Catching up on some reading: Dyson’s birds and frogs

The semester’s over and I’ve been cleaning off my desk. I found an old issue of the Notices of the AMS (February 2009) with a bookmark in it. It was Freeman Dyson‘s Einstein Lecture entitled “Birds and Frogs.” Here are some good quotes from it. He opens with: Some mathematicians are birds, others are frogs….

Turing’s topological proof that every written alphabet is finite

Recently one of my colleagues was reading Alan Turing‘s groundbreaking 1936 article “On Computable Numbers with an Application to the Entscheidungsproblem.” This is the article in which Turing introduced the turing machine, solved Hilbert’s Entscheidungsproblem (`decision problem’), and proved that the halting problem is undecidable. It is viewed by many as the foundation of computer…

Mathematics in novels and Martin Gardner RIP

I always enjoy encountering mathematics in non-mathematical works of fiction. (I posted excerpts from Candide and The Brothers Karamazov last fall.) Here are a few more that I came across recently. The first is in Dashiell Hammett’s 1934 murder mystery The Thin Man. Here is a conversation between private eye Nick Charles and his wife Nora at the…

Volumes of n-dimensional balls

We all know that the area of a circle is and the volume of a sphere is , but what about the volumes (or hypervolumes) of balls of higher dimension? For a fun exercise I had my multivariable calculus class compute the volumes of various balls using multiple integrals. The surprising results inspired this post….

Movie day in topology class: the Poincaré conjecture

Today was the last day of the topology class I’ve been teaching. I decided to devote the day to the Poincaré conjecture. I started by telling the students a little about the history of the problem. Then I showed them three videos. The first video was an excellent 50-minute lecture by Fields medalist Curt McMullen…

Interview on Strongly Connected Components

I had the pleasure of chatting with Samuel Hansen on the telephone a little while ago. Our conversation is now online as Episode 16 of his Strongly Connected Components podcast series. Check it out! While you’re at it, check out his other interviews as well as his other podcast series, Combinations and Permutation (he discussed my book…