When Andrew Wiles was 10, he found a library book which mentioned Fermat's Last Theorem. He understood the problem. You can find the numbers x, y and z in x2+y2=z2 (as proved by Pythagoras): they might be, for example, 3, 4 and 5. But you can never find the numbers in x3+y3=z3, or to the power of 4, 5 and so on. Apparently the 17th century amateur mathematician, Fermat, proved this was so but his proof was lost. In 1993 (now aged 40 with thinning hair and "looking the typical mathematician"), Wiles found the solution.
Amir D Aczel's Fermat's Last Theorem (Viking pound;9.99) is the surprisingly exciting story of Wiles's quest and, incidentally, an accessible history of mathematics. Poor, sad arts person that I am, I had to skip much of the maths, but I grasped enough to begin to appreciate the beauty of number theory. If the maths department doesn't read this column, recommend the book.
However, it does pale into irrelevance when set beside Requiem for Will by Will Fisher (pound;7 from Boughspring, Wyesham Road, Wyesham, Monmouth, Gwent NP5 3JU). Published by the author's niece, this First World War diary is a rarity because Will Fisher was in the ranks, and only officers were allowed to keep such records. His style is laconic, but the anger is still biting. "Shell burst among our chaps today, killed four, wounded three. Only a leg remained of one."
The book also contains three savage letters from 1913 describing Will Fisher's part in the rescue work following a pit explosion in Wales in which 439 men were killed. It was while working down the mine that Will developed TB, which he managed to hide so that he could enlist: it's a powerful, cussed story - and wonderful primary-source history.
Set against this, there's something wonderfully peaceful and reassuring about the late Jennifer Lash's On Pilgrimage (Bloomsbury pound;6.99). A mother of six, she developed cancer in 1986 and, after a painful operation, undertook a solitary pilgrimage across France (Lisieux, Paris for Easter, Taize, Lourdes) and on to Santiago de Compostela in Spain. A non-practising Catholic, she writes about holy people and places with knowledge, love and understanding - but also with a calm objectivity. It's a tribute to her style that her simple advice to potential pilgrims seems so logical: "Just go."
Not all that long ago, when belief was more general, blasphemies and profanities were the most potent swear words. Then came a period when the sexual four-letter words were the most taboo. Now the politically incorrect "cripple", "slag" and "bitch" cause far greater offence than "Jesus" or even "fuck". This is just one of many intriguing observations in Geoffrey Hughes's "social history of foul language", Swearing (Penguin pound;7.99).
Yes, it has all the childish fascination of looking up dirty words in the dictionary, but it's also genuinely thought-provoking on why the Victorians were both decorous and vulgar, the modern "explosion" of bad language, and whether women swore as much in the past as they do now.