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Twenty-five Fields Medalists object to proofs announced before anyone can check them
The Fields Medalists behind a new open letter accept that AI can speed up mathematics. Their objection is to solutions announced before anyone has had time to write them up properly or work out whose ideas they used.
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What happened
- Twenty-five Fields Medalists have signed an open letter criticizing the push by AI companies to solve famous mathematical problems as demonstrations of what their models can do.
- The signatories say rushed agentic mathematics proofs could disrupt how mathematicians verify discoveries, develop new ideas and pass knowledge to the next generation of researchers.
- OpenAI's recent proof has yet to receive verification from the wider mathematical community.
- OpenAI withdrew its sponsorship of a mathematics event at Caltech on Thursday after researchers criticized the company.
- A separate initiative, the Leiden Declaration, has called for changes in how mathematicians, institutions and policymakers approach increasingly capable mathematical AI.
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Why it matters
- constraint A lab can aim as much compute as it likes at an open problem, since the resources now available exceed what once took years of human effort, but the step that turns output into accepted knowledge is a mathematician reading it. The speed of that reading limits the pace of everything else.
- exposure Researchers who suspect an unpublished idea would help a model land a headline result have a reason to sit on it, and the ones most exposed are those already running their drafts through AI coding tools.
- decision Anyone publishing an AI-produced result into a professional field now has to decide who signs off and by when, because correctness and credit are two separate checks needing two separate readers.
- precedent Lab money in academic venues carries the risk that the researchers in the room reject it in public, and one sponsor backing out makes that the expected response next time.
A claimed proof arrives with a headline attached, and someone still has to read it. Mathematicians discuss results, challenge assumptions, simplify arguments and connect them to earlier work, and that process can take years before an initially obscure idea turns up in standard mathematical education [6].
The signatories argue that a correct answer alone does not capture what makes mathematical research valuable [2]. They care about the machinery behind a proof, because new techniques can reveal relationships between areas that looked unrelated and create tools other people later build on [14]. The letter's authors also say AI-generated ideas still need mathematicians to develop them and fold them into the broader body of knowledge [15].
"Often these solutions are announced in a rush," the mathematicians wrote, citing the lack of time for careful write-ups and proper attribution [5]. An agentic solution may draw on decades of existing research [7]. Working out where the genuinely new idea originated gets harder as a result [7].
Then there is what researchers do with their drafts. If someone believes an unpublished idea could help an AI system produce a major result, the letter argues, they may become less willing to share it [9]. Some mathematicians have already asked whether using coding tools from AI companies exposes their research to future model development [10].
Interesting Engineering reported the letter without naming the signatories or identifying which OpenAI proof is at issue [16].
For anyone shipping an AI-produced result to a professional audience, the complaint reduces to two axes. One is whether a qualified reader has finished checking it, with a name and a date attached. The other is whether the output only settles the question or hands the next person a method they can reuse [14]. Verified with a reusable method is the quadrant a field can build on. Verified and answer-only is a fact for the file, and unverified with a reusable method is a lead worth someone's month of work. The fourth box, unverified and answer-only, is where a capability demonstration sits until a mathematician reads it.
What to watch
- Whether a named mathematician publishes a verification of the OpenAI proof the letter's signatories say is still unchecked.
- Whether other labs follow OpenAI in pulling out of mathematics event sponsorships, or keep funding them.
- Whether the Leiden Declaration picks up institutional signatories, such as journals or departments, that change submission rules.