Algebraic numbers by Paula Ribenboim

By Paula Ribenboim

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Riemann had come to dislike this denial of the physical picture when he'd been reading Descartes in the comfort of Schmalfuss's library. Mathematicians around the turn of the nineteenth century had been burnt by an erroneous pictorial proof of a formula describing the relationship between the number of corners, edges and faces of geometric solids. Euler had conjectured that if a solid has C corners, E edges and F faces, then the numbers C, E and F must satisfy the relationship C - E + F = 2. For example, a cube has 8 corners, 12 edges and 6 faces.

His father's wish that he study theology had brought him to Gottingen, but it was the influence of the great Gauss and Gottingen's scientific tradition that left its mark during that first year. It was only a matter of time before Greek and Latin lectures gave way to the temptation of courses in physics and mathematics. With trepidation, Riemann wrote to his father suggesting that he would like to switch from theology to mathematics. His father's approval meant everything to Riemann. With a sense of relief he received his father's blessing, and immediately immersed himself in the scientific life of the university.

In the centre stands the medieval town hall, whose 63 Bernhard Riemann (1826-66). ' For those at the university that was certainly the feeling. The academic life was one of self-sufficiency. Although theology had predominated in the early years of the university, the winds of academic change sweeping across Germany had stimulated Gottingen's scientific curriculum. By the time Gauss was appointed as professor of astronomy and director of the observatory in 1807, it was science rather than theology for which Gottingen was becoming famous.

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