Submission + - Mathematicians Team Up to Close the Prime Gap
Hugh Pickens DOT Com writes: On May 13, an obscure mathematician garnered worldwide attention and accolades from the mathematics community for settling a long-standing open question about prime numbers. Yitang Zhang showed that even though primes get increasingly rare as you go further out along the number line, you will never stop finding pairs of primes separated by at most 70 million. His finding was the first time anyone had managed to put a finite bound on the gaps between prime numbers, representing a major leap toward proving the centuries-old twin primes conjecture, which posits that there are infinitely many pairs of primes separated by only two (such as 11 and 13). Now Erica Klarreich reports at Quanta Magazine that there is nothing magical about 70 million — it served Zhang’s purposes and simplified his proof but other mathematicians quickly realized that it should be possible to push this separation bound quite a bit lower. By the end of May, mathematicians had uncovered simple tweaks to Zhang’s argument that brought the bound below 60 million. Then Terence Tao, a winner of the Fields Medal, mathematics’ highest honor, created a “Polymath project,” an open, online collaboration to improve the bound that attracted dozens of participants and by July 27, the team had succeeded in reducing the proven bound on prime gaps from 70 million to 4,680. Now James Maynard has upped the ante by presenting an independent proof that pushes the gap down to 600. A new Polymath project is in the planning stages, to try to combine the collaboration’s techniques with Maynard’s approach to push this bound even lower. Zhang’s work and, to a lesser degree, Maynard’s fits the archetype of the solitary mathematical genius, working for years in the proverbial garret until he is ready to dazzle the world with a great discovery. The Polymath project couldn’t be more different — fast and furious, massively collaborative, fueled by the instant gratification of setting a new world record. “It’s important to have people who are willing to work in isolation and buck the conventional wisdom,” says Tao. Polymath, by contrast, is “entirely groupthink.” Not every math problem would lend itself to such collaboration, but this one did.
