Triumph and Tragedy, 1859–1866

Dirichlet's death in 1859 marked another major turning point for mathematics in Göttingen. Riemann might have seemed his natural successor, but the situation was complicated by the fact that Professors Stern and Ulrich were far older and had considerable seniority, having taught mathematics in Göttingen for many years. Thus, Karl Weierstrass was the first to receive this offer, but to the surprise of many, he declined. Riemann's appointment thus ended his years of financial hardship, and he soon moved into Gauss's former living quarters in the astronomical observatory. Dedekind, who had since joined the faculty at the Zurich Polytechnic, accompanied Riemann on a trip to Berlin, where the newly appointed full professor had also just been chosen as a corresponding member of the Berlin Academy. Conversations there with Weierstrass and Kronecker led Riemann to expound new results on Abelian functions as well as a famous number-theoretic problem, namely, to find an analytic expression for estimating the number of primes below any given number. Health problems had plagued Riemann nearly all his life, and these became more serious by the 1860s. In 1862, he married Elise Koch, a friend of his sisters, but unfortunately Riemann contracted pleurisy shortly thereafter and had to give up teaching. Much of the remainder of his life was spent in Italy, where he and his wife made many friends. Enrico Betti even arranged for Riemann's appointment to a professorship in Pisa, but after due consideration, Riemann had to decline the offer. Their third and final trip to Italy began just as Hanover went to war against Prussia, a fateful decision that ended in total defeat and annexation into the Prussian state. In the meantime, Riemann and his wife found refuge on the shores of Lago maggiore, though for less than one month before he died. The story of how his legacy lived on, especially through the efforts of Richard Dedekind and Heinrich Weber, is told in Chapter 12.