Open Conjecture Formalizations

Lean 4 formalizations of open mathematical conjectures, alongside a curated index of notable conjectures transcribed from Wikipedia’s List of Conjectures.

Formalizations

Each conjecture formalization lives in its own repository, included here as a git submodule. To clone everything:

git clone --recurse-submodules git@github.com:SamuelSchlesinger/open-conjecture-formalizations.git
Conjecture Field Repository
Agoh–Giuga Number Theory agoh-giuga-conjecture
Carmichael Totient Number Theory carmichael-totient-conjecture
Collatz Number Theory collatz-conjecture
Erdős–Straus Number Theory erdos-straus-conjecture
Legendre Number Theory legendre-conjecture
Oppermann Number Theory oppermann-conjecture
Strong Goldbach Number Theory goldbach-conjecture
Twin Prime Number Theory twin-prime-conjecture
Hadamard Combinatorics hadamard-conjecture
Herzog–Schönheim Algebra herzog-schonheim-conjecture
Sensitivity Combinatorics sensitivity-conjecture
Reconstruction Graph Theory reconstruction-conjecture

Conjecture Index

Open Problems

Conjectures that remain unproven, organized by mathematical field:

Up-to-date accounting lives on the field pages:

  1. Number Theory
  2. Graph Theory
  3. Algebra
  4. Geometry & Topology
  5. Analysis
  6. Combinatorics & Order Theory
  7. Other Fields

Conjectures Now Proved

Conjectures that have been resolved and are now theorems, listed chronologically from 1962 to 2019.

Disproved Conjectures

Conjectures that have been shown to be false via counterexample.

Refutations of Conventional Wisdom

Historical examples of widely-accepted mathematical beliefs that were later shown to be false.