Possibly the greatest unsung triumph in mathematics is the classification of the finite simple groups, put together by literally hundreds of mathematicians over the last century. Simple groups are the "building blocks" of symmetry, and the classification throws up 26 oddities, including the infamous "Monster Group".

The proof - spread over some 10000 pages of journal articles - uses some quite impenetrable specialised techniques. But we can get a flavour of it just by looking at some of the simplest cases, using the work of Lagrange, Sylow, Lie, Poincaré and many others.