The Routh–Hurwitz stability criterion, derived in 1895, remains a fundamental tool for determining the stability of linear systems. Adolf Hurwitz, who lived from 1859 until 1919, navigated a distinguished academic career across the German Empire, contributing extensively to analysis, number theory, and geometry before spending his final decades as a professor at ETH Zurich.
Early Education and Influences
Born in Hildesheim within the Kingdom of Hanover, Hurwitz attended the Gymnasium Andreanum starting in 1868. His mathematical promise was identified early by Hermann Schubert, who facilitated his transition to higher education. Supported by a family friend named Mr. Edwards, Hurwitz studied at Ludwig-Maximilians-Universität München starting in 1877 under Felix Klein. He subsequently attended Friedrich Wilhelm University in Berlin, where he learned from Weierstrass, Kummer, and Kronecker, before completing his doctorate at Leipzig University in 1881.
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Hurwitz held several key faculty positions throughout his professional life. He spent two years at the University of Göttingen before accepting an appointment as an Extraordinary Professor at the University of Königsberg in 1884. During this tenure, he significantly influenced colleagues David Hilbert and Hermann Minkowski. In 1892, he moved to Zurich to take a chair at the Eidgenössische Polytechnikum, now known as ETH Zurich. He maintained this position for the remainder of his life, despite receiving other offers, including a potential return to Göttingen.
Mathematical Contributions
His research output spanned multiple disciplines. He is known for the Riemann–Hurwitz formula and his work on Riemann surface theory, which yielded foundational results on algebraic curves. In number theory, he defined the Hurwitz quaternions and the Hurwitz zeta function. Beyond pure mathematics, his development of the Routh–Hurwitz stability criterion in 1895 provided an essential method for dynamical systems. He also proved the existence of the Haar measure on Lie groups, predating subsequent work by Alfréd Haar.
Health and Personal Life
Throughout his career in Zurich, Hurwitz faced persistent health challenges. His physical decline originated from a severe case of typhoid contracted during his student days in Munich, which left him prone to debilitating migraines. His condition worsened in 1905 when he developed kidney disease, a complication that necessitated the surgical removal of one kidney. Despite these recurring medical issues, he continued his academic duties until his death in 1919. He was married to Ida Samuel in 1884, and they raised three children.
Fast facts
- Born: 1859, Hildesheim
- Died: 1919, Zurich
- Education: Leipzig University, Gymnasium Andreanum, Ludwig-Maximilians-Universität München
- Key Employers: University of Königsberg, ETH Zurich
- Notable Contribution: Routh–Hurwitz stability criterion
- Professional Member: Accademia Nazionale dei Lincei
- Burial Site: Cemetery Sihlfeld
Questions readers ask
Where did Adolf Hurwitz conduct his final academic work?
He worked at the Eidgenössische Polytechnikum in Zurich, now known as ETH Zurich, from 1892 until his death in 1919.
Which notable mathematicians did Hurwitz influence at Königsberg?
During his time at the University of Königsberg, he had a significant influence on David Hilbert and Hermann Minkowski.
Achievements
- Notable work: Hurwitz zeta function
- Notable work: Hurwitz polynomial
- Notable work: Hurwitz's theorem
- Notable work: Hurwitz matrix
- Affiliated with University of Göttingen, University of Königsberg and ETH Zurich
- Educated at Leipzig University, Gymnasium Andreanum and Ludwig-Maximilians-Universität München
- Worked as mathematician and university teacher
