Mathematicians have reacted to recent AI advances in theorem proving with a mix of excitement and frustration. Some AI enthusiasts now argue that the time has come to formalize all of mathematics as a legacy for future generations. The authors, a group of expert formalizers including Jeremy Avigad, Kevin Buzzard, Johan Commelin, Rémy Degenne, Kim Morrison, Oliver Nash and Adam Topaz, say they are sympathetic to the proposal and optimistic about AI's role. They are, however, deeply concerned by calls to formalize everything as quickly as possible.
If done well, a large-scale, coordinated formalization effort could greatly expand mathematical exploration and discovery. Done poorly, the authors warn, it would be a waste of resources at best and could cause lasting damage at worst. They stress that the views expressed are their own and not those of any organization they are associated with, and that their colleagues hold a wide range of opinions on AI-driven formalization.
The authors point to recent examples. A project to formalize Maryna Viazovska's sphere-packing results was disrupted when an AI company tried to take it over. The original team found that cleaning up the AI-generated code was more trouble than it was worth, so they discarded it and rebuilt the work properly with AI assistance. Similarly, when Anthropic announced that Claude had formally verified Fermat's Last Theorem in 13 million lines of code, the result was impressive but of limited ongoing value, since the theorem was never seriously in doubt.
The central point is that a formal artifact is only valuable if people use it. Formalizations matter for what they enable beyond correctness, such as exploring generalizations, connecting branches of mathematics, and refining concepts. The authors argue that real understanding, not raw volume of verified code, should guide the effort.
Source: Hacker News · Summarized by HeadlinesBriefing