My Favorite Theorem

Episode 95 - Kyne Santos May 21, 2025 00:35:37 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 Feb 6, 2025 00:40:45 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 Dec 2, 2024 00:22:06 Robin Wilson likes the Hopf Index Theorem and we agree. Also, hot fudge.

Episode 92 - Kate Stange Jun 10, 2024 00:29:37 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.

Episode 91 - Karen Saxe Apr 3, 2024 00:34:17 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.

Episode 90 - Corrine Yap Jan 23, 2024 00:33:46 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 Nov 12, 2023 00:35:04 Allison Henrich studies knots and her favorite theorem is about how one might unknot a knot. Also, music.

Episode 88 - Tom Edgar Oct 9, 2023 00:26:15 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.

Episode 87 - Tatiana Toro Sep 7, 2023 00:23:42 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 Jul 20, 2023 00:41:14 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 Jun 2, 2023 00:30:49 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 May 2, 2023 00:50:21 Kevin visited Texas Christian University in March and recorded this episode with some math students. Excellent theorems and pairings.

Episode 83 - Cihan Bahran Feb 16, 2023 00:26:52 Cihan Bahran has a popular twitter feed in which he shares surprising theorems. His favorite? Matrix mortality is undecidable.

Episode 82 - Juliette Bruce Dec 30, 2022 00:29:20 Juliette Bruce is an algebraic geometer who loves to think about embedding curves in projective space. Also mountaineering.

Episode 81 - Christopher Danielson Nov 26, 2022 00:33:13 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.

Episode 80 - Kimberly Ayers Oct 21, 2022 00:33:56 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 Sep 15, 2022 00:34:32 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 Aug 11, 2022 00:27:40 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 Jul 13, 2022 00:25:53 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.

Episode 76 - Math Students of CSULA Jun 9, 2022 00:58:35 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 Mar 17, 2022 00:30:37 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.

Episode 74 - Priyam Patel Feb 11, 2022 00:42:41 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.

Episode 73 - Courtney Gibbons Jan 13, 2022 00:41:57 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.

Episode 72 - Kameryn Williams Dec 10, 2021 00:22:34 Kameryn Williams is a logician and their favorite theorem is the less well-known Condensation Lemma of Gödel. Also brie.

Episode 71 - Emily Howard Nov 11, 2021 00:39:57 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.

Episode 70 - Joel David Hamkins Sep 22, 2021 00:39:45 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.

Episode 69 - Ranthony Edmonds Aug 14, 2021 00:36:11 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.

Episode 68 - Rekha Thomas Jul 8, 2021 00:27:00 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.

Episode 67 - Liz Munch Jun 10, 2021 00:33:08 Mathematician Liz Munch really likes the duality inherent in the Max Flow-Min Cut Theorem. And harps.

Episode 66 - Érika Roldán May 15, 2021 00:37:08 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.

Episode 65 - Howard Masur Apr 8, 2021 00:28:50 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 Mar 11, 2021 00:48:35 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.

Episode 63 - Lily Khadjavi Feb 11, 2021 00:50:33 Mathematician Lily Khadjavi does more interviewing than we do in this episode, as she proposes a taxonomy of theorems.

Episode 62 - Tai-Danae Bradley Jan 15, 2021 00:31:50 Mathematician Tai-Danae Bradley is very excited about the singular value decomposition. And category theory. And Dum Dums.

Episode 61 - Yoon Ha Lee Dec 10, 2020 00:22:23 Science fiction author Yoon Ha Lee has degrees in mathematics and it shows. We revisit an old favorite, Cantor's diagonalization argument. Also waffles.

Episode 60 - Michael Barany Nov 12, 2020 00:40:36 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.

Episode 59 - Daniel Litt Oct 8, 2020 00:26:36 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.

Episode 58 - Susan D'Agostino Sep 10, 2020 00:25:11 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.

Episode 57 - Annalisa Crannell Aug 13, 2020 00:33:29 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.

Episode 56 - Belin Tsinnajinnie Jul 9, 2020 00:35:10 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.

