Knörrer studied from 1971 at University of Regensburg and University of Erlangen-Nuremberg and received a doctorate in 1978 from the University of Bonn under the supervision of Egbert Brieskorn (Isolierte Singularitäten von Durchschnitten zweier Quadriken). After that, he was a research assistant until 1985 in Bonn, interrupted by two years 1980 to 1982 at the Leiden University. In 1985 he completed his habilitation in Bonn and was a Heisenberg fellow the following two years. During 1986/87, he was a department representative at the University of Düsseldorf. Since 1987, he is a full professor of mathematics at the ETH Zurich.
Knörrer studies algebraic geometry and its connection to mathematical physics, for example, for integrable systems, as well as mathematical theory of many-particle systems in statistical mechanics and solid state physics (Fermi liquids). Together with Brieskorn, he wrote an extensive and rich illustrated textbook on algebraic curves, which also was translated into English.
- With Egbert Brieskorn: Ebene algebraische Kurven, Birkhäuser 1981 (englische Übersetzung: Plane Algebraic Curves, Birkhäuser 1986)
- Geometrie- ein Lehrbuch für Mathematik- und Physikstudierende, Vieweg/Teubner, 2. Auflage 2006, ISBN 3834802107
- With Daniel Bättig: Singularitäten, Birkhäuser 1991
- With Joel Feldman, Eugene Trubowitz: Riemann Surfaces of Infinite Genus, AMS (American Mathematical Society) 2003
- With Feldman, Trubowitz: Fermionic functional integrals and the renormalization group, AMS 2002
- With D. Gieseker, Trubowitz: Geometry of algebraic Fermi curves, Academic Press 1992
- Integrable Hamiltonsche Systeme und Algebraische Geometrie, Jahresbericht Deutscher Mathematikerverein, Bd.88, 1986, S.82-103
The original article was a translation of the corresponding German article.