bigideas

It’s been a while, but to celebrate the awarding of the 2008 Abel Prize to John Thompson and Jacques Tits we’ve decided to run an introductory series on the theory of groups. As usual with our mini-series we won’t assume you have any previous mathematical knowledge (beyond basic numeracy), so this will hopefully be a fun and gentle introduction into waters that go very deep indeed.

The Abel prize web site has a nice description of group theory, the field in which both this year’s laureates work. Thompson made a major contribution to the classification of the finite simple groups, whose proof in 1981 was one of the great achievements in mathematics. Those who already know some group theory can marvel at the first volume of Gorenstein, Lyons and Solomon’s projected 12-volume survey of the proof, which collates the many thousands of pages contributed by over a hundred mathematicians over several decades. Tits’s contributions to the field are, I regret to say, more obscure for those of us initiated only as far as the outer circles of modern algebra.

Did I say “algebra”? Well yes, in very general terms group theory is “algebra”, and we’ll do some algebra in the course of the mini-series. But the study of groups doesn’t have to begin with the manipulation of equations, and it can even give an insight into why mathematicians sometimes think such equations are beautiful.

We’ll start the mini-series on groups in a couple of weeks.