Hello, Here's my paper for the class. For fun I also attached the python script to get and run the thomas programs. It is actually silly though, because it just runs them and so if an error occurs in all but the last step it will just run the next one, and the user will possibly miss the error and thus think the proof complete. James Also, slides for a talk: http://itcs.tsinghua.edu.cn/~john/talk.pdf And a webpage: http://people.math.gatech.edu/~thomas/FC/fourcolor.html