As is well-known, the four-color theorem was proved about 1977, making heavy use of computers. And since then, minor errors were fixed and the computer part of the proof was simplified -- but the proof still relied heavily on computer verification. Now it appears that a new proof has been found, not relying on computers, that has been fully (human-) verified. This new proof is by a mathematician named Georges Gonthier. Thomas Hales (whose own 1998 proof of the Kepler conjecture relies heavily on computers) will speak on this new proof at Swarthmore College on Wed., Oct. 5, at 4:30 pm. Here is his abstract: << The four-color theorem states that any map can be colored with four colors in such a way that adjacent countries do not receive the same color. This theorem is one of the most famous math problems ever to be solved by computer. Last year, Georges Gonthier gave a completely formal proof of the four-color theorem. This means that every step of the proof has now been carefully checked all the way down to the fundamental axioms of mathematics. I will describe Gonthier's project and explain how it relates to my current work on packing spheres.
--Dan