section_path: Methods of proof/Proof by exhaustion
section_name: Proof by exhaustion
paragraph_text: Proof by exhaustion
  
  In proof by exhaustion, the conclusion is established by dividing it into a finite number of cases and proving each one separately. The number of cases sometimes can become very large. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof was controversial because the majority of the cases were checked by a computer program, not by hand.