Symmetry: A Journey into the Patterns of Nature by Marcus du SautoyThis book is really awesome and goes into a mathemetician's private obsession and delight in symmetry and the drama of the pursuit of a complete catalog of all symmetry types. The Moorish tiles in the Alhambra, the packing of spheres in the 24th dimension, error detection and correction codes, all are connected.
This has about the best explanation for the math loving quasi-layman of the Monster symmetry which emerges from the depths of the 196833rd dimension.
An object with rotations for this symmetry group needs 196833 dimensions to construct....
Yes, 196,833.... (The sphere packing solution, the so called Leech lattice, and the EDECs are all there for the taking in the 24th dimension, just to give you a sense of proportion.)
Um oddly if you add one to the dimensionality IT JUST SO HAPPENS to appear as a coefficient associated with the modular function, and the NEXT ONE is can be formed with this and other dimensionalities in which it occurs by a trivial bit of arithmetic and so on. Now this function connects to Wiles proof of Fermat's last theorem, and this symmetry is starting to show up in string theory--and essentially IT IS IN THE MIDDLE OF EVERYTHING.
(The monster group is the highest order sporadic group . It has group order, well, too long to type out.)
Well, this book was so fascinating I couldn't put it down (and I am rereading parts of it.) Of course your mileage my differ, but I enjoyed it a lot.
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