## May 22, 2013 2:08 pm

### An Aging Mathematician Made a Major Dent in One of Math’s Oldest Problems

Photo: SKopp

Editors at academic journals often receive random manuscripts claiming to have figured out the mysteries of the universe or solved fundamental puzzles in mathematics or physics. But when the editorial team of the Annals of Mathematics, one of the field’s most respected publications, took a look at a manuscript submitted by an obscure lecturer from the University of New Hampshire, the Simons Foundation reports, they realized this was something significant. Yitang Zhang, the author, had tackled one of mathematic’s oldest problems: the twin primes conjecture.

A number is prime if you can’t divide it by anything but 1 and itself. Twin primes are primes that are only two numbers apart – like 3 and 5, 5 and 7, and 11 and 13. The largest known twin primes are 3,756,801,695,685 × 2666,669 + 1 and 3,756,801,695,685 × 2666,669 - 1, and were discovered in 2011.

The twin prime conjecture states simply that there are an infinite number of these twin primes. Although simple in its concept, a proof of it has been stumping mathematicians since the idea was proposed in 1849 by French mathematician Alphonse de Polignac.

While vacationing at a friend’s home last summer, Zhang had an ah-ha! moment. He had noticed an overlooked technical detail that led him to his proof. He was able to show that there is an infinite number of prime pairs separated by a measurable finite distance. In other words, there’s a limit to how far away primes can get from each other. The New Scientist writes:

Unfortunately for lonely primes, that distance is still quite large: 70 million. But Zhang stresses that this is an upper bound.

“These values are very rough,” he says. “I think to reduce them to less than one million or even smaller is very possible” – although mathematicians may need another breakthrough to reduce the distance all the way down to just 2 and finally prove the twin prime conjecture.

What matters is that Zhang was able to show that the gap between adjacent primes cannot exceed a certain value.

As the Simons Foundation writes, Zhang really did come out of no where. He attended Purdue, but after graduation struggled to find a job in academia and even worked at Subway for a while.

“Basically, no one knows him,” said Andrew Granville, a number theorist at the Université de Montréal. “Now, suddenly, he has proved one of the great results in the history of number theory.”

In some ways, that’s the most surprising parts of this story. In mathematics, the age limit for genius discoveries is supposed to be about 30. Slate wrote about this assumption back in 2003:

It’s not hard to see where the stereotype comes from; the history of mathematics is strewn with brilliant young corpses. Evariste Galois, Gotthold Eisenstein, and Niels Abel—mathematicians of such rare importance that their names, like Kafka’s, have become adjectives—were all dead by 30. Galois laid down the foundations of modern algebra as a teenager, with enough spare time left over to become a well-known political radical, serve a nine-month jail sentence, and launch an affair with the prison medic’s daughter; in connection with this last, he was killed in a duel at the age of 21. The British number theorist G.H. Hardy, in A Mathematician’s Apology, one of the most widely read books about the nature and practice of mathematics, famously wrote: “No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man’s game.”

More from Smithsonian.com:

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Posted By: New Research |

1. How old is Zhang?

Comment by lagitha — May 22, 2013 @ 9:34 pm

2. Prominent references to age, but the article doesn’t tell us how old Zhang is…

Comment by Jeff — May 22, 2013 @ 11:58 pm

3. I find the headline’s use of “aging mathematician” extremely offensive, as though only people in their 20s and 30s can be creative and do great things. In addition, the man in question is 50-years-old, a fact the blog post failed to mention. With people in the U.S. living into their 80s, I don’t think 50 is old. In addition, what does his age have to do with his achievement? I think there’s so much agism in our society, I would hope that writers and editors would be more sensitive to this fact and not perpetuate the falsehood that people over 40 don’t have a useful role to play in society.

Comment by KScot — May 23, 2013 @ 12:01 pm

4. Zhang is 57. Here is an telling reference point: the Fields Medal is awarded to people under 40. This medal is considered the Nobel prize for mathematicians.

Comment by tz — July 17, 2013 @ 1:22 am

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