Marston Morse

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H. C. Marston Morse
Marston Morse.jpg
Marston Morse in 1965 (courtesy MFO)
Born (1892-03-24)24 March 1892
Waterville, Maine
Died 22 June 1977(1977-06-22) (aged 85)
Princeton, New Jersey
Nationality American
Fields Mathematics
Institutions Harvard University
Alma mater Colby College
Harvard University
Doctoral advisor G. D. Birkhoff
Doctoral students Emilio Baiada
Arthur B. Brown
Gustav Hedlund
Walter Leighton
Sumner Myers
Arthur Sard
Known for Morse theory

Harold Calvin Marston Morse (24 March 1892 – 22 June 1977) was an American mathematician best known for his work on the calculus of variations in the large, a subject where he introduced the technique of differential topology now known as Morse theory. In 1933 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis.


He was born in Waterville, Maine to Ella Phoebe Marston and Howard Calvin Morse in 1892. He received his bachelor's degree from Colby College (also in Waterville) in 1914. At Harvard University, he received both his master's degree in 1915 and his Ph.D. in 1917.

He taught at Harvard, Brown, and Cornell Universities before accepting a position in 1935 at the Institute for Advanced Study in Princeton, where he remained until his retirement in 1962.

He spent most of his career on a single subject, eponymously titled Morse Theory, a branch of differential topology. Morse Theory is a very important subject in modern mathematical physics, such as string theory.

Marston Morse should not be confused with Anthony Morse, famous for the Morse-Sard theorem.

See also[edit]



  • "A fundamental class of geodesics on any closed surface of genus greater than one". Trans. Amer. Math. Soc. 26 (1): 25–60. 1924. MR 1501263. 
  • "The foundations of a theory in the calculus of variations in the large". Trans. Amer. Math. Soc. 30 (2): 213–274. 1928. MR 1501428. 
  • "Singular points of vector fields under general boundary conditions". Proc Natl Acad Sci U S A 14 (5): 428–430. 1928. PMC 1085532. 
  • "The critical points of functions and the calculus of variations in the large". Bull. Amer. Math. Soc. 35 (1): 38–54. 1929. MR 1561686. 
  • "The foundations of the calculus of variations in the large in m-space (first paper)". Trans. Amer. Math. Soc. 31 (3): 379–404. 1929. MR 1501489. 
  • "Closed extremals". Proc Natl Acad Sci U S A 15 (11): 856–859. 1929. PMC 522574. 
  • "The foundations of a theory of the calculus of variations in the large in m-space (second paper)". Trans. Amer. Math. Soc. 32 (4): 599–631. 1930. MR 1501555. 
  • "The critical points of a function of n variables". Trans. Amer. Math. Soc. 33 (1): 72–91. 1931. MR 1501576. 
  • "Sufficient conditions in the problem of Lagrange without assumptions of normalcy". Trans. Amer. Math. Soc. 37 (1): 147–160. 1935. MR 1501780. 
  • with Walter Leighton: "Singular quadratic functions". Trans. Amer. Math. Soc. 40 (2): 252–288. 1936. MR 1501873. 
  • with Gustav A. Hedlund: "Manifolds without conjugate points". Trans. Amer. Math. Soc. 51 (2): 362–386. 1942. MR 006479. 
  • "Homology relations on regular orientable manifolds". Proc Natl Acad Sci U S A 38 (3): 247–258. 1952. PMC 1063540. 


  • Calculus of variations in the large, American Mathematical Society, 1934 [1]
  • Topological methods in the theory of functions of a complex variable, Princeton University Press, 1947 [2]
  • Lectures on analysis in the large, 1947 
  • with Stewart Cairns: Critical point theory in global analysis and differential topology, Academic Press, 1969 
  • Variational analysis: critical extremals and Sturmian extensions, Wiley, 1973; 2nd edn. Dover, 2007 
  • Global variational analysis: Weierstrass integrals on a Riemannian manifold, Princeton University Press, 1976 [3]
  • Morse, Marston (1981), Bott, Raoul, ed., Selected papers, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90532-7, MR 635124 
  • Morse, Marston (1987), Montgomery, Deane; Bott, Raoul, eds., Collected papers. Vol. 1--6, Singapore: World Scientific Publishing Co., ISBN 978-9971-978-94-5, MR 889255 


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