Richard L. Bishop
Richard L. Bishop (August 12, 1931 – December 18, 2019) was an American mathematician who studied differential geometry, the mathematics of curved spaces. He taught at the University of Illinois at Urbana–Champaign.
He was born in Allegan, Michigan. He earned a B.S. from Case Institute of Technology in 1954 and a Ph.D. from MIT in 1959 under Isadore Singer, with the thesis On Imbeddings and Holonomy. He joined UIUC that same year and worked there until his retirement in 1997. One of his doctoral students was Stephanie B. Alexander.
Bishop co-authored Geometry of Manifolds (1964) with Richard J. Crittenden and Tensor Analysis on Manifolds (1968) with Samuel I. Goldberg. He became a fellow of the American Mathematical Society in 2013.
His work includes the Bishop–Gromov inequality in Riemannian geometry (named with Mikhail Gromov), and he introduced the Bishop frame for curves. With Barrett O’Neill, he made important contributions to the study of convex functions and convex sets in curved spaces, with applications to negative curvature and warped products.
He passed away in Urbana, Illinois, in 2019 at the age of 88.
This page was last edited on 3 February 2026, at 08:14 (CET).