The Aronszajn–Cordes uniqueness theorem established a significant milestone in the study of elliptic partial differential equations, providing a foundational approach to proving the existence and nature of solutions. Heinz Otto Cordes, whose mathematical research spanned more than six decades, bridged the gap between abstract algebra and the practical application of operator theory in complex physical systems.
Academic Foundation
Born in 1925, Cordes received his early mathematical training at the University of Göttingen. He completed his doctoral dissertation in 1952, titled Separation von Variablen in Hilbertschen Raumen, under the supervision of Franz Rellich. Following his doctorate, he remained at the university in a junior academic capacity until 1956, when he accepted an assistant professorship at the University of Southern California.
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Cordes transitioned to the University of California, Berkeley, where he served as an assistant professor from 1958 to 1959. He ascended to the role of associate professor in 1959 and was promoted to a full professorship in 1963. He held this position for nearly three decades until his retirement as professor emeritus in 1991. During his tenure, he mentored 19 doctoral students, including Michael G. Crandall and Michael E. Taylor, and collaborated with Tosio Kato between 1963 and 1999.
Research and Contributions
His primary contributions to mathematics centered on partial differential equations and the application of C*-algebra techniques to singular integral and pseudodifferential operators. He extended operator symbol calculus from compact manifolds to various non-compact classes. This line of inquiry eventually directed his focus toward Dirac operators and their underlying relationship with relativistic quantum mechanics. Over his lifetime, Cordes published four books and authored or co-authored more than 60 articles.
Professional Distinctions
In 1959, Cordes was awarded an Alfred P. Sloan fellowship. He later served as a visiting professor at Lund University during the 1971–1972 academic year, where he lectured on pseudodifferential operators. Although invited to address the 1966 International Congress of Mathematicians in Moscow, he chose to decline the invitation. He maintained his research output even after his retirement until his death in 2018.
Fast facts
- Born: 1925
- Died: 2018
- Educated at: University of Göttingen
- Primary Employer: University of California, Berkeley
- Key Theorem: Aronszajn–Cordes uniqueness theorem
- Total books authored: 4
- Academic supervision: Franz Rellich
- Citizenship: Germany
Questions readers ask
What was the focus of his doctoral thesis?
His 1952 dissertation, supervised by Franz Rellich, was titled Separation von Variablen in Hilbertschen Raumen.
Did he continue his research after retirement?
Yes, he remained active in his field of mathematics after retiring as professor emeritus from the University of California, Berkeley, in 1991.
Achievements
- Held posts at University of California, Berkeley
- Fields: mathematics
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