Yitang Zhang is a largely unknown mathematician who has struggled to find an academic job after he got his PhD, working at a Subway sandwich shop before getting a gig as a lecturer at the University of New Hampshire. He's just had a paper accepted for publication in Annals of Mathematics, which appears to make a breakthrough towards proving one of mathematics' oldest, most difficult, and most significant conjectures, concerning "twin" prime numbers. According to the Simons Science News article, Zhang is shy, but is a very good, clear writer and lecturer.
For hundreds of years, mathematicians have speculated that there are infinitely many twin prime pairs. In 1849, French mathematician Alphonse de Polignac extended this conjecture to the idea that there should be infinitely many prime pairs for any possible finite gap, not just 2.
Since that time, the intrinsic appeal of these conjectures has given them the status of a mathematical holy grail, even though they have no known applications. But despite many efforts at proving them, mathematicians weren’t able to rule out the possibility that the gaps between primes grow and grow, eventually exceeding any particular bound.
Now Zhang has broken through this barrier. His paper shows that there is some number N smaller than 70 million such that there are infinitely many pairs of primes that differ by N. No matter how far you go into the deserts of the truly gargantuan prime numbers — no matter how sparse the primes become — you will keep finding prime pairs that differ by less than 70 million.
The result is “astounding,” said Daniel Goldston, a number theorist at San Jose State University. “It’s one of those problems you weren’t sure people would ever be able to solve.”
Unknown Mathematician Proves Elusive Property of Prime Numbers [Erica Klarreich/Wired/Simons Science News]
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