Abstract: Less than a year ago Yitang Zhang proved that the difference
between neighboring primes does not tend to infinity. In fact he
proved that the distance is at most 70 million infinitely often.
Currently we know the same result with 264 instead of 70 million,
thanks to the efforts of James Maynard, Janos Pintz, Terence Tao, and
other members of the PolyMath8 research group. I will show some
highlights of this fascinating story, and say a few personal words
about how I got involved with PolyMath8.