Marston Morse

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H. C. Marston Morse
Marston Morse.jpg
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
InstitutionsCornell University
Brown University
Harvard University
Institute for Advanced Study
ThesisCertain Types of Geodesic Motion of a Surface of Negative Curvature (1917)
Doctoral advisorGeorge David Birkhoff
Doctoral students

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.


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 wrote his Ph.D. thesis, Certain Types of Geodesic Motion of a Surface of Negative Curvature, under the direction of George David Birkhoff.[1]

Morse was a Benjamin Peirce Instructor at Harvard in 1919–1920, after which he served as an assistant professor at Cornell University from 1920 to 1925 and at Brown University in 1925–1926. He returned to Harvard in 1926, advancing to professor in 1929, and teaching there until 1935. That year, he accepted a position at the Institute for Advanced Study in Princeton, where he remained until his retirement in 1962.[2]

He spent most of his career on a single subject, now known as Morse theory, a branch of differential topology which enables one to analyze the topology of a smooth manifold by studying differentiable functions on that manifold. Morse originally applied his theory to geodesics (critical points of the energy functional on paths); these techniques were used in Raoul Bott's proof of his periodicity theorem. 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[edit]



  • Calculus of variations in the large, American Mathematical Society, 1934[3]
  • Topological methods in the theory of functions of a complex variable, Princeton University Press, 1947[4]
  • 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, 2007CS1 maint: postscript (link)
  • Global variational analysis: Weierstrass integrals on a Riemannian manifold, Princeton University Press, 1976[5]
  • 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[edit]