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| Unable to get an academic position, Zhang kept the books for a Subway franchise. Credit Photograph by Peter Bohler |
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.”
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