Last Thursday a select audience was treated to two excellent lectures.
The occasion was the presentation of the Crighton medals. This award is named in honour of David Crighton, who was president of the Institute for Mathematics and its Applications, and was president-elect of the London Mathematical Society at the time of his untimely death. This year the committee was unable to agree a single winner, so they awarded two, to Peter Neumann and Arieh Iserles, thus neatly encompassing the LMS/IMA duality as well as Oxford/Cambridge. The meeting was held on neutral ground at the Royal Society. The lectures were aimed at non-specialists.
Peter talked about his recent edition of the works of Évariste Galois, published for Galois’ 200th birthday. He told us enough about the theory of equations to put Galois’ contribution into context, but didn’t even give us the definition of a group – indeed, as he pointed out, neither did Galois, which helps to account for his contemporaries’ failure to undertand what he was on about.
The sense of Galois’ genius came across very powerfully. Before his seventeenth birthday he had published the construction of finite fields. Moreover, in answer to a question from the floor, Peter said that there is no hint in the manuscripts of where the idea of Galois theory came from, since it was complete in Galois’ mind when he wrote all the surviving material.
As Peter concluded, Galois gave us fields, groups, Galois theory, and the beginnings of modern algebra, all in a life of less than 21 years.
Arieh Iserles began his talk with a well-received attack on the attitude of the bureaucrats in EPSRC, REF, etc. Their notion of good research funding is to maximise the result of the worst project. Arieh pointed out that almost all money put into mathematics research is essentially wasted, but a very small amount pays off way beyond expectations, like Saul who went out to look for his father’s asses and found a kingdom instead (or more topically, the fast Fourier transform and the RSA cryptosystem, which were discovered before any applications could be made). Planning can take no account of this.
However, planning makes sense on different levels of “granularity”. His main point that the main driver of mathematics in the twentieth century was physics (e.g. functional analysis from quantum theory, differential geometry from general relativity, algebraic geometry from string theory). However, it seems very likely that information theory will take over from physics as the main driver of mathematics. We must be ready for this to happen.
His closing message, which struck a chord with all present, was:
KEEP CALM AND PROVE THEOREMS