When OpenAI released hundreds of claimed solutions to some of the world’s hardest math problems this week, the frontier lab stated that it had consulted an advisory group of elite mathematicians to avoid the controversy that followed the last time one of its models solved a long-standing problem.
Despite this precaution, OpenAI fell short of the expected standards, particularly regarding the need for human understanding of mathematical results. This concern was heightened by a new paper highlighting gaps between the natural language and the 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 Princeton University’s Institute for Advanced Studies, consists of nine prominent researchers from institutions around the world.
The organization released guidelines for frontier labs solving math problems in late September. Regarding the latest set of proofs, AGMAI noted that “it is ultimately up to the mathematical community to assess the extent to which our recommendations were followed successfully.”
However, the organization’s initial request was “to stop testing advanced mathematical problems on proprietary models,” yet OpenAI’s release explicitly indicates it is evaluating its proprietary models using open research problems.
The advisory group did not provide a detailed response when TechCrunch requested a more thorough evaluation of OpenAI’s latest proof release. While the lab adhered to some principles—such as releasing results promptly and including information on how models reached conclusions—it failed others: only ten of the 719 manuscripts included releases of the model’s chain of thought, and just 42% of the proofs had not undergone formalization.
Ultimately, it remains unclear if OpenAI is taking responsibility for ensuring human understanding, as required by AGMAI principles. The group suggested that OpenAI should help fund human mathematicians to validate the lab’s solutions meaningfully.
Prominent mathematician Terence Tao criticized OpenAI’s approach in a social media post, writing, “Problems are being solved autonomously by AI prompters who have no interest in the broader field itself once their initial target is ‘solved’, and do not understand the AI output well enough to answer questions on the result, give talks, or otherwise interact with the rest of the field.”
This issue is exemplified by a paper released this week by mathematicians at the University of Cambridge and King’s College London, which questions the methodology of frontier labs.
When AI models solve problems, they create a natural language explanation before attempting to express the result in Lean, a programming language designed to confirm proof accuracy by compiling it as code.
However, potential issues exist in how models translate natural language proofs into code; the paper documents at least two discrepancies between the natural language proof and the Lean code for a solution OpenAI offered to a problem derived from the Navier-Stokes equations.
These discrepancies do not necessarily invalidate the solutions but raise questions about relying solely on models to formalize their own work without human oversight. This is why AGMAI asked OpenAI to “include machine-readable metadata correlating the natural language and formal artifacts,” which the lab failed to do in these releases.
“Because of the phenomenon of mistranslations — as highlighted in this paper — 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,” the authors conclude.
Mathematicians emphasize that human discoverers take responsibility for their results and engage with the community through papers, talks, and seminars to enhance understanding and find practical applications.
According to Harvard University mathematics professor Melanie Wood, when a model is prompted to solve a hard problem and outputs a solution, “there is not human understanding of them at the point of release, and now the work begins.”
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