25 Fields Medalists: AI solves, but does not understand
A declaration signed by 25 Fields Medalists argues that benchmark-style problem solving misses what mathematical research is actually for.
In short
25 Fields Medalists say in a statement published on September 11, 2026 that AI systems racing to crack famous problems are optimized against the wrong target, because the goal of mathematics is conceptual understanding rather than a verdict of true or false.
At a glance
- 25 Fields Medalists signed the statement; Terence Tao posted it on his blog on September 11, 2026.
- Central claim: solving a problem is only a tool and a proxy for the real goal, conceptual understanding and insight.
- Four objections: speed over write-up, unresolved attribution, ideas never entering the canon, damage to training.
- The text points to the Leiden declaration as a precedent and asks for further signatures from the field.
- mathandai.org, the site meant to host the declaration, returned HTTP 403 when we called it, so its list is unverified.
A joint statement from 25 Fields Medalists, posted by Terence Tao on September 11, 2026, makes an unfamiliar kind of complaint about AI. It is not that the models are too weak for research mathematics. It is that the scoreboard they are being judged on measures the wrong thing.
Optimizing against a proxy
The declaration rests on one distinction. Solving a problem, the signatories write, is a tool and a proxy; the goal is conceptual understanding and insight. Treating famous open problems as proof of capability turns that proxy into the target, and an answer that nobody in the field can absorb leaves the underlying mathematics exactly where it was.
Their sharpest line is about volume rather than accuracy: an ever faster output of true-or-false statements, they warn, could “destroy fertile ground” instead of feeding new ideas.
Four objections beyond the leaderboard
- Announcement speed. Results get pushed out in a rush, with no room for a proper write-up, for separating out the genuinely new method, or for crediting earlier work.
- Attribution. The practice raises unsettled questions of authorship and plagiarism inside the discipline.
- Transmission. Unless working mathematicians fold machine-generated ideas into the canon, those ideas never really come alive.
- Training. Years of apprenticeship produce more than correct answers; they produce the ability to pose a new question at all.
An open letter with no policy ask
The declaration asks for more signatures and addresses mathematicians, AI companies and the wider public in the same breath. It proposes no rules, no deadlines and no oversight body. Its stated model is the Leiden declaration.
What it leaves out is telling: no company or model is named in the declaration itself. A corporate name reaches the reader only indirectly, through an Economist report linked from the blog post.
What we could not check
mathandai.org, where the declaration is supposed to collect signatures, answered our request with HTTP 403. That means the signature list, its current count and the full wording could not be verified independently. We also did not have access to the Economist report, so every claim above traces back to Terence Tao's blog post.
FAQ
Who signed the Fields Medalists' declaration on AI in mathematics?
According to Terence Tao's blog post, 25 Fields Medalists signed as initial signatories. The full list is meant to live on mathandai.org, but that site was unreachable when we called it (HTTP 403).
What exactly do the mathematicians accuse AI labs of?
Of treating solved problems as the measure of success when it is only a proxy for understanding, and of a release culture with rushed announcements, unclear attribution and knock-on effects on how young mathematicians are trained.
Does the declaration call for banning AI in mathematical research?
No. It contains no ban, no deadline and no oversight mechanism. It asks for additional signatures and for the issue to be taken up by mathematicians, industry and the public.
