Riemann publishes an essay in the monthly notes of the Berlin Academy. These ten dense pages of concepts on prime numbers will remain the only pages Riemann wrote on prime numbers, and yet they will forever change the subject. It is a visionary essay, yet deeply frustrating given the simplicity of its content: Riemann, like Gauss, loved covering his tracks. Buried in the document is the statement of the Riemann Hypothesis: or: every nontrivial zero of the zeta function is such that its real part is 1/2. If this is true, then Gauss’s function will provide an increasingly better approximation of the number of primes as we count. This period represents a brief interlude of happiness in Riemann’s life. He occupied the chairs of both his mentors, Gauss and Dirichlet, married Elise Koch, a friend of his sister, but then Riemann fell ill with pleurisy, took refuge in the countryside of Pisa, to which he was attached, and died in 1866.
