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Sperner's lemma

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#25,231 opened on May 27, 2025

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good first issuet-analysist-combinatorics

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Description

Sperner's lemma is a combinatorial statement about some colorings of the triangulations of a triangle. It can be used to prove the Brouwer fixed point theorem.

Bhavik and I had a go at implementing Sperner's lemma in Lean 3 back in 2021 (in fact, Bhavik had an even earlier go). We reduced the problem to some combinatorial statement with geometric input, and found a proof of it, but the effort petered out before that proof was formalised.

I would be happy to supervise someone to take over where we left things off.

Contributor guide

Research direction
Review the existing partial proof and understand the combinatorial reduction to formalize the remaining steps.
Tech stack
None
Domain
backend
Issue type
Feature
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
2
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
1-2 days
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
Active
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
Clear
Prerequisites
Lean
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
60