JLMS centenary

This year is the 100th anniversary of the Journal of the London Mathematical Society. They have celebrated the centenary by an issue of the journal containing ten papers, each starting from an important paper published in the Journal. The entire issue is open-access; I do encourage you to take a look: it can be found at this webpage (at least until the next issue of the journal comes out).

I have had several papers published in the JLMS in the past: one with Rosemary on “crested products”, a new product of association schemes and permutation groups whose name suggests that it is a combination of “crossed” and “nested”; one with six coauthors on transitive permutation groups without semiregular subgroups (this broke the then-new LMS style file which only allowed for four authors); one with Csaba Szabó on independence algebras; and several of my early papers on oligomorphic permutation groups.

But, in any case, I was honoured to be asked to write about Philip Hall’s “Marriage Theorem”, certainly a significant paper in the journal. The other papers are on dimension of well-approximable numbers, by Victor Beresnevich and Sanju Velani; Cartwright and Littlewood on van der Pol’s and similar equations, by John Guckenheimer; the Davenport–Heilbronn method, by Tim Browning; Terry Wall on 4-manifolds, by Mark Powell; a variational principle of Ledrappier and Walters, by Anthony Quas; moment bounds for the zeta-function, by Alexandra Florea; GJMS operators, by Jeffrey S. Case and A. Rod Gover; bundle gerbes, by Nigel Hitchin; and Coxeter’s classification of finite Coxeter groups, by Bernhard Mühlherr and Richard M. Weiss. Something for most tastes there!

One small observation. Some of the selected papers began the attack on a hard problem, and the surveys describe what has been achieved then and subsequently; others, like Hall’s, opened up a new field, and the surveys discuss how this has been developed in many different parts of mathematics. Of course this is an over-simplification. But Hall’s paper is less than 5 pages long, so I decided that a blow-by-blow account was not called for. There are now many different proofs of Hall’s marriage theorem or equivalent results, but I have not seen Hall’s argument before I was forced to read it.