Marston Morse Explained

H. C. Marston Morse
Birth Date:	24 March 1892
Birth Place:	Waterville, Maine, U.S.
Death Place:	Princeton, New Jersey, U.S.
Nationality:	American
Fields:	Mathematics
Workplaces:	Cornell University Brown University Harvard University Institute for Advanced Study
Alma Mater:	Colby College Harvard University
Thesis Title:	Certain Types of Geodesic Motion of a Surface of Negative Curvature
Thesis Year:	1917
Doctoral Advisor:	George David Birkhoff
Doctoral Students:	Emilio Baiada Nancy Cole Gustav Hedlund Sumner Myers Everett Pitcher Arthur Sard
Known For:	Morse theory
Awards:	Bôcher Memorial Prize (1933) National Medal of Science (1964)

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.

He was elected to the American Academy of Arts and Sciences in 1929,^[1] the United States National Academy of Sciences in 1932,^[2] and the American Philosophical Society in 1936.^[3] In 1933 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis. J. Robert Oppenheimer described Morse as "almost a statesman of mathematics."

Biography

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.^[4] At Harvard University, he received both his master's degree in 1915 and his PhD in 1917. He wrote his PhD thesis, Certain Types of Geodesic Motion of a Surface of Negative Curvature, under the direction of George David Birkhoff.

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.

He spent most of his career on a single subject, now known as Morse theory, a branch of differential topology that 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.

He died on June 22, 1977, at his home in Princeton, New Jersey.^[5] His second wife, Louise Jeffreys, died in 2016.^[6]

Marston Morse should not be confused with either his 5th cousin twice removed Samuel Morse,^{[7] [8] [9] [10] [11]} famous for Morse code, nor Anthony Morse, famous for the Morse–Sard theorem.

Selected publications

Articles

• A fundamental class of geodesics on any closed surface of genus greater than one . Trans. Amer. Math. Soc. . 1924 . 26 . 1 . 25–60 . 1501263 . 10.1090/s0002-9947-1924-1501263-9. free . Morse . Harold Marston .
• The foundations of a theory in the calculus of variations in the large . Trans. Amer. Math. Soc. . 1928 . 30 . 2 . 213–274 . 1501428 . 10.1090/s0002-9947-1928-1501428-x. free . Morse . Marston .
• Singular points of vector fields under general boundary conditions . Proc Natl Acad Sci U S A . 1928 . 14 . 5 . 428–430 . 1085532 . 10.1073/pnas.14.5.428 . 16577120. Morse . M. . 1928PNAS...14..428M . free .
• The critical points of functions and the calculus of variations in the large . Bull. Amer. Math. Soc. . 1929 . 35 . 1 . 38–54 . 1561686 . 10.1090/s0002-9904-1929-04690-1. free . Morse . Marston .
• The foundations of the calculus of variations in the large in m-space (first paper) . Trans. Amer. Math. Soc. . 1929 . 31 . 3 . 379–404 . 1501489 . 10.1090/s0002-9947-1929-1501489-9. free .
• Closed extremals . Proc Natl Acad Sci U S A . 1929 . 15 . 11 . 856–859 . 522574 . 10.1073/pnas.15.11.856 . 16577255. Morse . M. . 1929PNAS...15..856M . free .
• The foundations of a theory of the calculus of variations in the large in m-space (second paper) . Trans. Amer. Math. Soc. . 1930 . 32 . 4 . 599–631 . 1501555 . 10.1090/s0002-9947-1930-1501555-6. free .
• The critical points of a function of n variables . Trans. Amer. Math. Soc. . 1931 . 33 . 1 . 72–91 . 1501576 . 10.1090/s0002-9947-1931-1501576-4. 526733 . 16577308. Morse . Marston .
• Sufficient conditions in the problem of Lagrange without assumptions of normalcy . Trans. Amer. Math. Soc. . 1935 . 37 . 1 . 147–160 . 1501780 . 10.1090/s0002-9947-1935-1501780-9. free . Morse . Marston .
• Singular quadratic functions . Trans. Amer. Math. Soc. . 1936 . 40 . 2 . 252–288 . 1501873 . 10.1090/s0002-9947-1936-1501873-7. free . Morse . Marston . Leighton . Walter .
• Manifolds without conjugate points . Trans. Amer. Math. Soc. . 1942 . 51 . 2 . 362–386 . 006479 . 10.1090/s0002-9947-1942-0006479-x. free . Morse . Marston . Hedlund . Gustav A.. Gustav A. Hedlund .
• Homology relations on regular orientable manifolds . Proc Natl Acad Sci U S A . 1952 . 38 . 3 . 247–258 . 1063540 . 10.1073/pnas.38.3.247 . 16589087. Morse . M. . 1952PNAS...38..247M . free .

Books

• ^[12]
• ^[13]
  • Book: . Institute for Advanced Study . Princeton, NJ . 1966.
• with Stewart Cairns:
  • ^[14]

Film

• "Pits, Peaks, and Passes: A Lecture on Critical Point Theory", Mathematical Association of America Lecture Films, 1966

Biographical references

• .

References

• .
• (e-book:).

Notes and References

1. Web site: 2023-02-09 . Marston Morse . 2023-06-01 . American Academy of Arts & Sciences . en.
2. Web site: H. Marston Morse . 2023-06-01 . www.nasonline.org.
3. Web site: APS Member History . 2023-06-01 . search.amphilsoc.org.
4. Web site: 2019-12-09. Marston Morse - Scholars Institute for Advanced Study. 2021-12-26. www.ias.edu. en.
5. News: 1977-06-26. Harold Marston Morse Dies at 85; Served With Einstein at Princeton. en-US. The New York Times. 2021-12-26. 0362-4331.
6. Web site: Obituaries 12/7/16 . Town Topics . 2016-12-07 . 2024-01-14.
7. Book: National Academy of Sciences . Biographical Memoirs: Volume 65 . Marston Morse . 1994 . The National Academies Press . Washington, DC . 978-0-309-07359-2 .
8. Web site: Noteworthy Morses . Morse Society . 5 June 2022.
9. Book: Morse . J. Howard . Leavitt . Emily W. . Morse genealogy, comprising the descendants of Samuel, Anthony, William, and Joseph Morse and John Moss: being a revision of the Memorial of the Morses, published by Abner Morse in 1850 . 1903 . Springfield Printing and Binding Company . Anthony Morse and Four Generations . 2027/hvd.hxcrcu .
10. Web site: Howard Calvin MORSE . Pilgrim Edward Doty Society: A Family History Society . 5 June 2022.
11. Web site: Grimaud . Jessica . Cousin Chart—Family Relationships Explained . FamilySearch . 5 June 2022 . 23 July 2019.
12. Dresden, Arnold . Arnold Dresden . Review: Calculus of variations in the large, by Marston Morse . Bull. Amer. Math. Soc. . 1936 . 42 . 9, Part 1 . 607–612 . 10.1090/s0002-9904-1936-06362-7. free .
13. Ahlfors, L. . Lars Ahlfors . Review: Topological methods in the theory of functions of a complex variable, by Marston Morse . Bull. Amer. Math. Soc. . 1948 . 54 . 5 . 489–491 . 10.1090/s0002-9904-1948-09004-8. free .
14. Smale, Stephen . Stephen Smale . Review: Global variational analysis: Weierstrass integrals on a Riemannian manifold, by Marston Morse . Bull. Amer. Math. Soc. . 1977 . 83 . 4 . 683–693 . 10.1090/s0002-9904-1977-14345-0. free .