Marston Morse

Harold Calvin Marston Morse (March 24, 1892 – June 22, 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. The Morse–Palais lemma, one of the key results in Morse theory, is named after him, as is the Thue–Morse sequence, an infinite binary sequence with many applications. In 1933 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis.

H. C. Marston Morse
Morse in 1965 (courtesy MFO)
Born(1892-03-24)March 24, 1892
DiedJune 22, 1977(1977-06-22) (aged 85)
Alma materColby College
Harvard University
Known forMorse theory
AwardsBôcher Memorial Prize (1933)
National Medal of Science (1964)
Scientific career
InstitutionsHarvard University
Institute for Advanced Study
Doctoral advisorGeorge David Birkhoff
Doctoral studentsEmilio Baiada
Gustav Hedlund
Sumner Myers
Arthur Sard


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, now known as 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.

Selected publications


  • "A fundamental class of geodesics on any closed surface of genus greater than one". Trans. Amer. Math. Soc. 26 (1): 25–60. 1924. doi:10.1090/s0002-9947-1924-1501263-9. MR 1501263.
  • "The foundations of a theory in the calculus of variations in the large". Trans. Amer. Math. Soc. 30 (2): 213–274. 1928. doi:10.1090/s0002-9947-1928-1501428-x. MR 1501428.
  • "Singular points of vector fields under general boundary conditions". Proc Natl Acad Sci U S A. 14 (5): 428–430. 1928. doi:10.1073/pnas.14.5.428. PMC 1085532. PMID 16577120.
  • "The critical points of functions and the calculus of variations in the large". Bull. Amer. Math. Soc. 35 (1): 38–54. 1929. doi:10.1090/s0002-9904-1929-04690-1. 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. doi:10.1090/s0002-9947-1929-1501489-9. MR 1501489.
  • "Closed extremals". Proc Natl Acad Sci U S A. 15 (11): 856–859. 1929. doi:10.1073/pnas.15.11.856. PMC 522574. PMID 16577255.
  • "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. doi:10.1090/s0002-9947-1930-1501555-6. MR 1501555.
  • "The critical points of a function of n variables". Trans. Amer. Math. Soc. 33 (1): 72–91. 1931. doi:10.1090/s0002-9947-1931-1501576-4. MR 1501576. PMC 526733.
  • "Sufficient conditions in the problem of Lagrange without assumptions of normalcy". Trans. Amer. Math. Soc. 37 (1): 147–160. 1935. doi:10.1090/s0002-9947-1935-1501780-9. MR 1501780.
  • with Walter Leighton: "Singular quadratic functions". Trans. Amer. Math. Soc. 40 (2): 252–288. 1936. doi:10.1090/s0002-9947-1936-1501873-7. MR 1501873.
  • with Gustav A. Hedlund: "Manifolds without conjugate points". Trans. Amer. Math. Soc. 51 (2): 362–386. 1942. doi:10.1090/s0002-9947-1942-0006479-x. MR 0006479.
  • "Homology relations on regular orientable manifolds". Proc Natl Acad Sci U S A. 38 (3): 247–258. 1952. doi:10.1073/pnas.38.3.247. PMC 1063540. PMID 16589087.


  • 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
  • Symbolic dynamics, Mimeographed notes by R. Oldenberger. Princeton, NJ: Institute for Advanced Study. 1966.
  • 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 0635124
  • 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 0889255



Biographical references


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