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Formal mathematics and proof assistants — Clarity Today

Topic

Formal mathematics and proof assistants

The practice of writing mathematical definitions and proofs in machine-checkable code so a computer can verify every logical step. Proof assistants such as Lean, Coq and Isabelle are the main tools, and their shared libraries accumulate over years of community work.

Current clusters

science1 distinct publisher

Eleven days of machine time turned Wiles's 100 pages into 13 million lines of Lean

Anthropic says its Claude agents ran autonomously for 11 days to formalise Fermat's Last Theorem in 13 million lines of Lean, a result that rests on a finished human proof and 2 million lines of prior formalisation.

Publishers:newscientist.com

Reality

Evidence42
Adoption25
Hype gap+30
Incentives78

Confidence55