“A little-known mathematician in his late 50s shocked the field in 2013 by making a breakthrough on a long-standing prime number problem. Since then, the topic has undergone further significant development because of the efforts of a sizable online collaborative effort of the kind that was unimaginable in mathematics a few decades ago, as well as the insight and imagination of a young mathematician at the beginning of his career.

For thousands of years, Mathematicians have been fascinated, inspired, and enraged by prime numbers. Prime numbers are studied in schools and are beautiful, yet mathematicians’ struggles to understand some of their seemingly straightforward questions demonstrate the complexity and nuance of prime numbers.

Vicky Neale details the recent progress made in disproving the infamous Twin Primes Conjecture, as well as the two very different ways in which the discoveries were made: by a lone mathematician working alone and in secrecy and by a large collaboration that was more widely publicized than any prior mathematical collaboration and revealed a lot about how mathematicians approach their work. Highlights from a much older story about mathematicians’ attempts to understand the beauty and solve the puzzles of prime numbers, dating back at least two thousand years, are interspersed with this one.”