The 1998 proof of the Kepler Conjecture by Sam Ferguson and Tom Hales (original code).
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The 1998 Proof of the Kepler Conjecture

The Kepler conjecture asserts that no packing of congruent balls in Euclidean 3-space has density greater than the familiar pyramid-shaped packing used to stack oranges at the market.

This repository contains the computer code and other documentation for the 1998 proof of the Kepler Conjecture by Sam Ferguson and Tom Hales. This code is not regularly maintained, but it has been deposited at github as a historical record.

The non-computer portions of proof are given in a series of eight papers available from the arXiv.

Other repositories

Portions of this code have been deposited at the arXiv and with the Annals of Mathematics.

Computer portions of the proof

The computer portions of the proof fall into three main bodies of code, as reflected below in the directory structure.

  • The verification of nonlinear inequalities by interval arithmetic.
  • The verification of linear programs.
  • The generation of all planar graphs satisfying a technical list of properties.

Directory structure

documents/index.html This is the entry point for all html documentation.

documents Html code, graphics, and other documentation.

dodec Materials related to Sean McLaughlin's proof of the dodecahedral conjecture.

graph A java program to generate tame planar graphs.

honey Materials related to the proof of the honeycomb conjecture.

interval Interval arithmetic verification of nonlinear inequalities.

linear Linear programming. This directory contains the bulk of the project code in the form of

numerical Code for the numerical verification of nonlinear inequalities. This part is not mathematically rigorous.

samf Sam Ferguson's code related to the Kepler Conjecture.


This repository of code is essentially the same as the collection of files available from Hales's website at the University of Michigan and the University of Pittsburgh, from around 1997-2013. Html files have been moved to a new documents subdirectory, updating some links.

To accommodate github's 100MB size limits on files, we have split the zip file in linear/SHORT/PENT in two.

A more recent project,, gives a formal proof of the Kepler conjecture.