When OpenAI released hundreds of claimed solutions to some of the world’s hardest math problems this week, the frontier lab said it had consulted an advisory group of elite mathematicians. The goal was to avoid the controversy that came with the last time one of its models solved a long-standing problem in the field.
But OpenAI math solutions 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.
What Is the Advisory Group on Mathematics and AI?
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.
Where OpenAI Followed the Guidelines
The advisory group did not respond when asked for a more thorough evaluation of OpenAI’s latest proof release. The lab clearly followed some of its principles, including releasing results as soon as possible and including information about how the models reached their conclusions.
But not for all of them: Just 10 of the 719 manuscripts included releases of the model’s chain of thought.
For papers that people don’t understand, the mathematicians suggested the proofs should be formalized — but just 42% of the proofs released by OpenAI had not undergone this process.
Human Understanding Remains the Missing Piece
Ultimately, it’s still not clear that OpenAI is taking “responsibility for ensuring that human understanding will follow” when releasing its proofs, in accordance to the AGMAI principles. AGMAI suggested that OpenAI should help fund the work of human mathematicians who will be required to make the lab’s solutions meaningful in any real way.
“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,” Terence Tao, a prominent mathematician who has criticized OpenAI’s approach, wrote on social media after the release.
The Translation Problem Behind the Proofs
That problem is exemplified by a paper released this week by mathematicians at the University of Cambridge and King’s College in London that questions the way frontier labs are approaching these challenges.
When AI models solve mathematical problems, they first create a “natural language” explanation, then try to express that result in Lean, a programming language that in theory confirms the accuracy of the proof by compiling it as code.
However, there may be problems with the way the models translate their natural language proofs into code. This paper documents at least two discrepancies between the natural language proof and the Lean code behind the solution OpenAI has offered to a problem derived from the Navier-Stokes equations that describe the complex behavior of fluids.
These discrepancies don’t necessarily disprove either solution, but they do raise questions on whether we can simply rely on models to formalize their own solutions without human involvement. That’s one reason that AGMAI asked OpenAI to “include machine-readable metadata correlating the natural language and formal artifacts,” something the frontier lab did not do with 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 of the “lost in translation” paper conclude.
Why Peer Review Still Matters
Mathematicians stress that when new results are discovered by humans, they take responsibility for them and engage with the broader community through papers, talks, and seminars. That process increases understanding of the solutions, finds strategies that can be used to solve other problems, and allows the new knowledge to be applied in practical fields.
When a model is prompted to solve a hard problem and spits out a solution, “there is not human understanding of them at the point of release, and now the work begins,” Harvard University mathematics professor Melanie Wood told reporters.
The gap between raw problem-solving and genuine mathematical understanding remains wide. Until OpenAI math solutions come with the same rigor, peer review, and community engagement that human proofs receive, the field will continue to question whether these results truly advance mathematics or simply generate impressive-looking output.
