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 dynamical 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. In Lie theory, Hurwitz proved the existence of the Haar measure on Lie groups (which Haar then then extended to locally compact groups). Family 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. Ueber die Composition der quadratischen Formen von beliebig vielen Variablen. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1898, pp. 309–316. Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen (= Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete. vol. 3, ). Edited and supplemented by a section on geometric Funktionentheorie by Richard Courant. Springer, Berlin 1922 (4th, extended and edition with an appendix by Helmut Röhrl, ibid 1964, online text) Mathematische Werke. Publlished by the Department of Mathematics and Physics of the Eidgenössischen Technischen Hochschule in Zürich. 2 vols. Birkhäuser, Basel 1932–1933 (with a memoir on Hurwitz by Ernst Meissner) Übungen zur Zahlentheorie. 1891–1918 (= Schriftenreihe der ETH-Bibliothek. vol. 32, ). Translated by Barbara Aquilino. As a duplicated manuscript edited by Herbert Funk and Beat Glaus. ETH-Bibliothek, Zürich 1993, . Lectures on Number Theory. Edited for publication by Nikolaos Kritikos. Translated with some additional material (from the German) by William C. Schulz. Springer, New York 1986, . Karl Weierstraß: Einleitung in die Theorie der analytischen Funktionen. Vorlesung Berlin 1878 (= Dokumente zur Geschichte der Mathematik. vol. 4). In a transcript by Adolf Hurwitz. Edited by Peter Ullrich. Vieweg, Braunschweig 1988, . See also First Hurwitz triplet Hurwitz class number Hurwitz determinant Hurwitz matrix Hurwitz numbers Hurwitz polynomial Hurwitz problem Hurwitz quaternion order Hurwitz quaternion Hurwitz scheme Hurwitz surface Hurwitz zeta function Hurwitz's automorphisms theorem Hurwitz's theorem (complex analysis) Hurwitz's theorem (composition algebras) Hurwitz's theorem (normed division algebras) Hurwitz's theorem (number theory) Radon–Hurwitz numbers Riemann–Hurwitz formula Notes External links LMS obituary Recording of the 2008