My Favorite Theorem

At the 2019 Joint Mathematics Meetings in Baltimore, Kevin and Evelyn asked lots of folks to tell us about their favorite results, and do it in a hurry. The pairings, thought of on the fly, do not disappoint.

In this episode James Propp challenges the obvious notion that things that don't change must be constant. Indeed, it would be an odd universe in which this were not true, but it very much depends upon, and is in fact equivalent to, the completeness of the real numbers. Also potato chips.

Number theorist Matilde Lalin introduces us to the Congruent Number Problem: which integers can occur as the area of a right triangle with rational sides? This turns out to have deep connections to elliptic curves and the Birch and Swinnerton-Dyer Conjectures and other cool stuff.

Geometer Moon Duchin shares her favorite result, a wild generalization of the classical isoperimetric inequality to the landscape of infinite groups. Also politics and gerrymandering, of course.

Our first computer scientist guest tells us about Fano's Inequality and tells us the best snack to enjoy with it.

Mathematician Ursula Whitcher really likes mirror symmetry. And ramen. Find out what this is and why it pairs with noodle soup.

Middle school math teacher Fawn Nguyen gets excited about right triangles and tells us all kinds of trivia about one of the most famous theorems in all of mathematics.

Prof. Rob Ghrist likes dynamics and his favorite theorem unifies the continuous and the discrete by relating the two essential operations in each. Fueled by Monster energy drink.

Cynthia Flores likes uncertainty so much that Heisenberg's Uncertainty Inequality is her favorite theorem. Plus Rick and Morty.

Our guests' wedding went viral and we just had to talk to them. Also, the Intermediate Value Theorem.

Nira Chamberlain likes applied mathematical models. In this episode he tells us about the Lorenz attractor and how that pairs nicely with Caribbean food.

In middle school, mathematician Skip Garibaldi wondered how many real numbers you can actually name. The answer is not as many as you'd like.

Mathematician and writer Michele Audin lets us know why she loves Stokes's Theorem enough to have written a novel about it.

Mathematician Anil Venkatesh likes the Shapley Value, and it turns out to have applications unrelated to politics.

Mathematician-journalist Yen Duong joins us to talk about Ramsey theory and the first "real" theorem she learned--the Ramsey number R(3,3) is 6.

Join us to learn about the Fold and Cut Theorem, which asserts that it is possible to cut any polygonal shape via a single cut provided you fold the paper correctly.

Mike Lawler is a mathematician working in finance. Join us to learn an interesting theorem about insurance pricing.

Join mathematician Chawne Kimber for a journey into Archimedean groups, lattice-ordered groups, and quilting.

James Tanton is the MAA's "Mathematician at Large" and he joins us to talk about Sperner's Lemma.

Applied mathematician Erika Camacho tells us about modeling diseases of the eye using systems of differential equations. Her favorite theorem allows her to understand the solutions to these types of systems.

Our first repeat theorem! But our guest has a completely different take on the Brouwer Fixed Point Theorem, giving us a ton of facts about Brouwer the mathematician.

Contractions on complete metric spaces have unique fixed points. That's a pretty cool theorem, according to our guest Vidit.

Ingrid Daubechies has lots of favorite theorems, but right now it's all about planar graph embeddings. Find out why in this episode.

Euclid taught us that there are infinitely many primes. In this episode Ken Ribet tells us why this is his favorite theorem and gives us a couple of interesting proofs.

Mathematician Jana Rodriguez Hertz tells us about the Smale horseshoe map, symbolic dynamics, noodles, and all kinds of other fun stuff.

Join mathematician Francis Su to find out why he thinks the Brouwer Fixed Point Theorem is so appealing.

Category theorist Emily Riehl tells us her second-favorite theorem: right adjoints preserve limits. Since this is category theory we get another theorem for free by dualizing: left adjoints preserve colimits. Listen to find out Emily's favorite theorem, too.

Join former NFL lineman/current mathematician John Urschel to learn about how to take a dense graph and find a sparse graph whose Laplacian is very close to that of the original graph. Applied math at its finest.

Join applied mathematician Nalini Joshi to learn about Mittag-Leffler's theorem, a fundamental result in complex analysis that tells us how to build meromorphic functions on the plane with any prescribed set of poles.

If you stand at the origin in a forest whose trees lie at integer lattice points, what proportion of them can you see? Jayadev Athreya guides us to the answer and then goes further.

Mathematician Federico Ardila loves matroids and combinatorics. And he's a DJ. A great combination, you can count on it.

Join mathematician Laura Taalman for a journey into the realm of Reidemester moves on knots and just how many you may need to untangle an unknot. The answer may surprise you.

Our guest Patrick Honner tells us about Varignon's Theorem about the midpoints of quadrilaterals. Spoiler alert: if you connect them you always (!) get a parallelogram.

Our guest Candice Price tells us about Conway's rational tangles and how they relate to the topology of DNA. Also, shakes from In 'N' Out.

Mathematician Jeanne Nielsen Clelland tells us about the Gauss-Bonnet Theorem, connecting the curvature on a surface to its Euler characteristic. This episode ends with a bang.

Join our guest Mohamed Omar in his love of Burnside's Lemma and learn how to count the number of ways to paint blocks.

In this episode our guest tells us about Birkhoff's Ergodic Theorem and how it reminds her of certain minimalist music pieces.

Our guest Justin Curry really likes Platonic solids. So much so, in fact, that he has all five of them tattooed on his body. In this episode we talk about the classification of these solids and what ancient piece of literature they pair with best.

Henry Fowler is on the faculty of Dine College in the Navajo Nation. In this episode he tells us about traditional Navajo homes and their relationship to astronomical calculations. The Pythagorean theorem plays an important role.

We are joined by Eriko Hironaka, who tells us about the first theorem she proved. This episode deals with a lot more than just math and it's one of our favorites.

Dusa McDuff tells us about Gromov's non-squeezing theorem, a fundamental result in symplectic topology.

University of Wisconsin professor Jordan Ellenberg reveals that his favorite theorem is Fermat's Little Theorem, which, when you really boil it down, asserts that 1+1 = 2.

University of San Francisco math professor Emille Davie Lawrence joins us to talk about the classification of compact surfaces, west coast coffee, and where to find good donuts.

Math Horizons editor Dave Richeson joins us to talk about the area of a circle. You memorized the formula in grade school, but you've probably never thought about the proof or who proved it. Dave knows.

A conversation with Prof. Amie Wilkinson of the University of Chicago about her favorite theorem. It's a classic.

Your hosts math prof Kevin Knudson and math/science freelance writer Evelyn Lamb discuss their favorite theorems and reveal what pairs best with them.