What are applications of number theory in physics?

What are applications of number theory in physics?

I was reading Goro Shimura's The Map of My Life. He wrote the following
quote in the book. It made me come up with the title question.
Particularly is there any application of the theory of modular forms in
physics?
QUOTE: A well known math-physicist Eugene Wigner was in our department,
and so I occasionally talked with him. He was pompous and took himself
very seriously. That is the impression shared by all those who talked with
him. At a departmental party, he asked me what kind of mathematics I was
doing. He asked that question as if he met me for the first time. At that
time I had been a full professor and his colleague at least for six years,
perhaps more. I told him vaguely, "Well, mainly things related to modular
forms." Then he said, "Oh, modular forms; we physicists don't need such"
in a very contemptuous tone. I can add that there are some physicists who
are interested in modular forms. Once Edward Witten attended my graduate
course on Siegel modular forms, and often asked sensible questions in
class.