On Monday night I unexpectedly came across a TV programme about the code-crackers at Bletchley Park during World War II. Usually such a programme focuses on Turing and the cracking of Enigma but this was about two of the lesser known players: William Tutte who was a mathematician like Turing and Tommy Flowers, a Post Office engineer who arguably built a programmable computer before anyone else. Seeing Tutte was a coincidence as just last week I was trying to understand his graph embedding theorem. [I’d met the theorem before but had forgotten all about it until I was trying to understand the “No Free Lunch Theorem” for discrete Laplace operators by Wardetzky et al, see here. Well, I think I understand the theorem but I don’t understand the proof. In my attempt to understand the basics of discrete Laplace-Beltrami operators I set aside a day last week to understand the proof and perhaps attempt to give a different one. Unfortunately after three days I still didn’t understand all the details of their proof and didn’t have a version of my own either! If anyone knows the details, then get in touch. But I digress…]I found a good description of the theorem on a site by Graham Farr at Monash. You can find it here. It’s a bit long but the important bits are in the first part. I liked the programme, for a start it didn’t assume you were stupid (even though it assumed I wouldn’t have heard of Tutte). The codebreakers programme is of course available for the next few days on the...