Teaching and Learning Guide for: Explanation in Mathematics: Proofs and Practice

Mathematicians value and pursue proofs they consider explanatory, as opposed to those that merely verify a result without explaining it. This is philosophically interesting for at least two reasons. One is because we care about explanation: how does a proof explain a theorem, and what does this tell us about explanation in general? Another is because we care about mathematical practice: what kinds of proofs do mathematicians consider explanatory, and what does this tell us about how mathematics is done and why? The last twenty years has seen a surge of important work on explanatory proof; the article surveys some key recent developments.