The Great Mental Calculators: The Psychology, Methods, and Lives of Calculating Prodigies, Past and Present
by Steven B. Smith
Columbia University Press, 374 pp., $25.00
In Brunswick, Germany, in 1780, a stonemason was calculating the wages due his workmen at the end of the week. Watching was his three-year-old son. “Father,” said the child, “the reckoning is wrong.” The boy gave a different total which, to everyone’s surprise, was correct. No one had taught the lad any arithmetic. The father had hoped his son would become a bricklayer, but the boy, Carl Friedrich Gauss, thanks to his mother’s encouragement, became one of the greatest mathematicians in history.
Regardless of such anecdotes, the ability to calculate swiftly and accurately in one’s head seems to have little correlation with creative mathematical ability or high intelligence. Some eminent mathematicians—Gauss, John Wallis, Leonhard Euler, John von Neumann, to name four—had this ability, but most first-rate mathematicians were and are no more skilled in mental arithmetic than good accountants. A few calculating prodigies have even been mentally retarded. No one knows the extent to which this curious skill is genetic, or how much is the result of environment and arduous self-training.
Steven B. Smith, in his admirable history of calculating prodigies—the best, most comprehensive, most reliable book yet written on the subject—thinks that the talent springs mainly from strong childhood motivations. For a variety of reasons, not well understood, a child, often isolated and lonely, will fall passionately in love with numbers. “Children need friends,” Smith writes, “for amusement and companionship. They often devise imaginary friends to keep them company when flesh and blood friends are absent. Calculating prodigies have made numbers their friends.”
When you and I see a license plate on a car ahead of us, we usually see a meaningless number, but to calculating geniuses it is invariably rich in properties and associations. If it happens to be prime (a number with no factors except itself and I) they will instantly recognize it as a prime. If composite (nonprime), they may at once determine its factors. Consider 3,844. “For you it’s just a three and an eight and a four and a four,” said William Klein to Smith, who considers Klein the world’s greatest living mental calculator. “But I say, ‘Hi, 62 squared.’ ”
There is an interesting parallel, Smith suggests, between mental calculating and juggling. Almost anyone can learn to juggle, but only a few are driven to practice until they become experts, and even fewer make it their profession. Children who learn to juggle numbers in their head diverge in later life along similar paths. Some lose interest in the art, some preserve it as a hobby, some make good use of it in their careers. On rare occasions, when talent and passion are high and environmental influences appropriate, a young man or woman will work up a “lightning calculation” act and go into show business.
The stage calculators—like magicians, jugglers, acrobats, tap dancers, chess grandmasters, and pool hustlers—are a diversified breed, with almost nothing in common except their extraordinary ability. Consider Zerah Colburn …