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

Before his breakthrough involving the twin prime conjecture, Yitang Zhang struggled to find work in academia and even took a job at Subway

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.”

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