Unlike other academic fields, mathematics is notorious for being a young thinker's game. G.H. Hardy, in his 1940 book The Mathematician's Apology, ticked off a list of great math whizzes from Isaac Newton to Carl Friedrich Gauss and noted that they all made their most important discoveries in their 20s. He concluded, gloomily (and famously):
I do not know an instance of a major mathematical advance initiated by a man past fifty. If a man of mature age loses interest in and abandons mathematics, the loss is not likely to be very serious either for mathematics or for himself.
Fortunately, though, a once-obscure University of New Hampshire math instructor named Yitang "Tom" Zhang didn't conform to Hardy's truism. Zhang, who reportedly is in his 50s, has written a paper that apparently provides a major step forward in solving one of the twin prime conjectures, a problem that was first pondered back in the third century B.C. by the Ptolemaic Greek mathematician Euclid.
If figures make your head spin, Nature explains that primes are whole numbers, divisible only by one and themselves. Twin primes are pairs of primes that differ in value by 2. Examples of twin primes range from 3 and 5, to really huge numbers such as 2,003,663,613 í— 2 195,000 âˆ’ 1 and 2,003,663,613 í— 2 195,000 + 1. OK, we've probably confused you even more at this point. The key question is whether or not there is an infinite number of such twin primes.
Zhang didn't quite answer that question. But he came up with what other mathematicians say is a key piece of the puzzle. In a paper submitted in April and recently accepted by the prestigious journal Annals of Mathematics, Zhang presented a proof showing that the number of primes less than 70 million units apart is infinite.Though 70 million seems like a huge number, Nature explains: "The existence of any finite bound, no matter how large, means that that the gaps between consecutive numbers don't keep growing forever."
One of the mathematicians who evaluated Zhang's article called it a "landmark theorem." Daniel Goldston, a number theorist at San Jose State University, marveled that Zhang had made a dent in "one of those problems you weren't sure people would ever be able to solve."
But what really was mind-blowing was that the advance had been made by a virtual unknown - a Chinese immigrant who, after earning his doctorate at Purdue University in 1991, reportedly had experienced such difficulty finding a job in his field that he'd been compelled at one point to make hoagies at Subway to support himself.
"The big experts in the field had already tried to make this approach work," University of Montreal mathematician Andrew Granville explained in an article on the website of the Simons Foundation, a science and math organization. Zhang is "not a known expert, but he succeeded where all the experts had failed."
So how did Zhang do it? Perseverance was an important factor. He told the Simons Foundation writer Erica Klarreich that even as he struggled for years to make ends me, he continued to follow developments and read papers in number theory, a field of mathematics that fascinated him, even though it hadn't been his area of study at Purdue. "There are a lot of chances in your career," he said, "but the important thing is to keep thinking."
Zhang said that he spent several years contemplating the twin prime conjecture before suddenly having an epiphany while he killing time in a friend's backyard in Colorado, before leaving for a concert. "I immediately realized it would work," he explained.
Zhang, who recently was invited to give a talk at Harvard University about his discovery, says he doesn't feel any resentment about having labored in obscurity for so many years, and has no desire to become famous. "My mind is very peaceful," he explained. Those are remarkably gentle words, coming from someone who's struck a huge blow in the battle for respect for older intellects.
Photo: Lisa Nugent, UNH Photographic Services
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