[ironSkillet]

My math PhD has helped me be a better programmer in several ways. The first is in terms of reasoning above the behavior of complex systems, which mathematical domains and programs are both instances of. Another is in terms of problem solving via abstraction. Mathematics advances by building new abstractions that serve to encapsulate a set of ideas that can then be reasoned about efficiently and in new ways. The same way abstraction layers in programming allow you to build up more and more sophisticated behavior while "hiding" lower level details and not having to even think about them.