History and the Philosophy of Mathematical Practice: Pitzer 2015

Mathematicians often prove the same theorem over and over (and over!) again.  This suggests that there is more at stake than “just” obtaining a correct proof.  It might be a goal to obtain a simpler proof, a more explanatory proof, or a more beautiful proof, for example.  Philosophers of mathematical practice are interested in clarifying and assessing goals like these, and the history of mathematics is a rich resource we can draw upon.  In particular, by examining proofs of the same theorem from different time periods, we can potentially learn about the goals of mathematics, and the means by which they can be achieved.  To illustrate this, I’ll discuss examples from my own research involving the history of number theory.