Why I do mathematical research

[This is a guest post by Emily Riehl. This blog post was initially written in a different file format and converted using AI. — T.] Like many mathematicians, I was drawn to the field as a little girl by its aesthetics: questions that I found endlessly fascinating and arguments that struck me as delightful and elegant. As I grew older, I came to appreciate how personal mathematical aesthetics are. One of the great strengths of our community is the breadth of our collective view of what mathematics is. (Even better: those views are not static. My sense of what mathematics is has changed considerably in the 15 years since my PhD, but that’s a story for another time.) The point of this preamble is to clarify that what follows is a personal view of the purpose of mathematical research, or more precisely one aspect of it. It would be too strong to speak of “the” purpose of mathematics, even using category theorists’ “the”, so I’ll instead describe a purpose of mathematics, focusing on one…