Science in Mind

Obscure University of New Hampshire math professor takes major step toward elusive proof

Yitang Zhang, Mathematics
Yitang Zhang, a math lecturer at the University of New Hampshire Credit: Lisa Nugent, UNH Photographic Services

A soft-spoken, virtually unknown mathematician from the University of New Hampshire has found himself overnight a minor celebrity, flooded with requests to give talks at top universities as his work is debated and celebrated online by leaders in his field.

On May 9, mathematician Yitang Zhang, who goes by Tom, received word that the editors of a prestigious journal, Annals of Mathematics, had accepted a paper in which he took an important step toward proving a very old problem in mathematics.

Soon, he received an invitation to Harvard University from celebrated math professor Shing-Tung Yau, to present his proof. Zhang demurred at first, saying he was wrapping up the semester.

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“I said, ‘This is the final exam week. I would be busy. Can I arrange it on May 17?” Zhang recalled. “But he said, just come as early as possible.”

Last week, just days after he learned his paper was accepted, Zhang found himself giving a talk to a packed room full of Harvard mathematicians who had never heard of him.

For more than a century—and perhaps as far back as ancient Greece—mathematicians have conjectured there are an infinite number of prime numbers separated by two. That would mean that there are an infinite number of pairs such as 3 and 5, or 41 and 43, or 269 and 271. What Zhang showed was actually that there were an infinite number of primes separated by 70 million. As any child who knows how to count knows, 70 million is a far from two, but Zhang’s proof—of something called the “bounded gaps conjecture”—excites mathematicians because it is the first time anyone has proven there are an infinite number of primes separated by an actual number.

“These are the kinds of problems that you can explain to high school students, and yet difficult to solve,” Yau said. “Any problem of this sort, that you can explain to a high school student and yet it cannot be proved easily are usually not easy because people have thought about this for a long, long time.”

Yau, who invited Zhang to give the talk, said that he sends out invitations to seminars all the time. What was unusual about this one was the turnout: 50 people packed into the room to hear a talk by a virtual unknown—Yau said neither he nor his other colleagues had ever heard of Zhang before, who had taken accounting jobs prior to becoming a lecturer at the University of New Hampshire. Response to the exciting result rippled through the math world, with analyses of what Zhang had done exchanged and a summary of his talk circulating online.

“This is certainly one of the most spectacular results of the last decade,” Alex Kontorovich, a mathematician at Yale University, wrote in an e-mail. “What’s very surprising is that something this strong can be rigorously proved in today’s world. Many people expected not to see this result proved in their lifetime.”

Zhang said that he began to think seriously about solving the problem four years ago. He read some math papers that had taken a stab at the problem and he saw in his mind a key gap where he thought he could make progress. The epiphany did not come to him until July 3 of last year, when he realized he could modify existing techniques, building on what others had tried.

“It is hard to answer ‘how,’” Zhang wrote in an e-mail. “I can only say that it came to my mind very suddenly.”

The mathematician lives a simple life, working as a lecturer at the University of New Hampshire, teaching undergraduate calculus and other classes. His wife works in California, and they have no children. That gives him the ability to concentrate. And his achievement shows—even in an age of big experiments, super computers, and the ability to assemble a small army of scientists to tackle a problem—what can be accomplished by the elegant instrument of the human mind working alone.

“I didn’t use any computer, except I typed the paper using a computer,” Zhang said.

He told himself over and over again, “Keep thinking, think of it everyday,” Zhang recalled. “Even sometimes, for one period, I couldn’t sleep very well, because maybe [it was] in the dreams, dreaming the solution of the problem.”

Reactions to Zhang’s work ranged from astonishment to admiration, not only for the elegance of the work but because of the modesty of the man who quietly untangled the problem on his own.

“The old adage is that mathematics is a young person’s game, and moreover most of the top results come from people or groups of people known to produce them,” Kontorovich wrote. “Professor Zhang has demonstrated not only that one can continue to be creative and inventive well into middle-age, but that someone working hard enough, even (or especially) in isolation, can make astounding breakthroughs.”

The modest Zhang, who is in his 50s, said that he has been overwhelmed by the response to the paper, which he said has led to an inundation with “too many messages”—congratulations, requests to speak, questions about his proof.

He said the first thing his wife reminded him of after it began to attract public attention was to remember to comb his hair.

Zhang said that he is already returning to other problems he was working on before he shifted his focus to this one.

Asked what those problems might be, Zhang said that he didn’t want to say.