof release falls short of new field standards
OpenAI this week published hundreds of claimed solutions to hard math problems (719 manuscripts, per the article), saying it consulted an advisory group of elite mathematicians to avoid the controversy its earlier result sparked. But only ten of the manuscripts included the model's chain of thought, and by the article's account roughly 42% of the proofs had not gone through formalization in Lean; the Advisory Group on Mathematics and Artificial Intelligence (AGMAI), hosted by Princeton's Institute for Advanced Study, said it is ultimately up to the mathematical community to judge whether its recommendations were followed — its first request being to stop testing advanced problems on proprietary models. A paper from Cambridge and King's College London mathematicians also documents at least two discrepancies between OpenAI's natural-language proof and the Lean code for a problem derived from the Navier-Stokes equations, concluding such autoformalized proofs should not be trusted without peer review.
As frontier models increasingly produce mathematical results, ensuring humans can understand and verify those proofs is becoming central to the credibility of AI-driven science.
When OpenAI released hundreds of claimed solutions to some of the world’s hardest math problems this week, the frontier lab said that it had consulted an advisory group of elite mathematicians to avoid the controversy that came with the last time one of its models solved a long-standing problem in the field.
But OpenAI fell short of those standards, particularly where the mathematicians emphasized the need for human understanding of a mathematical result. That’s especially concerning after a new paper highlighted gaps between the natural language and formally expressed solution to a million-dollar problem ostensibly solved by OpenAI’s models.
The Advisory Group on Mathematics and Artificial Intelligence (AGMAI), hosted by the Institute for Advanced Study, is made up of nine prominent researchers at institutions around the world.
The organization released guidelines for frontier labs solving math problems at the end of September. In a statement on the latest set of proofs, the AGMAI said that “it is ultimately up to the mathematical community to assess the extent to which our recommendations were followed successfully.”
However, the organization’s first request was “to stop testing advanced mathematical problems on proprietary models.” OpenAI’s release explicitly says that it is evaluating its proprietary models using open research problems in mathematics.
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