I first encountered this essay from poking around in Philosophy of Math. If you picked up a survey of the topic, you might think it's all about formalism vs. pl

I first encountered this essay from poking around in Philosophy of Math. If you picked up a survey of the topic, you might think it's all about formalism vs. platonism. That's an interesting topic, but it seems to me as if there's a contemporary trend (maybe not the dominant one) towards trying to understand the practice of mathematics--what makes a proof good or interesting, what mathematicians value, and how to think about mathematical understanding. Unfortunately, the teacher I learned about this stuff from was not good at either (a) writing down his own ideas, or (b) telling us who in the literature was going down the same route. However, Kenny Easwaran's paper "Probabilistic proofs and transferability" (http://www.kennyeaswaran.org/research http://www.kennyeaswaran.org/research) seems somewhat in that vein. Jeremy Avigad has a paper called "Understanding Proofs" that seems relevant, though I never finished it (http://www.andrew.cmu.edu/user/avigad/papers.html http://www.andrew.cmu.edu/user/avigad/papers.html).