My Favorite Theorem

Historian of mathematics Michael Barany has a favorite definition, really, and it's about distributions. Also, we talk about the history of the Fields Medal and a well-thought-out pairing.

Daniel Litt really likes Dirichlet's theorem on primes in arithmetic progressions and it's easy to see why. But we'll let him explain. Also Holmes and Watson make an appearance.

The Jordan Curve Theorem is one of the most well-known results in mathematics and everyone thinks it's obvious. But as Susan D'Agostino points out, there are weird curves where it's not so clear. Also, poetry.

This special episode is a mashup with the Talk Math With Your Friends online seminar series and features mathematician Annalisa Crannell telling us all about Desargues' Theorem, or, as she would call it, the Fundamental Theorem of Perspective Geometry. Also, chopsticks.

Voting theory is on everyone's mind these days. Belin Tsinnajinnie joins us to talk about Arrow's Impossibility Theorem which asserts that the only voting system that conforms to some reasonable rules is a dictatorship by one person. Also tacos.

One of those first weird facts you learn in real analysis is that the rational numbers are dense in the reals. And then you learn later that they're measure zero. Our guest, Rebecca Garcia, says this still kind of blows her mind.

Steve Strogatz is famous for his work in dynamical systems, but his favorite theorem is due to Cauchy. A classic of complex analysis, it asserts that the integral of an analytic function around a closed contour is zero; one of the cleanest results in mathematics. Also, cubism.

Ruthi Hortsch has a very cool job working with middle school math students, but she's also a number theorist who really likes Faltings's Theorem. Also bagels.

Ben Orlin is famous for his bad drawings. In this episode he tells us about Weierstrass's ultimate bad drawing--a continuous function that is nowhere differentiable.

Mathematician Carina Curto really likes the Perron-Frobenius Theorem. Listen to find out why this simple-sounding result is so important and useful.

aBa took a circuitous path to becoming a math professor. His favorite theorem is a number theory fact he figured out on the bus one day and it changed the course of his life.

Mathematician and artist Edmund Harriss thinks about geometry. A lot. And that means considering the Gauss-Bonnet Theorem and how it manifests in the real world.

Bayes's Theorem: love it or hate it you can't deny that it's a useful tool in probability. Join this year's most interesting mathematician Sophie Carr to find out why she loves this theorem so much.

Judy Walker loves coding theory and tells us all about her favorite ones in this episode. Elliptic curves FTW!

Adriana Salerno loves one of the most famous arguments in mathematics--Cantor's Diagonalization Argument. We couldn't agree more (although we certainly agree plenty in the episode).