The global bifurcation theorem and the mountain pass theorem represent two foundational contributions to nonlinear analysis developed by Paul Rabinowitz. Born in Newark in 1939, this United States mathematician has spent his career examining partial differential equations and critical point theory, significantly influencing the trajectory of twentieth-century mathematical research through his academic work at the University of Wisconsin–Madison.
Academic Formation and Early Career
Paul Rabinowitz completed his formal mathematical training at New York University, where he earned a Ph.D. in 1966 under the supervision of Jürgen Moser. His early professional appointments included a tenure as an assistant professor at Stanford University, a position he held from 1966 until 1969. Throughout his career, he maintained international connections by visiting research institutions in Aarhus, Pisa, Paris, and Zurich.
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His primary research focus concerns partial differential equations and nonlinear analysis. Beyond the mountain pass theorem, which he developed alongside Antonio Ambrosetti, Rabinowitz is recognized for his work on linking and saddle point theorems. His research also covers the existence of periodic solutions within Hamiltonian systems. In collaboration with Vieri Benci, he investigated variational methods for critical points of strongly indefinite functionals, specifically addressing scenarios where Palais–Smale compactness conditions are absent.
Academic Appointments and Recognition
At the University of Wisconsin–Madison, Rabinowitz holds the titles of Edward Burr Van Vleck Professor of Mathematics and Vilas Research Professor. His professional standing is reflected in his membership in the National Academy of Sciences, the American Academy of Arts and Sciences, and the Accademia Nazionale dei Lincei. He has been awarded the George David Birkhoff Prize in 1998 and the Juliusz Schauder Medal in 2014. Additionally, he has received honorary doctorates from the Pierre and Marie Curie University and the University of Madrid Complutense.
Fast facts
- Born: 1939, Newark, United States
- Education: New York University (PhD, 1966)
- Primary Field: Logic and Foundations, Nonlinear Analysis
- Academic Home: University of Wisconsin–Madison
- Key Theorem: Mountain pass theorem
- Awards: George David Birkhoff Prize (1998), Juliusz Schauder Medal (2014)
- Fellowships: Guggenheim Fellow, American Mathematical Society, Society for Industrial and Applied Mathematics
Questions readers ask
Which major theorems is Paul Rabinowitz known for?
He is primarily recognized for his global bifurcation theorem and the mountain pass theorem.
Where has Paul Rabinowitz held academic teaching positions?
He served as an assistant professor at Stanford University and later held faculty roles at the University of Wisconsin–Madison.
Achievements
- George David Birkhoff Prize — 1998
- Held posts at University of Wisconsin–Madison
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