Proof has been an essential part of mathematics since the time of the ancient Greeks. Its centrality has engendered much controversy. What is the role of proof in mathematics? What makes for an adequate proof?
The recent use of computers in developing mathematical conjectures, and in checking cases when there are too many for humans to check in a reasonable amount of time, has led to questions about the role and importance of proof in mathematics, as well as what qualifies as a proof. The chapters in this section give three different views of these and other issues regarding relationships among proof, mathematics, and computers.