Lean: Formalizing Mathematics as Code
Lean is a programming language primarily used by mathematicians to formalize mathematics. It allows mathematicians to treat mathematics as code, breaking it into structures, theorems, and proofs, and sharing them on GitHub. The article uses a simple example, proving 2=2, to introduce Lean's syntax and basic concepts like tactics. It demonstrates how tactics are used to prove or disprove mathematical statements. A fictional axiom, '2=3', illustrates how a faulty axiom can lead to proving anything, highlighting the importance of formal verification. The article concludes by mentioning the ongoing Lean formalization of Fermat's Last Theorem as a testament to Lean's power.
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