The web could revolutionise the way we solve the world’s toughest mathematical problemsby Jim Giles / January 27, 2010 / Leave a comment
Published in February 2010 issue of Prospect Magazine
Early last year, a mathematician named Timothy Gowers floated an idea on his blog. Gowers writes as you would expect a mathematician to: precise sentences and plenty of caveats. But it was clear that he was proposing something significant. He had come up with a new way of doing mathematics.
Mathematicians tend to be solitary creatures. The stereotype of the lonely thinker holed up in a sparse study is, at least in this field, somewhat justified. The solution to Fermat’s last theorem, one of the most significant achievements of recent decades, was the creation of one man—Andrew Wiles—who toiled alone in an attic for seven years. Now Gowers was offering something completely different: a “massively collaborative” mathematics.
Gowers took an unsolved problem and threw it open, via his blog, to anyone who wanted to try and solve it. Of course, he was not the only mathematician to blog regularly. But he was the first to use it as a collaborative tool. And he did not want to start with anything easy. The goal was to prove part of the Density Hales-Jewett theorem, a thorny problem concerning bizarre structures that are a bit like noughts-and-crosses boards, except that they exist in multiple imaginary dimensions. The theorem says that a game played on one of these boards cannot remain undecided for long, as a player would be forced to make a line after filling only a tiny fraction of the board. The problem has no immediate practical application, but the field from which it is drawn—combinatorics—is a powerful tool for researchers in areas such as computer science and genetics. And it had defeated top mathematicians for years, including Gowers, who has won the Fields Medal, his discipline’s most prestigious prize.