“MATHEMATICS, more than any other art or science, is a young man’s game,” mused Godfrey Harold Hardy ruefully, in his 1940 memoir A Mathematician’s Apology. As if to prove him right, two mathematicians in their twenties have now solved a famous problem that Hardy himself struggled with.
Hardy’s great love was number theory, and one thing number theorists have always wanted to understand is the distribution of prime numbers – those whose only divisors are 1 and themselves. They seem to pop up randomly in the sequence of numbers, and yet paradoxically they also show hints of patterns. One type of pattern is called an arithmetic…
