Functional analysis by Rudin. I needed to check something for work but then I saw that Rudin had a proof of the prime number theorem using Riemann’s zeta function. It’s one of the great ironies of mathematics that a simple statement about the integers is most naturally proved by applying abstract analytical techniques to a function of complex numbers, and I decided I had to see how it was done, which entailed working through the theory of Fourier transforms and distributions.
There are ‘elementary’ proofs, most notably by Pal Erdos, that only use ordinary number theory, but elementary does not mean ‘easy’ in this context. I plan to try and work through one of the elementary proofs some time.
This reminds me to mention that my Erdos number is 3 (via Peter Wakker and Peter Fishburn). At a stretch, this blog could be claimed as a collaborative work, in which case all my commentators would obtain an Erdos number of 4 – highly prized in some circles.
*Thanks to my travels, everything is running behind. So I’ve skipped this week’s Word for Wednesday, and put in last weeks Sunday feature instead