My Favorite Theorem

Jeremy Alm likes the Rado graph, a weird object that captures all sorts of interesting properties of finite graphs. Also cheese.

Robin Wilson likes the Hopf Index Theorem and we agree. Also, hot fudge.

Kate Stange is a number theorist who loves quadratic forms (and who doesn't, really). Her favorite theorem is the bijection between them and ideal classes. Also chocolate.

Karen Saxe is an analyst who spends her days representing mathematics on Capitol Hill. She really likes the isoperimetric inequality and its many uses. Also tennis.

Corrine Yap loves math, graph theory in particular, and also loves to perform her one-person play about Sonya Kovalevskaya. Also, tofu.

Allison Henrich studies knots and her favorite theorem is about how one might unknot a knot. Also, music.

We all know the (probably apocryphal) story of Gauss adding up the first 100 positive integers as a child. Well, Tom Edgar really likes this result and will be happy to tell you about dozens of different ways to prove it. Also, Groundhog Day.

Tatiana Toro is a geometer and therefore loves the ur-theorem of geometry, "due" to Pythagoras. She also likes to walk.

Gresham Professor of Geometry Sarah Hart likes cycloids and we talk at length about all their fascinating properties. Also, Moby Dick (or The Whale).

Euler's polyhedral formula continues to amaze Matthew Kahle as he finds it showing up in different places in mathematics. Also, Bach.

Kevin visited Texas Christian University in March and recorded this episode with some math students. Excellent theorems and pairings.

Cihan Bahran has a popular twitter feed in which he shares surprising theorems. His favorite? Matrix mortality is undecidable.

Juliette Bruce is an algebraic geometer who loves to think about embedding curves in projective space. Also mountaineering.

Technically this is a theorem, but it seems so obvious that it's unclear that it needs a proof. In this episode Christopher Danielson points out that polygons have same number of sides as vertices. Many shapes make an appearance.

Kimberly Ayers likes dynamics and so obvs her fave theorem is Sharkovskii's result that "period 3 implies chaos." Also taffy.

Philip Ording wrote a cool book (you should check it out) and he likes the Erlangen Program. Not really a theorem, but we're not purists around here.

Daina Taimina is famous for her adventures in mathematical crocheting, but her favorite theorem comes from Desargues. She also likes to travel.

Tien Chih loves combinatorics, which means he really loves proving things by induction. In this episode we have a good time learning about this incredibly useful technique in mathematics.

We are joined by a group of math students at Cal State University in Los Angeles for a diverse collection of theorems and pairings.

We can't believe it took 75 episodes to get to the Banach-Tarski paradox, but finally Dave Kung chose it as his favorite theorem. Also, Enigma Variations.

An old favorite theorem makes its third appearance on the pod, but we always like to learn new points of view. Priyam Patel likes the Brouwer Fixed Point theorem, and this time we learn how it helps classify isometries of hyperbolic space. Also, rock climbing.

Courtney Gibbons likes isomorphism theorems. All three of them, in fact, and she wants to remind you they are due to Emmy Noether, despite most textbooks ignoring that fact. Also, bunnies.

Kameryn Williams is a logician and their favorite theorem is the less well-known Condensation Lemma of Gödel. Also brie.

Composer Emily Howard uses mathematical objects and ideas as inspiration for her orchestral and chamber pieces. In this episode we talk to her about "Torus" which was inspired by work with dynamicists.

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).

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.