Research · Updated 9 Oct, 11:12 pm IST
Thomas Hales on Lean theorem prover, formalization and AI
Why it matters for readers: If you care about whether math can be fully trusted, this explains how computers are now checking major theorems.
- Formal proofs are checked exhaustively by computer using proof assistants to ensure foundational correctness.1
- Several major results have been formalized, including the four-color theorem, Feit–Thompson theorem, Kepler conjecture, sphere packing in 8 and 24 dimensions, Navier–Stokes forced blowup, and Fermat’s Last Theorem.1
- Software systems for formalization are called proof assistants or theorem provers, with examples such as Lean, Coq (renamed Rocq last year), Isabelle, Metamath, and Mizar.1
- The post emphasizes the value of consistency and reliability in mathematics as a support for science and civilization.1
- The blog post includes an editorial note that it was converted from a different file format using AI.1
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