Thompson greatly extended algorithms and data structures for carrying out perfect analysis of chess endgame positions with at most five pieces on the board—three besides the kings. You could be better than him and better than Belle overall, but if you got down to 5 pieces, you might as well be “playing chess against God” as he called it. It was a chess version of Paul Erdős’ proofs from the “Book,” in giving you not only the answer but the shortest route to the win or draw. His database overturned centuries of belief that certain endgames were drawn. You can win them—if you have the patience to find over 100 perfect moves