Suppose we take “applied mathematics” in an extremely broad sense that includes math developed for use in electrical engineering, population biology, epidemiology, chemistry, and many other fields. Suppose we look for mathematical structures that repeatedly appear in these diverse contexts — especially structures that aren’t familiar to pure mathematicians. What do we find? The answers may give us some clues about how to improve the foundations of mathematics!
This is what I’m talking about at the Category-Theoretic Foundations of Mathematics Workshop at U.C. Irvine this weekend.
You can see my talk slides here. You can click on any picture or anything written in blue in these slides to get more information — for example, references.