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 Georg Friedrich Bernhard Riemann (1826–1866) was born at Breselenz in Hanover. His father wished him to study theology, and he accordingly entered upon philological and theological studies at Göttingen. He attended also some lectures on mathematics. Such was his predilection for this science that he abandoned theology. After studying for a time under Gauss and Stern, he was drawn, in 1847, to Berlin by a galaxy of mathematicians, in which shone Dirichlet, Jacobi, Steiner, and Eisenstein. Returning to Göttingen in 1850, he studied physics under Weber, and obtained the doctorate the following year. The thesis presented on that occasion, Grundlagen für eine allgemeine Theorie der Funktionen einer veränderlichen complexen Grösse, excited the admiration of Gauss to a very unusual degree, as did also Riemann's trial lecture, Ueber die Hypothesen welche der Geometrie zu Grunde liegen. Riemann's Habilitationsschrift was on the Representation of a Function by means of a Trigonometric Series, in which he advanced materially beyond the position of Dirichlet. Our hearts are drawn to this extraordinarily gifted but shy genius when we read of the timidity and nervousness displayed when he began to lecture at Göttingen, and of his jubilation over the unexpectedly large audience of eight students at his first lecture on differential equations.

Later he lectured on Abelian functions to a class of three only,—Schering, Bjerknes, and Dedekind. Gauss died in 1855, and was succeeded by Dirichlet. On the death of the latter, in 1859, Riemann was made ordinary professor. In 1860 he visited Paris, where he made the acquaintance of French mathematicians. The delicate state of his health induced him to go to Italy three times. He died on his last trip at Selasca, and was buried at Biganzolo.

Like all of Riemann's researches, those on functions were profound and far-reaching. He laid the foundation for a