Adolf Hurwitz | |
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| Born | (1859-03-26)26 March 1859 Hildesheim,Kingdom of Hanover (now part of Germany) |
| Died | 18 November 1919(1919-11-18) (aged 60) Zürich, Switzerland |
| Alma mater | Leipzig University |
| Known for | Riemann–Hurwitz formula Hurwitz quaternion |
| Scientific career | |
| Fields | Mathematician |
| Institutions | ETH Zürich Albertus Universität Königsberg |
| Doctoral advisor | Felix Klein |
| Doctoral students | Ernst Amberg L. Gustave du Pasquier |
Adolf Hurwitz (German:[ˈaːdɔlfˈhʊʁvɪts]; 26 March 1859 – 18 November 1919) was a Germanmathematician who worked onalgebra,analysis,geometry andnumber theory.
He was born inHildesheim, then part of theKingdom of Hanover, to aJewish family and died inZürich, in Switzerland. His father Salomon Hurwitz, a merchant, was not wealthy. Hurwitz's mother, Elise Wertheimer, died when he was three years old.[1] Family records indicate that he had siblings and cousins, but their names have yet to be confirmed except for an older brother, Julius, with whom he developed an arithmetical theory for complex continued fractions circa 1890.[2] Hurwitz entered theRealgymnasium Andreanum [de] in Hildesheim in 1868. He was taught mathematics there byHermann Schubert.[3] Schubert persuaded Hurwitz's father to allow him to attend university, and arranged for Hurwitz to study withFelix Klein at Munich.[3] Salomon Hurwitz could not afford to send his son to university, but his friend, Mr. Edwards, assisted financially.
Hurwitz entered theUniversity of Munich in 1877, aged 18. He spent one year there attending lectures by Klein, before spending the academic year 1877–1878 at theUniversity of Berlin where he attended classes byKummer,Weierstrass andKronecker,[1] after which he returned to Munich.
In October 1880, Felix Klein moved to theUniversity of Leipzig. Hurwitz followed him there, and became a doctoral student under Klein's direction, finishing a dissertation onelliptic modular functions in 1881. Following two years at theUniversity of Göttingen, in 1884 he was invited to become an Extraordinary Professor at theAlbertus Universität inKönigsberg; there he encountered the youngDavid Hilbert andHermann Minkowski, on whom he had a major influence. Following the departure ofFrobenius, Hurwitz took a chair at theEidgenössische Polytechnikum Zürich (today theETH Zürich) in 1892 (having to turn down a position at Göttingen shortly after[1]), and remained there for the rest of his life.
Throughout his time in Zürich, Hurwitz was in continual ill health, which had been originally caused when he contractedtyphoid whilst a student in Munich. He had severemigraines, and then in 1905, his kidneys became diseased and he had one removed.
He was one of the early students of theRiemann surface theory, and used it to prove many of the foundational results onalgebraic curves; for instanceHurwitz's automorphisms theorem. This work anticipates a number of later theories, such as the general theory of algebraic correspondences,Hecke operators, andLefschetz fixed-point theorem. He also had deep interests innumber theory. He studied themaximal order theory (as it now would be) for thequaternions, defining theHurwitz quaternions that are now named for him. In the field ofcontrol systems anddynamical systems theory he derived theRouth–Hurwitz stability criterion for determining whether a linear system is stable in 1895, independently ofEdward John Routh who had derived it earlier by a different method.[4]In Lie theory, Hurwitz proved the existence of theHaar measure onLie groups (which Haar then extended to locally compact groups).[5]
In 1884, whilst atKönigsberg, Hurwitz met and married Ida Samuel, the daughter of a professor in the faculty of medicine. They had three children.
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