A field where breakthroughs are hard to come by produces two big advances on a single day
Problems in number theory often have a certain exasperating charm: They are extraordinarily simple to state, but so difficult to prove that centuries of effort haven’t sufficed to crack them. So it’s pretty remarkable that on one day this May, mathematicians announced results on two of these mathematical conundrums. Both proofs address one of the most fundamental questions in all of mathematics, the relationship between multiplication and addition.
On May 13, a virtually unknown lecturer at the University of New Hampshire, Yitang Zhang, shocked experts when he announced in a talk at Harvard a proof that takes steps toward solving one of the oldest problems in all of mathematics: the twin prime conjecture.
“Zhang’s result came completely out of the blue,” says Andrew Granville of the University of Montreal. “It’s huge.”
Prime numbers — those divisible only by 1 and themselves — are like the fundamental particles of mathematics, the indivisible building blocks out of which all other numbers are formed. Mathematicians have long noticed that primes often occur in pairs that differ by 2, like 5 and 7 or 137 and 139. They suspect that there are infinitely many pairs of primes that differ by 2, as well as infinitely many that differ by any even number.