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Care for a little more AI?

Hugo Duminil-Copin (Proofs and Prompts) · blog · 2026-08-30 · ★★★ · archived

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Fields Medalist argues AI proofs of famous conjectures 'petrify' mathematics. He names θ(p_c)=0 as the kind of problem AI may soon take, days before a Claude-written Lean proof of it appeared.

Summary

Duminil-Copin (Université de Genève and IHES) writes that frontier models already outperform humans at many mathematical tasks. He expects AI to resolve famous conjectures, using the dying-percolation conjecture θ(p_c)=0 as his example, before humans would. In his view this loses the real value of open problems: the failed attempts, collaborations, auxiliary methods and intuition built across generations. Open problems act as "lighthouses" for communities, and quick AI solutions risk "decapitating entire fields before they have time to develop", which leaves young mathematicians without problems to grow on. He offers no simple remedy. He says he personally has chosen not to let AI replace his creative process and argues for keeping a culture of search, doubt and failure.

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