Riemann’s Formative Years, 1826–1847

Beginning with his home life in a small, remote village, this chapter delves into Riemann's difficult years as a teenager attending secondary schools in the cities of Hanover and Lüneburg. The headmaster at the latter school happened to be his mathematics teacher, a circumstance that did much to further the youngster's natural talent. After graduating, he took a variety of courses in Göttingen, but soon realized that the mathematics offerings in Berlin were far more challenging. During his first semester, he enrolled in Benjamin Goldschmidt's course on terrestrial magnetism, which thereafter became one of Riemann's main fields of interest. The following semester he took Gauss's standard course on the method of least squares, but he also spent a good deal of time and effort reading various works by Gauss, starting with Disquisitiones Arithmeticae, his famous book on number theory. After just one year, Riemann left Göttingen and went to Berlin, where he took courses with Dirichlet, Jacobi, and Eisenstein, who had just habilitated. Riemann's letters to his family make clear that he took an ambivalent view of his remarkable rival. The chapter ends with an account of Riemann's reaction to the conflict between Jacobi and Eisenstein, which had broken forth in a public priority dispute.