I don’t see what difference it can make now to reveal that I passed high-school math only because I cheated. I could add and subtract and multiply and divide, but I entered the wilderness when words became equations and x’s and y’s. On test days, I sat next to Bob Isner or Bruce Gelfand or Ted Chapman or Donny Chamberlain—smart boys whose handwriting I could read—and divided my attention between his desk and the teacher’s eyes. Having skipped me, the talent for math concentrated extravagantly in one of my nieces, Amie Wilkinson, a professor at the University of Chicago. From Amie I first heard about Yitang Zhang, a solitary, part-time calculus teacher at the University of New Hampshire who received several prizes, including a MacArthur award in September, for solving a problem that had been open for more than a hundred and fifty years.

The problem that Zhang chose, in 2010, is from number theory, a branch of pure mathematics. Pure mathematics, as opposed to applied mathematics, is done with no practical purposes in mind. It is as close to art and philosophy as it is to engineering. “My result is useless for industry,” Zhang said. The British mathematician G. H. Hardy wrote in 1940 that mathematics is, of “all the arts and sciences, the most austere and the most remote.” Bertrand Russell called it a refuge from “the dreary exile of the actual world.” Hardy believed emphatically in the precise aesthetics of math. A mathematical proof, such as Zhang produced, “should resemble a simple and clear-cut constellation,” he wrote, “not a scattered cluster in the Milky Way.” Edward Frenkel, a math professor at the University of California, Berkeley, says Zhang’s proof has “a renaissance beauty,” meaning that though it is deeply complex, its outlines are easily apprehended. The pursuit of beauty in pure mathematics is a tenet. Last year, neuroscientists in Great Britain discovered that the same part of the brain that is activated by art and music was activated in the brains of mathematicians when they looked at math they regarded as beautiful.

Zhang’s problem is often called “bound gaps.” It concerns prime numbers—those which can be divided cleanly only by one and by themselves: two, three, five, seven, and so on—and the question of whether there is a boundary within which, on an infinite number of occasions, two consecutive prime numbers can be found, especially out in the region where the numbers are so large that it would take a book to print a single one of them. Daniel Goldston, a professor at San Jose State University; János Pintz, a fellow at the Alfréd Rényi Institute of Mathematics, in Budapest; and Cem Yıldırım, of Boğaziçi University, in Istanbul, working together in 2005, had come closer than anyone else to establishing whether there might be a boundary, and what it might be. Goldston didn’t think he’d see the answer in his lifetime. “I thought it was impossible,” he told me.

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.

With a friend’s help, Zhang eventually got his position in New Hampshire, in 1999. Having chosen bound gaps in 2010, he was uncertain of how to find a way into the problem. “I am thinking, Where is the door?” Zhang said. “In the history of this problem, many mathematicians believed that there should be a door, but they couldn’t find it. I tried several doors. Then I start to worry a little that there is no door.”

“Were you ever frustrated?”

“I was tired,” he said. “But many times I just feel peaceful. I like to walk and think. This is my way. My wife would see me and say, ‘What are you doing?’ I said, ‘I’m working, I’m thinking.’ She didn’t understand. She said, ‘What do you mean?’ ” The problem was so complicated, he said, that “I had no way to tell her.”

According to Deane Yang, a professor of mathematics at the New York University Polytechnic School of Engineering, a mathematician at the beginning of a difficult problem is “trying to maneuver his way into a maze. When you try to prove a theorem, you can almost be totally lost to knowing exactly where you want to go. Often, when you find your way, it happens in a moment, then you live to do it again.”

Zhang is deeply reticent, and his manner is formal and elaborately polite. Recently, when we were walking, he said, “May I use these?” He meant a pair of clip-on shades, which he held toward me as if I might want to examine them first. His enthusiasm for answering questions about himself and his work is slight. About half an hour after I had met him for the first time, he said, “I have a question.” We had been talking about his childhood. He said, “How many more questions you going to have?” He depends heavily on three responses: “Maybe,” “Not so much,” and “Maybe not so much.” From diffidence, he often says “we” instead of “I,” as in, “We may not think this approach is so important.” Occasionally, preparing to speak, he hums. After he published his result, he was invited to spend six months at the Institute for Advanced Study, in Princeton. The filmmaker George Csicsery has made a documentary about Zhang, called “Counting from Infinity,” for the Mathematical Sciences Research Institute, in Berkeley, California. In it, Peter Sarnak, a member of the Institute for Advanced Study, says that one day he ran into Zhang and said hello, and Zhang said hello, then Zhang said that it was the first word he’d spoken to anyone in ten days. Sarnak thought that was excessive, even for a mathematician, and he invited Zhang to have lunch once a week.

