Edward J. McShane
Born(1904-05-10)10 May 1904
Died1 June 1989(1989-06-01) (aged 85)
Alma materUniversity of Chicago
AwardsChauvenet Prize (1953)[1]
Scientific career
Doctoral advisorsGilbert Ames Bliss
Lawrence Murray Graves

Edward James McShane (May 10, 1904 – June 1, 1989) was an American mathematician noted for his advancements of the calculus of variations, integration theory, stochastic calculus, and exterior ballistics.[2][3][4][5] His name is associated with the McShane–Whitney extension theorem[6] and McShane integral. McShane was professor of mathematics at the University of Virginia,[2][4] president of the American Mathematical Society,[2][3][5] president of the Mathematical Association of America,[5] a member of the National Science Board[5] and a member of both the National Academy of Sciences and the American Philosophical Society.[2][3][5][7]

Life and career

McShane was born and raised in New Orleans. He received his bachelor of engineering and Bachelor of Science degrees from Tulane University in 1925, following with a M.S. degree from Tulane in 1927. McShane received his Ph.D. in mathematics from the University of Chicago.[2][3] He taught at the University of Virginia for 39 years until he retired in 1974. His doctoral students include Victor Klee, Billy James Pettis, and David Lowdenslager, who collaborated with Henry Helson. McShane died of congestive heart failure at the University of Virginia hospital.

Selected publications



as translator


  1. ^ McShane, E. J. (1952). "Partial Orderings and Moore-Smith Limits". Amer. Math. Monthly. 59 (1): 1–11. doi:10.2307/2307181. JSTOR 2307181.
  2. ^ a b c d e National Academies Press:Biographical Memoirs:Edward James McShane,By Leonard D. Berkovitz and Wendell H. Fleming
  3. ^ a b c d New York Times:Edward McShane, 85, Mathematician, Dies; June 06, 1989
  4. ^ a b New York Times:4 New Members Named To National Science Boards;July 17, 1962
  5. ^ a b c d e Proceedings of the American Philosophical Society, vol 140, no. 4, Dec 1996, pp. 572–578
  6. ^ arXiv:1005.3727 Smoothness and smooth extensions; Generalization of MWK functions and gradually varied functions;Li Chen;Department of Computer Science and Information Technology, Columbia University]
  7. ^ "E. J. McShane". www.nasonline.org. Retrieved 2022-12-07.
  8. ^ Agnew, R. P. (1945). "Review of Integration by E. J. McShane". Bull. Amer. Math. Soc. 51: 51–53. doi:10.1090/S0002-9904-1945-08285-8.
  9. ^ Howarth, L. (1954). "Review: Exterior ballistics by E. J. McShane, J. L. Kelley, and F. V. Reno" (PDF). Bull. Amer. Math. Soc. 60 (3): 274–276. doi:10.1090/s0002-9904-1954-09802-6.
  10. ^ Olmsted, John M. H. (1961). "Review of Real analysis by E. J. McShane and T. A. Botts". Bull. Amer. Math. Soc. 67: 86–89. doi:10.1090/S0002-9904-1961-10506-5.
  11. ^ Henstock, R. (March 1971). "Book Review: A Riemann-type integral that includes Lebesgues-Stieltjes Bochner and stochastic integrals by E. J. Shane". Bulletin of the London Mathematical Society. 3 (1): 105. doi:10.1112/blms/3.1.105a.
  12. ^ Stroock, D. W. (1976). "joint review of The theory of stochastic processes, vol. I by I. I. Gihman and A. V. Skorohod; Stochastic calculus and stochastic models by E. J. McShane; Mesures cylindriques, espaces de Wiener, et fonctions aléatoires Gaussiennes by Albert Badrikian and Simone Chevet; Almost sure convergence by William F. Stout; Integration in Hilbert space by A. V. Skorohod". Bull. Amer. Math. Soc. 82: 227–232. doi:10.1090/S0002-9904-1976-13996-1. MR 1566848.
  13. ^ Saab, Elias (1985). "Review of Unified integration by E. J. McShane". Bull. Amer. Math. Soc. 13: 68–70. doi:10.1090/S0273-0979-1985-15369-8.