This was the first theorem to be proved by a computer, in a "proof by exhaustion". In proof by exhaustion, the conclusion is established by dividing it into cases, and proving each one separately. There may be a lot of cases. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof was controversial because most of the cases were checked by a computer program, not by hand. The shortest known proof of the four color theorem today still has over 600 cases.