# Strategies for Proofs

• Ethan D. Bloch

## Abstract

Not all mathematics involves proofs. We learn a good bit of arithmetic in grade school long before we learn how to prove that what we learned in grade school is true. 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 Thaïes 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 more details on ancient Greek mathematics.)

## Keywords

Real Number Prime Number Direct Proof Mathematical Proof Rigorous Proof
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.