Two families of plane solutions of the four body problem formed the basis of the 1965 doctoral thesis written by Michael G. Crandall at the University of California, Berkeley. Born in 1940 in Baton Rouge, he established a career focused on partial differential equations, shaping the development of evolution equations and viscosity solutions during a career spanning several decades.
Academic Formation and Early Appointments
Crandall began his formal education at the University of California, Berkeley, where he earned a baccalaureate in engineering physics in 1962. He transitioned into the mathematics department, securing a master's degree in 1964 and a PhD in 1965 under the supervision of Heinz Cordes. Following his graduation, he served as an instructor at Berkeley in 1965 and as an assistant professor at Stanford University in 1966. By 1969, he joined the faculty of the University of California, Los Angeles, advancing to the rank of professor there between 1973 and 1976.
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In 1974, Crandall moved to the Mathematics Research Center at the University of Wisconsin–Madison, where he remained for a decade. He served as the Hille-Professor of Mathematics from 1984 until 1990. During this period, his work concentrated on bifurcation theory, the generation of semigroups of transformations on Banach spaces, and Hamilton–Jacobi equations. In 1988, he accepted a position at the University of California, Santa Barbara, maintaining his affiliation with the institution until his retirement.
Professional Contributions and Recognition
Crandall maintained a strong international presence, notably as a visiting professor at the University of Paris. His collaborative research with Pierre-Louis Lions on viscosity solutions provided significant advancements in the field of partial differential equations. His contributions were acknowledged through his role as an invited lecturer at the 1974 International Congress of Mathematicians in Vancouver. He received an honorary doctorate from Paris Dauphine University in 1996 and the Leroy P. Steele Prize for Seminal Contribution to Research in 1999.
Institutional Memberships
Over the course of his career, Crandall became an active member of the American Mathematical Society, eventually achieving the status of fellow in 2013. His standing in the scientific community was further solidified by his election to the American Academy of Arts and Sciences in 2000 and the National Academy of Sciences in 2023. Beyond his own research, he mentored doctoral students, including Lawrence C. Evans and Panagiotis E. Souganidis.
Fast facts
- Born: 1940, Baton Rouge
- Doctoral Advisor: Heinz Cordes
- Primary Research: Partial differential equations
- 1999 Steele Prize recipient
- 2013 Fellow of the American Mathematical Society
- 2023 Elected member of the National Academy of Sciences
Questions readers ask
What was the subject of Crandall's doctoral thesis?
His thesis, completed in 1965, solved a problem in celestial mechanics known as the two families of plane solutions of the four body problem.
What are viscosity solutions?
Viscosity solutions are a specialized approach to partial differential equations that Crandall developed in collaboration with Pierre-Louis Lions.
Achievements
- Steele Prize for Seminal Contribution to Research — 1999
- Held posts at University of California, Los Angeles, University of Wisconsin–Madison and University of California, Santa Barbara
- Fields: mathematical analysis and partial differential equation
