# Lean

Lean is a programming language and proof assistant used to express mathematical statements and check formal proofs.

Type: concept. Context selected by Escape Meridian; inclusion is not endorsement.

[Collection](/entities/lean)
[Original website](https://lean-lang.org/)

## Sources

- [Lean](https://lean-lang.org/): Understand what machine-checked proofs establish, which assumptions they use and what people still need to decide.

## Perspectives


## Terminal notes

- [A generated proof can come with a checkable result](/notes/aristotle-proof-checking-2025.md): Harmonic's Aristotle paper combines informal reasoning with Lean proof search and a geometry solver, reporting gold-medal-equivalent performance on 2025 IMO problems. The practical possibility is generated work that can be checked against an explicit mathematical statement.

## Parallels

- [The answer is right. Was the question?](/parallels?parallel=right-answer-wrong-question): When producing an answer gets cheaper, where does the useful work move?

## Context references

- [https://lean-lang.org/](https://lean-lang.org/)
- [https://lean-lang.org/theorem\_proving\_in\_lean4/Axioms-and-Computation/](https://lean-lang.org/theorem_proving_in_lean4/Axioms-and-Computation/)

Latest published distillations: [Publications API](/api/pipeline/publications?entity=lean)