My Favorite Theorem

Mathematician and philosopher Joel David Hamkins likes games (whatever those are) and his favorite theorem is that winning strategies exist. This requires defining "games", "strategies", and all kinds of other stuff. Also chess.

Mathematician Ranthony Edmonds likes factorization in general, so it's no surprise her favorite theorem is the Fundamental Theorem of Arithmetic. And some history. And mead.

Mathematician Rekha Thomas likes things to have applications, and nothing fits that bill better than linear algebra. In this episode we learn that the singular value decomposition gives us a lot more information than you might have realized. Also, migratory birds.

Mathematician Liz Munch really likes the duality inherent in the Max Flow-Min Cut Theorem. And harps.

Mathematician Érika Roldán likes probability and topology and all kinds of fun stuff. Her favorite theorem involves card shuffling, but it eventually leads to Tetris. Also 3D art.

Howard Masur likes the Riemann Mapping Theorem, a result relating topology (simply connected subsets of the plane) and geometry (conformal mappings).

Pamela Harris and Aris Winger have a podcast you should check out, but they also have favorite theorems as diverse as Zeckendorf's theorem about unique representations of integers as sums of Fibonacci numbers and the Fundamental Theorem of Calculus. Also ceviche and pizza.

Mathematician Lily Khadjavi does more interviewing than we do in this episode, as she proposes a taxonomy of theorems.

Mathematician Tai-Danae Bradley is very excited about the singular value decomposition. And category theory. And Dum Dums.

Science fiction author Yoon Ha Lee has degrees in mathematics and it shows. We revisit an old favorite, Cantor's diagonalization argument. Also waffles.

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).