I’m going to Tim Gowers’s graduate course on Computational Complexity, and we’re four sessions in. It must be the first time I’ve followed a full-blown maths lecture course since I was a Part III student (once upon a time, when the world was young), and I’m enjoying it hugely. Partly because the topic is fascinating, and I’m being prompted to read around a bit. And partly because the performance is terrific.

At five past the hour, Tim Gowers picks up a piece of chalk, and — without notes, it seems — proceeds to explain ideas and proof-strategies and outline proof-steps. Not using overheads or a data projector means that things go at a pace you can take in, and there’s a sense of the proofs being re-created in real time which is very engaging. And his running commentary of incidental comments can be extremely illuminating. For Tim Gowers characteristically wants to show that proof-ideas aren’t just rabbits to be pulled out of the hat in a mysterious way, but are in fact rather natural ideas to try. And that — I warmly agree — is how mathematical proofs should be presented.