Zerah Colburn was not exactly the reigning intellect of Cabot, Vermont. Still only five years old, and with just six weeks’ schooling, he had not yet learned to read either letters or numbers. Left to amuse himself in his father’s carpentry workshop one day in August 1810, he was playing among the wood shavings when his father Abia heard a most unexpected childish prattle. “5 times 7 are 35,” Zerah muttered to himself. “6 times 8 are 48.” Zerah continued to run through multiplication tables while his father listened in astonishment. What, Abia finally asked the child, was 13 times 97? “1261,” the boy answered without hesitation. The career of America’s most amazing “lightning calculator” had begun.
“Lightning calculators” – prodigies who can perform extraordinary computations in their heads at high speed – seem to be born, not made. It’s a curious worldwide fraternity (most are boys), and many of them have come from humble backgrounds: at least four notable prodigies were poor shepherds, and one of the best known, Thomas Fuller, was a slave in 18th-century Virginia. Many calculators could neither read nor write, nor even recognise written numbers. Zerah Colburn, a boy from Cabot, Vermont, bore this same hallmark of lightning talent: his abilities were unrelated to written computation.
Zerah’s father Abia, a carpenter with a wife and six children to support, sensed an opportunity. Within weeks he and his young talent were knocking at the door of Dartmouth College in nearby Hanover, New Hampshire. The college president John Wheelock was so impressed he made Abia a handsome offer: leave Zerah here, he said, and I will raise and educate him without charge. Abia turned him down. He reckoned there were greater riches to be had further afield.
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On a stagecoach from Hanover to Boston, the boy calculated exponents and roots. Increasingly large numbers now came to him with ease. In Boston, Zerah was a sensation. What, one Bostonian asked, is the square of 1449? “2,099,601” the boy replied. What, another demanded, is the number of seconds in 2000 years? “63,072,000,000,” pronounced Zerah.
Three months after that fateful day in the carpenter’s workshop, Bostonians had raised $5000 so that the boy would never have to be exhibited publicly. His father would receive half the money with no strings attached; the other half would go towards raising and educating Zerah in Boston. All Abia Colburn had to do was to sign his name. No, the father said. He wanted more.
Zerah couldn’t explain his technique: when asked, he burst into tears. During calculations, though, he muttered to himself and his body often seemed to spasm. Some lightning calculators have had epilepsy, and an unusually large number have synaesthesia, a neurological condition in which two or more senses are coupled, so that sounds or words – or numbers – are perceived as smells or colours. To Uranie Diamandi, a rare female calculator, the number 1 was black, while 4 was brown. “One hundred and four is easy to remember,” she once explained, “because zero, which is white, is here placed between two dark colours.”
“When asked to explain his technique, Zerah burst into tears”
Epilepsy, synaesthesia and savant syndrome – in which a person has both a mental handicap and extraordinary mental abilities – are unusually prevalent among autistic people, and some calculators have indeed showed signs of autism. For instance, when the 18th-century English calculator Jedediah Buxton was taken to watch the famous actor David Garrick, he could not say whether he liked the play: he had, however, counted how many words Garrick had spoken and how many steps the dancers took on stage. Zerah Colburn’s peculiarities were not nearly so conspicuous, save for one: like his father, he had 12 fingers and 12 toes.
Abia took his peculiar son to seek their fortune in Europe. When they arrived in London in May 1812, Abia booked exhibition rooms and charged a shilling a head to hapless patrons who tried to stump the child. “Zerah Colburn has excited much astonishment here,” artist and inventor Samuel Morse wrote to a friend after one exhibition.
During a visit to the London Stock Exchange, a merchant handed Zerah a guinea and demanded: “How many years, months and days have elapsed since its coinage?” Zerah answered flawlessly, as he did when another questioner asked him to square 888,888. The answer (790,121,876,544) was child’s play to Zerah. The 8-year-old was also asked this innocuous question: is 4,294,967,297 a prime number? No, the boy replied: it is divisible by 641. Unknown to him, this was a shocking feat. He had successfully disproved a Fermat number – a class of numbers that the legendary 17th-century mathematician Pierre de Fermat had conjectured were all prime. This same exception had only previously been found by the equally legendary Leonhard Euler.
As public attention grew, Abia invited subscriptions for the young boy’s memoir. But two years passed without the book appearing. Promises to explain Zerah’s success also came to nothing. When Zerah tried to explain himself to diplomat and future US president John Quincy Adams, Abia kept interrupting. “I might have perhaps understood him, but for the continued interposition of the father himself,” Adams grumbled.
Exhausting patrons in London, the pair then tried Paris. The expatriate American author Washington Irving took an interest in Zerah and arranged his enrolment at the Lyceum Napoleon. These years were the closest the boy had to a normal childhood. Later he fondly recalled his studies and visiting a kindred child spectacle, Victor, the feral “wild child” of Aveyron: Zerah said Victor’s “habits and manners were gentle and inoffensive”. Napoleon himself considered visiting Zerah, a plan permanently postponed by the emperor’s defeat at Waterloo.
The Colburns eventually drifted back to London, where Humphry Davy, the most famous scientist in England, finally persuaded Abia to reveal his son’s secret. “Mr Colburn, the father of the American boy who has such extraordinary powers of calculation, will explain to you the method his son uses in confidence; I wish to ascertain if it can be used profitably,” he wrote to his assistant Michael Faraday. The explanation never came.
By 1819, London had tired of Zerah. Casting about for work, the 15-year-old joined a theatrical troupe on a tour of Ireland, and improbably found himself playing the lead in Richard III. After a couple of fruitless years acting and writing plays, Colburn had scarcely settled into an ideal job calculating for the UK government’s Board of Longitude when his father fell ill. Abia’s dying wish was that his son should return to his family. Yet when Zerah reached home, his mother didn’t recognise him, and his siblings remembered him only as the freak who had taken their father away 13 years before.
History has not been much kinder. When Colburn is remembered at all, it is as a squandered talent. Yet he had a profound effect on the history of mathematics thanks to a contest in 1817 that pitted him against William Hamilton, an Irish linguistic prodigy who also showed promise as a calculator.
Meeting Colburn, Hamilton later recalled, was a defining moment in his life. Zerah recognised a kindred spirit and gave him a tutorial. “I have been considering the methods which Zerah imparted to me of calculating square and cube roots in particular,” Hamilton wrote to a cousin. He was so fired by the encounter that he turned from languages to mathematics. Hamilton became the era’s pre-eminent mathematician, and his discoveries now underlie everything from quantum mechanics to computer graphics.
Zerah himself lost all taste for computation. He drifted into obscurity as a Methodist minister and then taught languages at Norwich University in Vermont. Married and with three daughters to support, in 1833 he made one last attempt to cash in on his talent by writing the long-promised Memoir of Zerah Colburn. Forgotten today, it is a unique document – the first autobiography of a maths prodigy. In it, Colburn also tried to explain his methods. For a square root, he looked at the first number and the last pair of numbers:
What is the square root of 92,416?
1. What number squared ends in 16? Ans. 04.
2. What number squared comes closest to 9? Ans. 3.
Put them together, 304 – the number sought.
But the squares of three other numbers (46, 54 and 96) also end in 16. How did Zerah know which to use? He could not say. As his fellow prodigy George Bidder noted, “unhesitating confidence is half the battle”, and lightning calculation apparently demanded a leap beyond conscious decision-making.
To one admirer who pressed him for the secret to his talent, Zerah Colburn’s explanation was even simpler. “God has put it in my head,” he told her, “and I cannot put it into yours.”
