Adolf Hurwitz was a German mathematician who worked on algebra, analysis, geometry and number theory.
Background
He was born in Hildesheim, former Kingdom of Hanover, to a Jewish family and died in Zürich, in Switzerland. His father Salomon Hurwitz, a merchant was not particularly well off, Hurwitz"s mother, Elise Wertheimer, died when he was only three years old.
Education
He spent one year there attending lectures by Klein, before spending the academic year 1877–1878 at the University of Berlin where he attended classes by Kummer, Weierstrass and Kronecker, after which he returned to Munich.
Career
Hurwitz entered the Realgymnasium Andreanum in Hildesheim in 1868. He was taught mathematics there by Hermann Schubert. Schubert persuaded Hurwitz"s father to allow him to go to university, and arranged for Hurwitz to study with Felix Klein at Munich.
Hurwitz entered the University of Munich in 1877, aged 17.
In October 1880, Felix Klein moved to the University of Leipzig. Hurwitz followed him there, and became a doctoral student under Klein"s direction, finishing a dissertation on elliptic modular functions in 1881.
Following two years at the University of Göttingen, in 1884 he was invited to become an Extraordinary Professor at the Albertus Universität in Königsberg. There he encountered the young David Hilbert and Hermann Minkowski, on whom he had a major influence.
Following the departure of Frobenius, Hurwitz took a chair at the Eidgenössische Polytechnikum Zürich (today the Eidgenössische Technische Hochschule Zürich) in 1892 (having to turn down a position at Göttingen shortly after ), and remained there for the rest of his life.
Throughout his time in Zürich, Hurwitz suffered from continual ill health, which had been originally caused when he contracted typhoid whilst a student in Munich. He suffered from severe migraines, and then in 1905, his kidneys became diseased and he had one removed. 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.
Foreign 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. In the field of control systems and dynamic systems theory he derived the Routh–Hurwitz stability criterion for determining whether a linear system is stable in 1895, independently of Edward John Routh who had derived it earlier by a different method.
They had three children.
Membership
Göttingen Academy of Sciences. Lincean Academy.