Richard Lawrence Bishop (August 12, 1931 – December 18, 2019) was an American mathematician who specialized in differential geometry and taught at the University of Illinois at Urbana–Champaign.

Next he earned his Ph.D. from the Massachusetts Institute of Technology in 1959, and immediately joined the UIUC faculty,[2] where he stayed until his retirement in 1997.

[3] He is the author of Geometry of Manifolds (with Richard J. Crittenden, AMS Chelsea Publishing, 1964,[4] translated into Russian 1967[5] and reprinted 2001[6]) and Tensor Analysis on Manifolds (with Samuel I. Goldberg, Macmillan, 1968,[7] reprinted by Dover Books on Mathematics, 1980[8]).

[9] The Bishop–Gromov inequality in Riemannian geometry, one form of which appeared in his book with Crittenden, is named after him and Mikhail Gromov, who gave an improved formulation of Bishop's result.

With Barrett O'Neill he made foundational contributions to the study of convex functions and convex sets in Riemannian geometry and their applications in the study of negative sectional curvature, including to the geometry of warped products.