Background: I started my undergraduate career in computer science and transitioned to mathematics leaving computer science as a minor. I have just recently completed my Bachelors in Mathematics with a research project in Galois theory, algebraic geometry, and additive number theory. For the next academic year, I am pursuing a Masters in Mathematics which I will complete in a year through a 5-year (BS/MS) program.
Although I did not complete more than a minor in computer science, I have been interested in having it play a vital role in my career goals in academia.
My goal after finishing my masters is to transition into a Ph.D. program in mathematics, but I have not yet decided what I want to focus my research on.
I would like to learn about what Theoretical Computer Science is for academia and what background someone needs to become a theoretical computer scientist.
Questions: Do most theoretical computer science professors have their Ph.D. in mathematics?
How much formal background does one need from computer science itself? Can this be achieved outside of a school setting?
What fields of mathematics play an important role in theoretical cs?