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.
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.
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.
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 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
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.
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.