In May 2013, the mathematician Yitang Zhang launched what has proven to be a banner year and a half for the study of prime numbers, those numbers that aren’t divisible by any smaller number except 1.

Peruvian mathematician Harald Helfgott gained worldwide attention in 2013 when he solved a 271-year-old problem: the so-called Goldbach’s weak conjecture, according to which every odd number greater ...