Richard S. Palais is an American mathematician known for his contributions to the fields of topology and differential geometry. He has worked extensively on the mathematical foundations of various physical theories, particularly in relation to general relativity and quantum mechanics. Palais is also recognized for his role in mathematics education and has authored several influential texts. He has been involved in the development of the Palais-Smale condition, which is significant in the study of critical points in calculus of variations and differential equations. His work has had a lasting impact on both mathematics and its applications in physics.