Adolf Hurwitz (26 March 1859- 18 November 1919) was a German mathematician, and one of the most important figures in mathematics in the second half of the nineteenth century (according to Jean-Pierre Serre, 'always something good in Hurwitz'). He was born in a Jewish family in Hildesheim, and died in Zurich, in Switzerland.
He was a doctoral student of Felix Klein in Leipzig, finishing a dissertation on elliptic modular functions in 1881. In 1884 he was offered a professorial position at Königsberg; there he encountered the young David Hilbert, on whom he had a major influence. He took a chair at the Eidgenössische Polytechnikum Zürich in 1892, and remained there for the rest of his life.
He was one of the early masters of the Riemann surface theory, and used it to prove many of the foundational results on algebraic curves; for instance Hurwitz's automorphisms theorem. This work anticipates a number of later theories, such as the general theory of algebraic correspondences, Hecke operators, and Lefschetz fixed-point theorem. He also had deep interests in number theory. He studied the maximal order theory (as it now would be) for the quaternions, defining the Hurwitz quaternions that are now named for him.
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