The sphere eversion project

This project formalizes the proof of a theorem implying the existence of sphere eversions. It was carried out by Patrick Massot, Floris van Doorn and Oliver Nash, with crucial help from the wider Lean community. The proof of the main theorem was completed on November 12th 2022. Details can be found on the project website.

This project originally used Lean 3 but was ported to Lean 4 with crucial help from Yury Kudryashov.

Build the Lean files

To build the Lean files of this project, you need to have a working version of Lean. See the installation instructions (under Regular install).

To build the project, run lake exe cache get and then lake build.

Build the blueprint

To build the web version of the blueprint, you need a working LaTeX installation. Furthermore, you need some packages:

sudo apt install graphviz libgraphviz-dev
pip3 install invoke pandoc
cd .. # go to folder where you are happy clone git repos
git clone
pip3 install ./plastex
git clone
pip3 install ./leanblueprint
cd sphere-eversion

To actually build the blueprint, run

lake exe cache get
lake build
inv all

To view the web-version of the blueprint locally, run inv serve and navigate to http://localhost:8000/ in your favorite browser.