As a boy in Shanghai, China, Yitang Zhang believed he would someday solve a great problem in mathematics. In 1964, at around the age of nine, he found a proof of the Pythagorean theorem, which describes the relationship between the lengths of the sides of any right triangle. He was 10 when he first learned about two famous number theory problems, Fermat's last theorem and the Goldbach conjecture. While he was not yet aware of the centuries-old twin primes conjecture, he was already taken with prime numbers, often described as indivisible “atoms” that make up all other natural numbers.But soon after, the anti-intellectual Cultural Revolution shuttered schools and sent him and his mother to the countryside to work in the fields. Because of his father’s troubles with the Communist Party, Zhang was also unable to attend high school. For 10 years, he worked as a laborer, reading books on math, history and other subjects when he could.
Not long after the revolution ended, Zhang, then 23, enrolled at Peking University and became one of China’s top math students. After completing his master’s at the age of 29, he was recruited by T. T. Moh to pursue a doctorate at Purdue University in Lafayette, Ind. But, promising though he was, after defending his dissertation in 1991 he could not find academic work as a mathematician.
In George Csicsery’s new documentary film Counting From Infinity, Zhang discusses his difficulties at Purdue and in the years that followed. He says his doctoral adviser never wrote recommendation letters for him. (Moh has written that Zhang did not ask for any.) Zhang admits that his shy, quiet demeanor didn’t help in building relationships or making himself known to the wider math community. During this initial job-hunting period, Zhang sometimes lived in his car, according to his friend Jacob Chi, music director of the Pueblo Symphony in Colorado. In 1992, Zhang began working at another friend’s Subway sandwich restaurant. For about seven years he worked odd jobs for various friends.
In 1999, at 44, Zhang caught a break. A mathematician friend helped him secure work as a math lecturer at the University of New Hampshire. When he wasn’t teaching his popular calculus classes, where students called him “Tom,” he thought about number theory. By 2009, he had turned his attention to the twin primes conjecture, which postulates that there are an infinite number of prime number pairs with a difference of two. Examples of twin prime pairs include 5 and 7, 11 and 13, and 17 and 19, but no one could prove that these pairs continue to exist all the way up the number line. In fact, no one could prove that there is any bounded prime gap at all, that primes don’t just grow infinitely far apart.
On April 17, 2013, the then-58-year-old Zhang submitted his proof of a bounded prime gap lower than 70 million to the Annals of Mathrmatics, one of the field’s most prestigious journals. Within a remarkably expeditious three weeks, the paper’s referees confirmed that Zhang, an unknown mathematician, had proved “a landmark theorem in the distribution of prime numbers.”
“Never heard of him. Absolutely never heard of him,” said Andrew Granville, a number theorist at the University of Montreal, in Counting From Infinity. When Granville heard about the result and the techniques that Zhang used, he recalled saying, “There’s no way that somebody I’ve never heard of has done this.”
Over the past two years, Zhang has traveled the world giving talks and has received the Ostrowski Prize, the Cole Prize, the Rolf Schock Prize, a MacArthur fellowship and the attention of The New York Times, The New Yorker and many major media outlets. Zhang fielded numerous job offers and was promoted to full professor by the University of New Hampshire.