Open main menu

Richard Lawrence Bishop (born c. 1932) is an American mathematician, a professor emeritus of mathematics at the University of Illinois at Urbana–Champaign.[1] The Bishop–Gromov inequality in Riemannian geometry is named after him (with Mikhail Gromov).

Richard L. Bishop
Bornc. 1932 (age 86–87)
Alma materMassachusetts Institute of Technology
Case Institute of Technology
Scientific career
InstitutionsUniversity of Illinois at Urbana–Champaign
Doctoral advisorIsadore Singer
Doctoral studentsStephanie B. Alexander

Bishop went to Case Institute of Technology as an undergraduate, earning a B.S. in 1954. Next he earned his Ph.D. from the Massachusetts Institute of Technology in 1959, and immediately joined the UIUC faculty.[2] His thesis, On Imbeddings and Holonomy, was supervised by Isadore Singer.[3] At UIUC, his doctoral students included future UIUC colleague Stephanie B. Alexander.[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]).

In 2013, Bishop became one of the inaugural fellows of the American Mathematical Society.[9]


  1. ^ Emeritus faculty Archived 2014-07-14 at the Wayback Machine, UIUC Mathematics, retrieved 2014-06-16.
  2. ^ Information from Bishop's web page at UIUC, retrieved 2014-06-16.
  3. ^ a b Richard Lawrence Bishop at the Mathematics Genealogy Project
  4. ^ Review of Geometry of Manifolds by W. Klingenberg, MR0169148
  5. ^ MR0213981
  6. ^ 1852066
  7. ^ Review of Tensor Analysis on Manifolds by T. J. Willmore, MR0224010
  8. ^ MR0615912
  9. ^ List of Fellows of the American Mathematical Society, retrieved 2014-06-16.