  Ivan Niven's succinct proof that pi is irrational is easy to verify, but it
begins with a magical formula that appears to come out of nowhere, and whose
origin remains mysterious even after one goes through the proof. The goal of
this expository paper is to describe a thought process by which a mathematician
might come up with the proof from scratch, without having to be a genius.
Compared to previous expositions of Niven's proof, perhaps the main novelty in
the present account is an explicit appeal to the theory of orthogonal
polynomials, which leads naturally to the consideration of certain integrals
whose relevance is otherwise not immediately obvious.
