Strategies for Proofs

Abstract

Not all mathematics involves proofs. We learn a good bit of arithmetic in grade school long before we learn how to prove that the rules of arithmetic are correct. Mathematics originated in the ancient world, in various cultures, prior to the notion of proof. It was the contribution of the ancient Greeks (who, contrary to popular misconception, did not invent mathematics, nor even geometry) to bring the notion of proof into mathematics. The first use of proof is generally attributed to Thales of Miletus, who lived in the sixth century B.C.E. Euclid, who lived in Alexandria in the third century B.C.E., brought the notion of proofs based on axioms to its first peak of success. See [Hea21] for a discussion of ancient Greek mathematics.