2022-23 Academic Catalog

An introduction to the philosophy of mathematics focusing on the history and development of mathematical proofs. The course is organized around three central questions: i. What is the relationship between a mathematical proof and our knowledge of the theorem that it proves? ii. Do some mathematical proofs go beyond establishing the truth of their theorems and actually explain why the theorems are true? iii. How has our mathematical knowledge grown throughout history? We will first address these questions by reading and discussing Imre Lakatos's book Proofs and Refutations. We will continue with readings drawn from classic and contemporary sources in the history and philosophy of mathematics. This course has no formal prerequisites, though it does presuppose a willingness to read, assess, and write about mathematical proofs.