was what was in the mind of a student who was at the same university where gauss was teaching, bernhard riemann. is that right? >> yes, yes. so riemann studied the area between the jagged function, which counts the primes, and this smooth curve. >> that's right, so the smooth curve again is some approximation, but the actual number, it's not getting right generally. >> right, it's either above -- overshoots or undershoots, and so there's this funny area that you have to understand. and what riemann -- the great idea basically of viewing this funny wave, kind of like a sound wave, looking for like -- like frequencies, or musical notes, if you will, in this -- in this sound. and the sound is what's called "the music of the primes." >> your work is actually finding what i think most people would recognize as real patterns in the primes. it's related to the notion of twin primes. >> right, so twin primes are a very simple kind of pattern in the primes, primes that are just a distance of two apart, and we still can't even find those. but working with ben green, we were able to find -- to prove that