THE MAN WHO COUNTED

Something of an oddity: Tahan, a Brazilian mathematician, casts a series of mathematical puzzles into the form of a continuous narrative describing the adventures of a 13th-century Persian mathematician, Beremiz Samir, secretary to a vizier in Baghdad. There are puzzles here about how to apportion an odd number of camels among three sons so that one receives half, the second a third, and the last a ninth; how to divide 21 casks of wine (seven full, seven half full, and seven empty) so that three friends get an equal number of casks and the same amount of wine—and there are variations on the theme involving pearls, apples, what have you. Tahan also includes asides on the lore of numbers—``perfect'' numbers (equal to the sum of their divisors, excluding the numbers themselves), numerical ``friends,'' magic squares, the weird properties of the number 142,857, and so on. What is curious is the extent to which elements of Islam are woven into the ``plot''—with quotes from the Koran, epigrams, and idealistic statements—as well as brief takes on the history of mathematics. It's also apparent that, for Tahan, mathematics is to be appreciated as a pursuit of pure reason without regard to practical applications. The final test of Beremiz's power consists of seven trials, including a typical truth-teller-vs.-liar puzzle. Our hero triumphs, of course, and asks as his reward the fair Telassim, with whom he lives happily ever after (avoiding the Mongol conquest of Baghdad by moving to Constantinople). A good bet for puzzlers and budding math students. (Thirty- four drawings.)