Matthew Emerton, a professor of math at the University of Chicago, also met Zhang at Princeton. “I wouldn’t say he was a standard person,” Emerton told me. “He wasn’t gregarious. I got the impression of him being reasonably internal. He had received another prize, so the people around him were talking about that. Probably most mathematicians are very low-key about getting a prize, because you’re not in it for the prize, but he seemed particularly low-key. It didn’t seem to affect him at all.” Deane Yang attended three lectures that Zhang gave at Columbia in 2013. “You expect a guy like that to want to show off or explain how smart he is,” Yang said. “He gave beautiful lectures, where he wasn’t trying to show off at all.” The first talk that Zhang gave on his result was at Harvard, before the result was published. A professor there, Shing-Tung Yau, heard about Zhang’s paper, and invited him. About fifty people showed up. One of them, a Harvard math professor, thought Zhang’s talk was “pretty incomprehensible.” He added, “The problem is that this stuff is hard to talk about, because everything hinges on some delicate technical understandings.” Another Harvard professor, Barry Mazur, told me that he was “moved by his intensity and how brave and independent he seemed to be.”

In New Hampshire, Zhang works in an office on the third floor of the math and computer-science building. His office has a desk, a computer, two chairs, a whiteboard, and some bookshelves. Through a window he looks into the branches of an oak tree. The books on his shelves have titles such as “An Introduction to Hilbert Space” and “Elliptic Curves, Modular Forms, and Fermat’s Last Theorem.” There are also books on modern history and on Napoleon, who fascinates him, and copies of Shakespeare, which he reads in Chinese, because it’s easier than Elizabethan English.

Eric Grinberg, the chairman of the math department at the University of Massachusetts Boston, was a colleague of Zhang’s in New Hampshire from 2003 to 2010. “Tom was very modest, very unassuming, never asked for anything,” Grinberg told me. “We knew he was working on something important. He uses paper and a pencil, but the only copy was on his computer, and about once a month I would go in and ask, ‘Do you mind if I make a backup?’ Of course, it’s all in his head anyway. He’s above average in that.”

Zhang’s memory is abnormally retentive. A friend of his named Jacob Chi said, “I take him to a party sometimes. He doesn’t talk, he’s absorbing everybody. I say, ‘There’s a human decency; you must talk to people, please.’ He says, ‘I enjoy your conversation.’ Six months later, he can say who sat where and who started a conversation, and he can repeat what they said.”

“I may think socializing is a way to waste time,” Zhang says. “Also, maybe I’m a little shy.”

A few years ago, Zhang sold his car, because he didn’t really use it. He rents an apartment about four miles from campus and rides to and from his office with students on a school shuttle. He says that he sits on the bus and thinks. Seven days a week, he arrives at his office around eight or nine and stays until six or seven. The longest he has taken off from thinking is two weeks. Sometimes he wakes in the morning thinking of a math problem he had been considering when he fell asleep. Outside his office is a long corridor that he likes to walk up and down. Otherwise, he walks outside.

Zhang met his wife, to whom he has been married for twelve years, at a Chinese restaurant on Long Island, where she was a waitress. Her name is Yaling, but she calls herself Helen. A friend who knew them both took Zhang to the restaurant and pointed her out. “He asked, ‘What do you think of this girl?’ ” Zhang said. Meanwhile, she was considering him. To court her, Zhang went to New York every weekend for several months. The following summer, she came to New Hampshire. She didn’t like the winters, though, and moved to California, where she works at a beauty salon. She and Zhang have a house in San Jose, and he spends school vacations there.

Until Zhang was promoted to professor, last year, as a consequence of his proof, his appointment had been tenuous. “I was chair of the math department, and I had to go to him from time to time and remind him this was not a permanent position,” Eric Grinberg said. “We were grateful to him, but it’s not guaranteed. He always said that he very much appreciated the time he had spent in New Hampshire.”

Zhang devoted himself to bound gaps for a couple of years without finding a door. “We couldn’t see any hope,” he said. Then, on July 3, 2012, in the middle of the afternoon, “within five or ten minutes, the way is open.”

Zhang was in Pueblo, Colorado, visiting his friend Jacob Chi, who is a music professor at Colorado State University-Pueblo. A few months earlier, Chi had reminded Zhang that he had promised one day to teach his son, Julius, calculus, and since Julius was about to be a senior in high school Chi had called and asked, “Do you keep your promise?” Zhang spent a month at the Chis’. Each morning, he and Julius worked for about an hour. “He didn’t have a set curriculum,” Julius told me. “It all just flowed from his memory. He mentioned once that he didn’t have any numbers in his phone book. He memorized them all.”

You’re beyond praise 🥇

Uh, and explain, please, because I do not quite understand the subject, it how?