Where does the talent come from? Will tries to explain by comparing himself to Mozart, "He looked at a piano . . . he could just play. I could always just play. That's the best I can explain it."
Is it possible to identify some kind of biological gift for maths? Surely, prodigies started with a few more of the relevant brain cells than you or I. A few years ago, the papers carried the story of the (re)discovery of Einstein's brain. Its left parietal lobe - the area of the brain crucially involved in numerical processes - had brain cells more densely packed than normal. Are these extra cells what made him a great mathematician?
This idea sounds plausible, but it cannot be proved by correlating the number of parietal cells with numerical ability, because, as we all know, correlation is not cause. Being good at numbers could be the cause of more cells rather than the consequence. That is, the brain could assign more parietal cells to number tasks, or hold on to more parietal cells (since brain cells start dying from the day we are born), precisely because that part of the brain is constantly exercised. Activity-dependent brain changes are now well-documented. For example, a Braille-reader's reading finger is connected with a far larger network of brain cells than the other fingers. What is more, the size of the network increases with Braille-reading, and decreases after a couple of days rest from it.
Does this mean anyone can be a prodigy if they work at it long enough and hard enough? We can't be sure, but there is an intriguing piece of evidence. At the end of the last century, Alfred Binet, inventor of the intelligence test, compared the two outstanding prodigies of the day who made their living demonstrating calculating prowess, with three university students and with four cashiers at the Paris department store Bon Marche. The prodigies were much faster than the students, but on most tests they were slower than the cashiers! The cashiers were a fairly random selection of Parisians, but they'd had at least 14 years practice at the tills, learning factors, products and tricks of the calculating trade.
All mathematical prodigies spend most of their waking hours on mathematics. They aren't just working on their own new ideas, they are also learning what other mathematicians have discovered. Imagine going back in time, and presenting Archimedes, the greatest mathematician of antiquity, with an equation that the average A-level student would find easy, such as finding the roots of a quadratic equation. Without doing a lot of homework, Archimedes would be completely stumped. The notation itself would have posed the first barrier. The numerals with zero were invented by Hindu mathematicians 700 years after his death, and "=" by the Englishman Robert Recorde in the 16th century when, as it happens, the idea that equations could have negative roots had just reached the West.
How then could Will even understand the problems that the MIT professor was setting his class? However gifted, he would have had to have spent less time in his cups, and more time in his books. In his study of geniuses, Francis Galton concluded that there could be no exceptional ability, "without an adequate power of doing a great deal of very laborious work".
Brian Butterworth is Professor of Cognitive Neuropsychology at University College London, and author of `The Mathematical Brain', published this month by Macmillan