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Science in Mind

Math expert lauded for prime number feat

Yitang Zhang untangled an  old problem.
Yitang Zhang untangled an old problem. 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.

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.

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 less than 70 million. As any child who knows how to count knows, 70 million is a far cry from two, but Zhang’s proof — of something called the “bounded gaps conjecture” — excites mathematicians because it is the first time anyone has proved 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,” said Shing-Tung Yau, a Harvard math professor who invited Zhang to present his work in Cambridge just days after it was accepted for publication. “Any problems of this sort . . . are usually not easy because people have thought about this for a long, long time.”


News of the feat rippled across the math world.

“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. “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 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 that he says gives him the ability to concentrate on his work. In an age of big experiments, super computers, and the ability to assemble a small army of scientists to tackle a problem, Zhang’s achievement shows what can be accomplished by the elegant instrument of the human mind, working alone.

“Keep thinking, think of it everyday,” Zhang said he would tell himself. “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, heightened by 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.”


Zhang, who is in his 50s, said that he has been overwhelmed by the response to the paper — and noted that the first thing his wife reminded him of after it began to attract public attention was to remember to comb his hair.

The mathematician is already returning to other problems. Asked what those might be, Zhang declined to elaborate.

Carolyn Y. Johnson can be reached at cjohnson@globe.com. Follow her on Twitter @carolynyjohnson.