My Favorite Theorem

Episode 95 - Kyne Santos

21 May 2025

Contributed by Lukas

Kyne Santos, a drag queen and mathematics educator living in Canada, is a big fan of the Fundamental Theorem of Calculus. Also hiking.

Episode 94 - Jeremy Alm

06 Feb 2025

Contributed by Lukas

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

Episode 93 - Robin Wilson

02 Dec 2024

Contributed by Lukas

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

Episode 92 - Kate Stange

10 Jun 2024

Contributed by Lukas

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 cla...

Episode 91 - Karen Saxe

03 Apr 2024

Contributed by Lukas

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

Episode 90 - Corrine Yap

23 Jan 2024

Contributed by Lukas

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

Episode 89 - Allison Henrich

12 Nov 2023

Contributed by Lukas

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

Episode 88 - Tom Edgar

09 Oct 2023

Contributed by Lukas

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 an...

Episode 87 - Tatiana Toro

07 Sep 2023

Contributed by Lukas

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

Episode 86 - Sarah Hart

20 Jul 2023

Contributed by Lukas

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

Episode 85 - Matthew Kahle

02 Jun 2023

Contributed by Lukas

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

Episode 84 - The Students of TCU

02 May 2023

Contributed by Lukas

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

Episode 83 - Cihan Bahran

16 Feb 2023

Contributed by Lukas

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

Episode 82 - Juliette Bruce

30 Dec 2022

Contributed by Lukas

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

Episode 81 - Christopher Danielson

26 Nov 2022

Contributed by Lukas

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 ...

Episode 80 - Kimberly Ayers

21 Oct 2022

Contributed by Lukas

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

Episode 79 - Philip Ording

15 Sep 2022

Contributed by Lukas

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.

Episode 78 - Daina Taimina

11 Aug 2022

Contributed by Lukas

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

Episode 77 - Tien Chih

13 Jul 2022

Contributed by Lukas

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

Episode 76 - Math Students of CSULA

09 Jun 2022

Contributed by Lukas

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

Episode 75 - Dave Kung

17 Mar 2022

Contributed by Lukas

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 Variati...

Episode 74 - Priyam Patel

11 Feb 2022

Contributed by Lukas

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 Po...

Episode 73 - Courtney Gibbons

13 Jan 2022

Contributed by Lukas

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 textbo...

Episode 72 - Kameryn Williams

10 Dec 2021

Contributed by Lukas

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

Episode 71 - Emily Howard

11 Nov 2021

Contributed by Lukas

Composer Emily Howard uses mathematical objects and ideas as inspiration for her orchestral and chamber pieces. In this episode we talk to her about "...

Episode 70 - Joel David Hamkins

22 Sep 2021

Contributed by Lukas

Mathematician and philosopher Joel David Hamkins likes games (whatever those are) and his favorite theorem is that winning strategies exist. This requ...

Episode 69 - Ranthony Edmonds

14 Aug 2021

Contributed by Lukas

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

Episode 68 - Rekha Thomas

08 Jul 2021

Contributed by Lukas

Mathematician Rekha Thomas likes things to have applications, and nothing fits that bill better than linear algebra. In this episode we learn that the...

Episode 67 - Liz Munch

10 Jun 2021

Contributed by Lukas

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

Episode 66 - Érika Roldán

15 May 2021

Contributed by Lukas

Mathematician Érika Roldán likes probability and topology and all kinds of fun stuff. Her favorite theorem involves card shuffling, but it eventuall...

Episode 65 - Howard Masur

08 Apr 2021

Contributed by Lukas

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

Episode 64 - Pamela Harris and Aris Winger

11 Mar 2021

Contributed by Lukas

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 uniqu...

Episode 63 - Lily Khadjavi

11 Feb 2021

Contributed by Lukas

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

Episode 62 - Tai-Danae Bradley

15 Jan 2021

Contributed by Lukas

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

Episode 61 - Yoon Ha Lee

10 Dec 2020

Contributed by Lukas

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

Episode 60 - Michael Barany

12 Nov 2020

Contributed by Lukas

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

Episode 59 - Daniel Litt

08 Oct 2020

Contributed by Lukas

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...

Episode 58 - Susan D'Agostino

10 Sep 2020

Contributed by Lukas

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, th...

Episode 57 - Annalisa Crannell

13 Aug 2020

Contributed by Lukas

This special episode is a mashup with the Talk Math With Your Friends online seminar series and features mathematician Annalisa Crannell telling us al...

Episode 56 - Belin Tsinnajinnie

09 Jul 2020

Contributed by Lukas

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 vo...

Episode 55 - Rebecca Garcia

11 Jun 2020

Contributed by Lukas

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 m...

Episode 54 - Steve Strogatz

14 May 2020

Contributed by Lukas

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 ...

Episode 53 - Ruthi Hortsch

09 Apr 2020

Contributed by Lukas

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...

Episode 52 - Ben Orlin

12 Mar 2020

Contributed by Lukas

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 ...

Episode 51 - Carina Curto

13 Feb 2020

Contributed by Lukas

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

Episode 50 - aBa

09 Jan 2020

Contributed by Lukas

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...

