He was born in Hildesheim, then part of the 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. Family records indicate that he had siblings and cousins, but their names have yet to be confirmedexcept for an older brother, Julius, with whom he developed an arithmetical theory for complex continued fractions in around 1890. Hurwitz entered the 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. Salomon Hurwitz could not afford to send his son to university, but his friend, Mr Edwards, agreed to help out financially.
Educational career
Hurwitz entered the University of Munich in 1877, aged 18. 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. 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 in 1892, 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.
In 1884, whilst at Königsberg, Hurwitz met and married Ida Samuel, the daughter of a professor in the faculty of medicine. They had three children.
Selected publications
Hurwitz, A., 1898. . Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1898, pp. 309–316.
Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen. Edited and supplemented by a section on geometric Funktionentheorie by Richard Courant. Springer, Berlin 1922
Mathematische Werke. Publlished by the Department of Mathematics and Physics of the Eidgenössischen Technischen Hochschule in Zürich. 2 vols. Birkhäuser, Basel 1932–1933
Übungen zur Zahlentheorie. 1891–1918. Translated by Barbara Aquilino. As a duplicated manuscript edited by Herbert Funk and Beat Glaus. ETH-Bibliothek, Zürich 1993,.
Edited for publication by Nikolaos Kritikos. Translated with some additional material by William C. Schulz. Springer, New York 1986,.
Karl Weierstraß: Einleitung in die Theorie der analytischen Funktionen. Vorlesung Berlin 1878. In a transcript by Adolf Hurwitz. Edited by Peter Ullrich. Vieweg, Braunschweig 1988,.
