In April 2013, a 58-year-old mathematician named Yitang Zhang submitted a paper to the prestigious Annals of Mathematics. At the time, he was virtually unknown in the mathematical community. After earning his PhD from Purdue University in 1991, Zhang struggled to find a permanent academic position. For years, he worked outside academia, including at a Subway sandwich shop, before eventually becoming a lecturer at the University of New Hampshire, where he taught undergraduate mathematics. Yet throughout those difficult years, he continued pursuing his own mathematical research, particularly the mysteries of prime numbers. In July 2012, while visiting a friend in Colorado, Zhang was sitting quietly in the backyard when an idea came to him. He had spent three years working on a problem involving the gaps between prime numbers, and suddenly he saw a way past an obstacle that had frustrated some of the world's leading number theorists. Over the following months, he carefully developed that insight into a rigorous mathematical proof. On April 17, 2013, he submitted his manuscript to the Annals of Mathematics. The response was remarkable. Within just three weeks, the referees had delivered an unusually enthusiastic report, recognizing the work as a landmark achievement. The paper was formally accepted on May 21. For centuries, mathematicians had wondered whether infinitely many pairs of prime numbers could occur within some fixed distance of one another. The famous twin prime conjecture predicts that infinitely many pairs differ by exactly 2, such as 11 and 13 or 17 and 19. Zhang did not prove the twin prime conjecture itself. Instead, he established something that had never been proved before: there are infinitely many pairs of consecutive primes whose difference is less than 70 million. Seventy million might seem enormous when compared with 2. But the crucial breakthrough was that the gap was bounded by a fixed number, no matter how far along the number line one went. It was the first proof that bounded gaps between consecutive primes occur infinitely often. His discovery opened an entirely new chapter in number theory, inspiring mathematicians around the world to improve his bound. In 2014, Zhang received a MacArthur Fellowship in recognition of his extraordinary achievement.

At a conference, Evelyn Boyd Granville was asked about her greatest accomplishments. Many people expected her to mention her work on Project Mercury, which helped send astronaut John Glenn into orbit in 1962. Instead, she said, “First of all, I proved that women understand math.” She also said, “As an African American, I showed people that we have the same ability to think and learn.” We later learned that Evelyn Boyd Granville passed away on June 27 at the age of 99, at her home in Silver Spring, Maryland.