Timothy Gowers, a Fields medallist himself, has published a blog post explaining why he declined to sign a letter signed by 25 Fields medallists about the impact of AI on mathematics. The letter argued that the mass production of "true/false" statements by AI could "destroy fertile ground instead of breathing life into new ideas." Gowers agrees that a crisis exists but offers a different diagnosis.
Gowers opens with a personal story: at age 11, he attempted Fermat's Last Theorem, discovered difference sequences on his own, and empirically found that starting with nth powers and taking successive differences eventually yields a constant sequence. He never turned this into a proof — but the experience taught him more than formal instruction would have. He cites this as an illustration of the letter's own premise: one learns from grappling with problems regardless of solving them.
His central argument is that the letter implicitly privileges one mathematical temperament over another. Gowers describes a spectrum: at one end, mathematicians primarily motivated by solving problems, who see conceptual understanding as a means to that end; at the other, mathematicians primarily motivated by conceptual understanding, who see problem-solving as a means to that end. He worries that the letter's framing — "solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding" — signals that the "right" attitude is to prioritize understanding, which would implicitly declare a large fraction of mathematicians' temperaments "wrong."
He contrasts two scenarios. In the first, publicly available AI models surpass virtually all mathematicians at solving problems; answers arrive faster than the community can absorb them, often with zero human effort — just prompts like "Thank you, please continue." In the second, an international agreement blocks public release of powerful models, and mathematicians within tech companies solve problems only when requested by a representative body. Gowers compares these for their effects on individual and collective understanding but reaches no definitive conclusion, instead posing the hard questions: which aim matters more — advanced collective understanding or answers to as many problems as possible? And "important" for whom — mathematicians or society?
Gowers discloses that he has contacts in OpenAI's mathematics group, has received early access to their models, and has used their Pro models — but has never been paid by OpenAI. He also notes that his Cambridge group works on automatic theorem proving by studying how humans prove theorems; the rise of LLMs that can prove theorems without those insights represents what he calls "the bitter lesson" — a possibility his group always knew was on the table, even if the speed surprised them.
What remains uncertain: Gowers explicitly invites counterarguments to his claim that deep individual involvement with proofs may not be necessary in a world where AI finds proofs instead. He also does not resolve whether the social structures supporting mathematical "digestion" of results can be replaced — a concern raised implicitly by the letter's signatories.