Episode 55 - Rebecca Garcia Jun 11, 2020 00:24:33 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.

Episode 54 - Steve Strogatz May 14, 2020 00:32:55 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.

Episode 53 - Ruthi Hortsch Apr 9, 2020 00:28:47 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.

Episode 52 - Ben Orlin Mar 12, 2020 00:27:16 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.

Episode 51 - Carina Curto Feb 13, 2020 00:29:15 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 Jan 9, 2020 00:35:22 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.

Episode 49 - Edmund Harriss Dec 12, 2019 00:31:07 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.

Episode 48 - Sophie Carr Nov 14, 2019 00:23:24 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.

Episode 47 - Judy Walker Oct 10, 2019 00:31:38 Judy Walker loves coding theory and tells us all about her favorite ones in this episode. Elliptic curves FTW!

Episode 46 - Adriana Salerno Sep 12, 2019 00:30:55 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).

Episode 45 - Your Flash Favorite Theorems Aug 8, 2019 00:35:40 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.

Episode 44 - James Propp Jul 11, 2019 00:29:12 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.

Episode 43 - Matilde Lalin Jun 13, 2019 00:28:32 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.

Episode 42 - Moon Duchin May 9, 2019 00:24:45 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.

Episode 41 - Suresh Venkatasubramanian Apr 25, 2019 00:30:10 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 Apr 11, 2019 00:27:56 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 Mar 28, 2019 00:28:40 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.

Episode 38 - Robert Ghrist Mar 14, 2019 00:23:47 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.

Episode 37 - Cynthia Flores Feb 28, 2019 00:25:20 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 Feb 14, 2019 00:29:34 Our guests' wedding went viral and we just had to talk to them. Also, the Intermediate Value Theorem.

Episode 35 - Nira Chamberlain Jan 24, 2019 00:21:49 Nira Chamberlain likes applied mathematical models. In this episode he tells us about the Lorenz attractor and how that pairs nicely with Caribbean food.

Episode 34 - Skip Garibaldi Jan 10, 2019 00:23:59 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 Dec 27, 2018 00:29:24 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 Dec 13, 2018 00:25:13 Mathematician Anil Venkatesh likes the Shapley Value, and it turns out to have applications unrelated to politics.

Episode 31 - Yen Duong Nov 29, 2018 00:17:53 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 Nov 8, 2018 00:24:34 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.

Episode 29 - Mike Lawler Oct 25, 2018 00:19:38 Mike Lawler is a mathematician working in finance. Join us to learn an interesting theorem about insurance pricing.

Episode 28 - Chawne Kimber Oct 11, 2018 00:20:25 Join mathematician Chawne Kimber for a journey into Archimedean groups, lattice-ordered groups, and quilting.

Episode 27 - James Tanton Sep 27, 2018 00:24:22 James Tanton is the MAA's "Mathematician at Large" and he joins us to talk about Sperner's Lemma.

Episode 26 - Erika Camacho Sep 13, 2018 00:26:31 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.

Episode 25 - Holly Krieger Aug 23, 2018 00:23:39 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.

Episode 24 - Vidit Nanda Aug 9, 2018 00:19:46 Contractions on complete metric spaces have unique fixed points. That's a pretty cool theorem, according to our guest Vidit.

Episode 23 - Ingrid Daubechies Jul 26, 2018 00:31:36 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 Jul 12, 2018 00:29:48 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.

Episode 21 - Jana Rodriguez Hertz Jun 28, 2018 00:22:49 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 Jun 14, 2018 00:21:31 Join mathematician Francis Su to find out why he thinks the Brouwer Fixed Point Theorem is so appealing.

Episode 19 - Emily Riehl May 24, 2018 00:32:05 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.

Episode 18 - John Urschel May 10, 2018 00:23:44 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.

Episode 17 - Nalini Joshi Apr 26, 2018 00:26:55 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.

Episode 16 - Jayadev Athreya Apr 12, 2018 00:33:00 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.

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