Title: How do we know we can trust mathematics?

Abstract:Mathematics is said to be the most certain part of human knowledge.Other kinds of knowledge may be tested by their power to predict the outcome of experiments.  If mathematics can pass any such test, it is never asked to.  It is said to be certain without any test outside of itself.  In this lecture, I will ask whether we are right in giving mathematics such special belief, and how we can achieve better reasons to trust it.

Note: This is a philosophical talk, but it is addressed to mathematicians.  No background in foundations is assumed.