2006*Symmetry and the Monster*.

This is the story of group theory, from the early days when Galois invented the subject, up to the present day with the identification of the "Monster" group, and a peer into the future with bizarre links to apparently unrelated branches of mathematics, and maybe even to physics. It is about the search for the complete set of all "atomic" groups (groups that form the basis of all the other groups), that mainly fall into a few neat families, with a few strange exceptions, including the biggest exception of the lot: the "Monster" group.

One thing I've noticed, reading this along with other books telling
parallel stories (such as Fermat's Last
Theorem and the Riemann
Hypothesis), is the tragic similarities in the histories of all
these essentially disjoint groups of mathematicians (except for the few
*very* famous who crop up everywhere), and I wonder how on earth
they managed to do *any* work. Europe was at war most of the time,
and they kept moving round, and their contemporaries kept getting killed,
right up to the utter devastation inflicted on German mathematics by the
Nazis. Yet the ones that survived seem to have been supremely productive.

We get quite a lot of historical detail of the mathematicians involved
here. (It is interesting to see a totally different explanation for
Galois' death.) Now, I usually don't much like books that dwell on the
personalities to the exclusion of the technicalities. But here, I'm not
sure how much a non-mathematician would get the maths -- I already knew a
little of the earlier stuff (if not the later) and still found it a
struggle. But in some sense that doesn't matter. What we do get is a story
of the sheer breathless *excitement*, of how mathematicians are
drawn by patterns and beauty (and how it seems that most of the early
mathematicians, at least, were completely bonkers!), with just enough of
the flavour of the underlying maths to help ground it. We get to see the
fevered excitement of the group theorists as they near completion of their
task, and the bewilderment and skepticism of their non-group-theoretic
colleagues, wondering if all these 200 page and 400 page proofs are *proper*
mathematics.

And the end is quite intriguing, in much the same way as the end of
Riemann Hypothesis story. There
seem to be links between certain characteristic values of the Monster
group, and some *apparently* totally unrelated number theory. Now,
*some* of these might just be consequences of Guy's "Strong
Law of Small Numbers", that "There aren't enough
small numbers to meet the many demands made of them", and so
coincidences *will* arise. But some of these numbers are big enough
(20-odd *billion*) that mere coincidence doesn't seem to be the
right answer. And then there are the possible links with string theory and
why space many be 26-dimensional (related to a peculiarly compact packing
of hyperspheres in 24d). There's something going on here...