Yitang Zhang, an unknown mathematician who worked at Subway while trying to find an academic position earlier in his career, has written a paper that makes significant progress towards understanding the twin prime conjecture, “one of mathematics’ oldest problems”.

Editors of prominent mathematics journals are used to fielding grandiose claims from obscure authors, but this paper was different. Written with crystalline clarity and a total command of the topic’s current state of the art, it was evidently a serious piece of work, and the Annals editors decided to put it on the fast track.

Just three weeks later — a blink of an eye compared to the usual pace of mathematics journals — Zhang received the referee report on his paper.

“The main results are of the first rank,” one of the referees wrote. The author had proved “a landmark theorem in the distribution of prime numbers.”

Rumors swept through the mathematics community that a great advance had been made by a researcher no one seemed to know — someone whose talents had been so overlooked after he earned his doctorate in 1992 that he had found it difficult to get an academic job, working for several years as an accountant and even in a Subway sandwich shop.

“Basically, no one knows him,” said Andrew Granville, a number theorist at the Universite de Montreal. “Now, suddenly, he has proved one of the great results in the history of number theory.”

Reminds me of a certain patent clerk and his theories about time and space. History doesn’t repeat itself, but it does rhyme. (via @daveg)

**Update:** Here’s a good profile of and interview with Zhang.

Erica Klarreich, a Berkeley-based science writer who has a Ph.D. in mathematics and has written about Zhang, says his proof demonstrates the remarkable balance between order and randomness within the prime numbers. “Prime numbers are anything but random — they are completely determined,” Klarreich says. “Nevertheless, they seem to behave in many respects like randomly-sprinkled numbers that eventually display all possible clumps and clusters. Zhang’s work helps to put this conjectured picture of the primes on a solid footing.”

**Update:** Alec Wilkinson has a profile of Zhang in the Feb 2, 2015 issue of the New Yorker: The Pursuit of Beauty.

Zhang, who also calls himself Tom, had published only one paper, to quiet acclaim, in 2001. In 2010, he was fifty-five. “No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man’s game,” Hardy wrote. He also wrote, “I do not know of an instance of a major mathematical advance initiated by a man past fifty.” Zhang had received a Ph.D. in algebraic geometry from Purdue in 1991. His adviser, T. T. Moh, with whom he parted unhappily, recently wrote a description on his Web site of Zhang as a graduate student: “When I looked into his eyes, I found a disturbing soul, a burning bush, an explorer who wanted to reach the North Pole.” Zhang left Purdue without Moh’s support, and, having published no papers, was unable to find an academic job. He lived, sometimes with friends, in Lexington, Kentucky, where he had occasional work, and in New York City, where he also had friends and occasional work. In Kentucky, he became involved with a group interested in Chinese democracy. Its slogan was “Freedom, Democracy, Rule of Law, and Pluralism.” A member of the group, a chemist in a lab, opened a Subway franchise as a means of raising money. “Since Tom was a genius at numbers,” another member of the group told me, “he was invited to help him.” Zhang kept the books. “Sometimes, if it was busy at the store, I helped with the cash register,” Zhang told me recently. “Even I knew how to make the sandwiches, but I didn’t do it so much.” When Zhang wasn’t working, he would go to the library at the University of Kentucky and read journals in algebraic geometry and number theory. “For years, I didn’t really keep up my dream in mathematics,” he said.

“You must have been unhappy.”

He shrugged. “My life is not always easy,” he said.