Starting with a table of fractions, it goes on to calculate pi and area. A clay tablet dating from 1900 bc Babylon shows the Pythagorean triplets 3,4,5 or 5,12,13 - more than 1,000 years before Pythagoras proved that for any right-angled triangle the square of the hypoteneuse equals the sum of the square on the other two sides. "God," said Plato, "ever geometrises."
Numbers are us, as Brian Butterworth tells us in The Mathematical Brain (Macmillan pound;20). Woven into our neural structures, part of everyday life; woven into the very fabric of matter, light, energy, number as an organising principle may be, as A K Dewdney suggests in A Mathematical Mystery Tour (Wiley pound;17.99) integral to the whole cosmos. So the teaching of mathematics, as Sherman K Stein wittily illuminates in Strength in Numbers (Wiley pound;19.99) is still a key "to all that exists", even more so today than in the time of the pyramids. For example, aeroplane computers use Pythagoras's theorem to work out distances. Why, then, do so many of us shy away from maths?
Perhaps one clue might be found in a truly wonderful book, The Joy of Pi by David Blatner (Penguin pound;6.99), which narrates our attempts to "solve" the relationship between the diameter and perimeter of a circle. Pi, roughly represented by 227, is that fixed relation, not only an irrational but a transcendent number: it can be accurately written neither as a relation between whole numbers nor in algebra. However, pi can be calculated to many decimal places - currently more than 51 billion, with no discernible pattern. Such calculation has been among the life tasks of the Chudnovsky brothers, Ukrainian emigres who built a super-computer in their New York apartment. One thinks of the Chudnovskys, plugged into mathematical exploration, unplugged from the 20th century; one thinks of Archimedes, pondering circles in the sand as the Romans invade Syracuse. "Don't touch my circles!" warns the sage. The soldier brains him. Mathematics gives us a choice - pure thought versus the messy mundane - but we don't want to choose The Joy of Pi over The Joy of Sex.
Our culture does not value cold, chaste contemplation. Blatner sprinkles his tightly argued expositions of the evolution of circle theory with amusing fables and quotations (especially hilarious is his account of police evidence at the O J Simpson trial); Dewdney uses a rather coy tour through space and time to connect key mathematical discoveries - Pythagoras and the Greeks, algebra and the Arabs, Newtonian physics and calculus; Stein pulls the reader into the thrumming hypotheses of a mathematician's brain. Paul Hoffman goes a step further in The Man Who Loved Only Numbers (Fourth Estate pound;7.99) which traces the story of Paul Erdos, a Hungarian prodigy.
Before his death in 1996, at 83, Erdos published more papers (1,475), with more collaborators, on more mathematical problems, than anyone else. Reviewers have emphasised his "weirdness" - that he thought all the time, never had a sexual relationship, amassed no possessions. Hoffman's empathy for his unusual subject envelopes the reader in Erdos's own enthusiasms for "problems that fight back".
Readers who cannot feel the joy of pi or who flunk a quick trip from trigonometry to artificial intelligence may warm to a man who often said that if he could not do mathematics he would have to commit suicide. Once, in the 1930s, he sat with a fellow-mathematician in silence for an hour, with furrowed brow. Then, in the words of Anne Davenport, the collaborator's widow, "Harold broke the silence to say, 'It is not nought. It is one.' Then all was relief and joy."