A field where breakthroughs are hard to come by produces two big advances on a single day

By Julie Rehmeyer, 10:02 AM June 24, 2013

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...