The Math Is Haunted — overreacted
13 hours ago
- Lean is a programming language used by mathematicians to formalize mathematics as code, enabling modularity and verification.
- The article demonstrates proving a simple theorem (2 = 2) using the `rfl` tactic, which closes goals of the form `x = x`.
- Introducing a false axiom (`math_is_haunted : 2 = 3`) allows proving contradictory statements, illustrating the importance of sound axioms.
- A proof checker only verifies logical conclusions from chosen axioms; if axioms are sound, proofs are sound, regardless of length.
- Efforts are ongoing to formalize Fermat's Last Theorem in Lean, a project expected to take many years.
- Resources for learning Lean include the Natural Numbers Game, Mathematics in Lean, and Tao's Analysis with a Lean companion.