Polymath and Small Gaps Between Primes

Monday, 16 February 2015: 9:45 AM-11:15 AM
Room LL21C (San Jose Convention Center)
Terence Tao, UCLA, Los Angeles, CA
After Zhang's breakthrough on establishing a bound of 70,000,000 on the narrowest gap between primes that occurs infinitely often, there was immense interest from many in the mathematical community, from professional number theorists to amateurs, in adapting Zhang's argument to lower the bound.  We describe how, over a period of about ten months, dozens of mathematicians worked together, both via an online "Polymath" project and via more traditional research channels, to steadily whittle the bound down from 70,000,000 to the final value of 246, while also improving the result and its proof in other technical directions.  We also speculate as to why this project ended up being one of the more successful Polymath projects, and how widely this model can be replicated for future problems.