In 1897, Indiana physician Edwin J. Goodwin believed he had discovered a way to square the circle, and proposed a bill to Indiana Representative Taylor I. Record which would secure Indiana’s the claim to fame for his discovery. About the time the debate about the bill concluded, Purdue University professor Clarence A. Waldo serendipitously came across the claimed discovery, and pointed out its mathematical impossibility to the lawmakers. It had only be shown just 15 years before, by the German mathematician Ferdinand von Lindemann, that it was impossible to square the circle because $\pi$ is an irrational number. This fodder became ignominiously known as the “Indiana Pi Bill” as Goodwin’s result would force $\pi = 3.2$.
In this talk, we review this humorous history of the irrationality of $\pi$. We introduce a method to compute its digits, present Lindemann’s proof of its irrationality (following a simplification by Miklos Laczkovich), discuss the relationship with the Hermite-Lindemann-Weierstrass theorem, and explain how Edwin J. Goodwin came to his erroneous conclusion in the first place.