Flyspeck

Flyspeck is a mathematical project that aimed to formally verify the computer proof of the Four Color Theorem. The Four Color Theorem, first stated in 1913, posits that any map in a plane can be colored using four colors in such a way that no two adjacent regions have the same color. A computer-assisted proof was developed by Kenneth Appel and Wolfgang Haken in 1976, though it was initially met with skepticism due to its reliance on computer calculations.

The Flyspeck project, initiated by Thomas Hales in 2003, took on the task of providing an extremely rigorous and verifiable proof of the Four Color Theorem. The goal was to use formal proof assistants to check every step of the proof, eliminating any possibility of human error. This involved translating the original proof into a formal language that could be understood and verified by specialized software. The project also aimed to prove the Kepler conjecture, a related problem concerning the most efficient way to pack spheres.

After years of development and collaboration, the Flyspeck project announced the completion of its formal proof of the Kepler conjecture in 2014. The proof of the Four Color Theorem was also formally verified as part of this extensive undertaking. The success of Flyspeck demonstrated the power of formal verification methods in mathematics and computer science, offering a new level of confidence in complex proofs.