Episode 49 - Edmund Harriss

12 Dec 2019

Contributed by Lukas

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

Episode 48 - Sophie Carr

14 Nov 2019

Contributed by Lukas

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...

Episode 47 - Judy Walker

10 Oct 2019

Contributed by Lukas

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

Episode 46 - Adriana Salerno

12 Sep 2019

Contributed by Lukas

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

Episode 45 - Your Flash Favorite Theorems

08 Aug 2019

Contributed by Lukas

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 hurr...

Episode 44 - James Propp

11 Jul 2019

Contributed by Lukas

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...

Episode 43 - Matilde Lalin

13 Jun 2019

Contributed by Lukas

Number theorist Matilde Lalin introduces us to the Congruent Number Problem: which integers can occur as the area of a right triangle with rational si...

Episode 42 - Moon Duchin

09 May 2019

Contributed by Lukas

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

Episode 41 - Suresh Venkatasubramanian

25 Apr 2019

Contributed by Lukas

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

Episode 40 - Ursula Whitcher

11 Apr 2019

Contributed by Lukas

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

Episode 39 - Fawn Nguyen

28 Mar 2019

Contributed by Lukas

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 al...

Episode 38 - Robert Ghrist

14 Mar 2019

Contributed by Lukas

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

Episode 37 - Cynthia Flores

28 Feb 2019

Contributed by Lukas

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

Episode 36 - Nikita Nikolaev & Beatriz Navarro Lameda

14 Feb 2019

Contributed by Lukas

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

Episode 35 - Nira Chamberlain

24 Jan 2019

Contributed by Lukas

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

Episode 34 - Skip Garibaldi

10 Jan 2019

Contributed by Lukas

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.

Episode 33 - Michele Audin

27 Dec 2018

Contributed by Lukas

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

Episode 32 - Anil Venkatesh

13 Dec 2018

Contributed by Lukas

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

Episode 31 - Yen Duong

29 Nov 2018

Contributed by Lukas

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.

Episode 30 - Katie Steckles

08 Nov 2018

Contributed by Lukas

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 p...

Episode 29 - Mike Lawler

25 Oct 2018

Contributed by Lukas

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

Episode 28 - Chawne Kimber

11 Oct 2018

Contributed by Lukas

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

Episode 27 - James Tanton

27 Sep 2018

Contributed by Lukas

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

Episode 26 - Erika Camacho

13 Sep 2018

Contributed by Lukas

Applied mathematician Erika Camacho tells us about modeling diseases of the eye using systems of differential equations. Her favorite theorem allows h...

Episode 25 - Holly Krieger

23 Aug 2018

Contributed by Lukas

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...

Episode 24 - Vidit Nanda

09 Aug 2018

Contributed by Lukas

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

Episode 23 - Ingrid Daubechies

26 Jul 2018

Contributed by Lukas

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

Episode 22 - Ken Ribet

12 Jul 2018

Contributed by Lukas

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 i...

Episode 21 - Jana Rodriguez Hertz

28 Jun 2018

Contributed by Lukas

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

Episode 20 - Francis Su

14 Jun 2018

Contributed by Lukas

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

Episode 19 - Emily Riehl

24 May 2018

Contributed by Lukas

Category theorist Emily Riehl tells us her second-favorite theorem: right adjoints preserve limits. Since this is category theory we get another theor...

Episode 18 - John Urschel

10 May 2018

Contributed by Lukas

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 cl...

Episode 17 - Nalini Joshi

26 Apr 2018

Contributed by Lukas

Join applied mathematician Nalini Joshi to learn about Mittag-Leffler's theorem, a fundamental result in complex analysis that tells us how to build m...

Episode 16 - Jayadev Athreya

12 Apr 2018

Contributed by Lukas

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 th...

Episode 15 - Federico Ardila

22 Mar 2018

Contributed by Lukas

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

Episode 14 - Laura Taalman

08 Mar 2018

Contributed by Lukas

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 ...

Episode 13 - Patrick Honner

22 Feb 2018

Contributed by Lukas

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

Episode 12 - Candice Price

08 Feb 2018

Contributed by Lukas

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.

Episode 11 - Jeanne Nielsen Clelland

25 Jan 2018

Contributed by Lukas

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

Episode 10 - Mohamed Omar

11 Jan 2018

Contributed by Lukas

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

Episode 9 - Ami Radunskaya

28 Dec 2017

Contributed by Lukas

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

Episode 8 - Justin Curry

07 Dec 2017

Contributed by Lukas

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 a...

Episode 7 - Henry Fowler

16 Nov 2017

Contributed by Lukas

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...

Episode 6 - Eriko Hironaka

26 Oct 2017

Contributed by Lukas

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 ou...

Episode 5 - Dusa McDuff

05 Oct 2017

Contributed by Lukas

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

Episode 4 - Jordan Ellenberg

14 Sep 2017

Contributed by Lukas

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

Episode 3 - Emille Davie Lawrence

24 Aug 2017

Contributed by Lukas

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

Episode 2 - Dave Richeson

03 Aug 2017

Contributed by Lukas

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 t...

Episode 1 - Amie Wilkinson

26 Jul 2017

Contributed by Lukas

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

Episode 0 - Your Hosts' Favorite Theorems

21 Jul 2017

Contributed by Lukas

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