Episode 4: Most Valuable Theorems

In this episode, we discuss we consider the periodic table as a metaphor for certain mathematical structures, and we discuss the extent to which various theorems or research fit or don't fit into that paradigm.

We welcome math professor (and our close friend) Tony Várilly-Alvarado as guest. We ask: "What is the most valuable theorem that you cover in [various courses]?" We cover second semester calculus, linear algebra, graduate algebra, and graduate number theory, and you can hear our hot takes on trig substitution, the Rank-Nullity Theorem, and the Sylow Theorems.

In this episode, we discuss aspects of doing like what makes for a good research problem, what to do when you're stuck, and how to avoid proving false things.

In this episode, we discuss some of the best advice we've received, and how it shaped our research.

In this episode, we explore how various modern research topics in algebra and number theory stem from the fundamental desire to understand solutions to polynomial equations.