Richard Palais

A 1956 doctoral thesis titled A Global Formulation of the Lie Theory of Transformation Groups established the research foundation for Richard Sheldon Palais. Born in Lynn in 1931, Palais spent a career spanning seven decades navigating the complexities of differential geometry, non-linear global analysis, and the development of digital visualization tools for mathematical education.

Academic Trajectory

Palais completed his formal education at Harvard University, receiving a B.A. in 1952, an M.A. in 1954, and a Ph.D. in 1956 under the supervision of Andrew M. Gleason and George Mackey. Following his doctoral studies, he held research positions at the University of Chicago and the Institute for Advanced Study. In 1960, he joined the faculty of Brandeis University, where he progressed from assistant professor to full professor, maintaining that position until his 2003 retirement. From 2004, he served as an adjunct professor at the University of California, Irvine.

THE FREE TEST

How high is yours?

Twenty questions, eight minutes on the clock, and a percentile measured against everyone who has taken it. No sign-up.

Take the IQ test →

Contributions to Geometry and Analysis

The research output of Palais centered on the geometry of submanifolds, Morse theory, and the theory of compact differentiable groups of transformations. His work resulted in several mathematical principles and lemmas that bear his name, including the principle of symmetric criticality, the Mostow–Palais theorem, the Lie–Palais theorem, the Morse–Palais lemma, and the Palais–Smale compactness condition. Throughout his career, he authored or co-authored significant texts such as Foundations of Global Nonlinear Analysis and Critical point theory and submanifold geometry.

Professional Service and Technology

Beyond his academic research, Palais participated in the infrastructure of mathematics. He served as an editor for the Journal of Differential Geometry between 1965 and 1982, and for the Transactions of the American Mathematical Society from 1966 to 1969. In 1979, he co-founded the TeX Users Group, serving as its first president. In his later years, he focused on mathematical visualization, developing software such as 3D-XplorMath and receiving the NSF/Science Visualization Challenge prize in 2006.