Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they? Introduction “There are five fundamental operations in mathematics,” the German mathematician Martin Eichler supposedly said. “Addition, subtraction, multiplication, division and modular forms.” Part of the joke, of course, is that one of those is not like the others. Modular forms are much more complicated and enigmatic functions, and students don’t typically encounter them until graduate school. B...