Greg Chaitin on famous physicist John Wheeler asking Gödel about uncertainty: 'Well, one day I was at the Institute for Advanced Study, and I went to Gödel's office, and there was Gödel. I said "Professor Gödel, what connection do you see between your incompleteness theorem and Heisenberg's uncertainty principle?" And Gödel got angry and threw me out of his office!'

Whiteson and Warner tell this in their book. Others say that Gödel just changed the topic of the conversation (which it seems more plausible to me). Anyway, W & W explain that in physics you look for the axioms instead of building from them, which "sidesteps incompleteness". You are constantly adding extra axioms whenever you need them, which is something that is not seen as elegant, mathematically speaking.