PIMS 20th Anniversary Distinguished Lecture at University of Regina

It is a famous unsolved problem whether there are infinitely many primes $p$ such that $p+2$ is also prime. Such primes are called twin primes.

Recently, some spectacular progress was made towards this conjecture by Yitang Zhang, Maynard and Tao. After surveying some of these results, we indicate what further steps may be taken and indicate a possible approach towards its solution.