Years of Struggle, 1854–1858

Riemann's postdoctoral thesis received a very short, but laudatory assessment from Gauss, paving the way for his Habilitation lecture. Gauss requested that he speak about the third on his list of proposed topics: On the Hypotheses underlying the Foundations of Geometry. Many months passed before this took place, however, as Gauss was in ill health. After Riemann read his text, he left Göttingen to begin preparing his first lecture course on partial differential equations as well as a paper on recent experimental findings related to electrical phenomena. He never mentioned his Habilitation lecture again, yet its ideas were clearly related to his ongoing physical speculations from this time. These have often been interpreted as an anticipation of later developments in field physics, though they can be more accurately described as a type of ether physics that attempted to unite gravity, light, and magnetism. Riemann's teaching career began shortly before Dirichlet arrived in Göttingen as Gauss's successor. Dedekind had also just habilitated, so starting in 1855 the course offerings in mathematics were far more advanced than before. Riemann continued to pursue his physical interests, but his lecture courses now took up much of his time. Following in the tradition of his Berlin teachers, Dirichlet and Jacobi, Riemann used his lectures as a platform for presenting many of his current research results. His famous papers on generalized hypergeometric functions and on Abelian functions were, in effect, spin-offs from courses he taught from 1855 to 1857. Unfortunately, family tragedies and other personal discouragements undermined Riemann's mental health during these years of stupendous mathematical achievement. Dedekind did his best to help his friend attain a healthier outlook, but Riemann only recovered gradually.