American mathematician
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."
[4]
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.
[5] 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 .
[6]
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.
[7]
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 .
[8] His second wife, Louise Jeffreys, died in 2016.
[9]
Marston Morse should not be confused with either his 5th cousin twice removed
Samuel Morse ,
[10]
[11]
[12] : 183 (Entry 2696), 217 (Entry 3297)
[13]
[14] famous for
Morse code , nor
Anthony Morse , famous for the
Morse–Sard theorem .
Selected publications
Articles
Morse, Harold Marston (1924).
"A fundamental class of geodesics on any closed surface of genus greater than one" . Trans. Amer. Math. Soc . 26 (1): 25–60.
doi :
10.1090/s0002-9947-1924-1501263-9 .
MR
1501263 .
Morse, Marston (1928).
"The foundations of a theory in the calculus of variations in the large" . Trans. Amer. Math. Soc . 30 (2): 213–274.
doi :
10.1090/s0002-9947-1928-1501428-x .
MR
1501428 .
Morse, M. (1928).
"Singular points of vector fields under general boundary conditions" . Proc Natl Acad Sci U S A . 14 (5): 428–430.
Bibcode :
1928PNAS...14..428M .
doi :
10.1073/pnas.14.5.428 .
PMC
1085532 .
PMID
16577120 .
Morse, Marston (1929).
"The critical points of functions and the calculus of variations in the large" . Bull. Amer. Math. Soc . 35 (1): 38–54.
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 .
Morse, M. (1929).
"Closed extremals" . Proc Natl Acad Sci U S A . 15 (11): 856–859.
Bibcode :
1929PNAS...15..856M .
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 .
Morse, Marston (1931).
"The critical points of a function of n variables" . Trans. Amer. Math. Soc . 33 (1): 72–91.
doi :
10.1090/s0002-9947-1931-1501576-4 .
MR
1501576 .
PMC
526733 .
PMID
16577308 .
Morse, Marston (1935).
"Sufficient conditions in the problem of Lagrange without assumptions of normalcy" . Trans. Amer. Math. Soc . 37 (1): 147–160.
doi :
10.1090/s0002-9947-1935-1501780-9 .
MR
1501780 .
Morse, Marston; Leighton, Walter (1936).
"Singular quadratic functions" . Trans. Amer. Math. Soc . 40 (2): 252–288.
doi :
10.1090/s0002-9947-1936-1501873-7 .
MR
1501873 .
Morse, Marston;
Hedlund, Gustav A. (1942).
"Manifolds without conjugate points" . Trans. Amer. Math. Soc . 51 (2): 362–386.
doi :
10.1090/s0002-9947-1942-0006479-x .
MR
0006479 .
Morse, M. (1952).
"Homology relations on regular orientable manifolds" . Proc Natl Acad Sci U S A . 38 (3): 247–258.
Bibcode :
1952PNAS...38..247M .
doi :
10.1073/pnas.38.3.247 .
PMC
1063540 .
PMID
16589087 .
Books
Calculus of variations in the large , American Mathematical Society, 1934
[15]
Topological methods in the theory of functions of a complex variable ,
Princeton University Press , 1947
[16]
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{{
citation }}
: CS1 maint: postscript (
link )
Global variational analysis: Weierstrass integrals on a Riemannian manifold , Princeton University Press, 1976
[17]
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
Film
Notes
^
"Marston Morse" . American Academy of Arts & Sciences . February 9, 2023. Retrieved June 1, 2023 .
^
"H. Marston Morse" . www.nasonline.org . Retrieved June 1, 2023 .
^
"APS Member History" . search.amphilsoc.org . Retrieved June 1, 2023 .
^
A Conversation with J. Robert Oppenheimer on
YouTube
^
"Marston Morse - Scholars | Institute for Advanced Study" . www.ias.edu . December 9, 2019. Retrieved December 26, 2021 .
^
Marston Morse at the
Mathematics Genealogy Project
^ O'Connor, John J.;
Robertson, Edmund F. ,
"Marston Morse" ,
MacTutor History of Mathematics Archive ,
University of St Andrews
^
"Harold Marston Morse Dies at 85; Served With Einstein at Princeton" . The New York Times . June 26, 1977.
ISSN
0362-4331 . Retrieved December 26, 2021 .
^
"Obituaries 12/7/16" . Town Topics . December 7, 2016. Retrieved January 14, 2024 .
^ National Academy of Sciences (1994). "Marston Morse".
Biographical Memoirs: Volume 65 . Washington, DC: The National Academies Press.
ISBN
978-0-309-07359-2 .
^
"Noteworthy Morses" . Morse Society . Retrieved June 5, 2022 .
^ Morse, J. Howard; Leavitt, Emily W. (1903). "Anthony Morse and Four Generations".
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 . Springfield Printing and Binding Company.
hdl :
2027/hvd.hxcrcu .
^
"Howard Calvin MORSE" . Pilgrim Edward Doty Society: A Family History Society . Retrieved June 5, 2022 .
^ Grimaud, Jessica (July 23, 2019).
"Cousin Chart—Family Relationships Explained" . FamilySearch . Retrieved June 5, 2022 .
^
Dresden, Arnold (1936).
"Review: Calculus of variations in the large , by Marston Morse" . Bull. Amer. Math. Soc . 42 (9, Part 1): 607–612.
doi :
10.1090/s0002-9904-1936-06362-7 .
^
Ahlfors, L. (1948).
"Review: Topological methods in the theory of functions of a complex variable , by Marston Morse" . Bull. Amer. Math. Soc . 54 (5): 489–491.
doi :
10.1090/s0002-9904-1948-09004-8 .
^
Smale, Stephen (1977).
"Review: Global variational analysis: Weierstrass integrals on a Riemannian manifold , by Marston Morse" . Bull. Amer. Math. Soc . 83 (4): 683–693.
doi :
10.1090/s0002-9904-1977-14345-0 .
Biographical references
Pitcher, Everett (1994),
"H. Marston Morse" (PDF) , in
National Academy of Sciences of the United States of America (ed.),
Biographical Memoirs , Biographical Memoirs, vol. 65, Washington, D.C.:
National Academies Press , pp. 223–240,
ISBN
978-0-309-07359-2 .
References
Bott, Raoul (1980), "Marston Morse and his mathematical works",
Bulletin of the American Mathematical Society , New Series, 3 (3): 907–950,
doi :
10.1090/s0273-0979-1980-14824-7 ,
MR
0585177 ,
Zbl
0469.01012 .
Nadis, Steve;
Yau, Shing-Tung (2013), "Chapter 4. Analysis and Algebra Meet Topology: Marston Morse, Hassler Whitney, and Saunders Mac Lane", A History in Sum ,
Cambridge, MA :
Harvard University Press , pp. 86–115,
doi :
10.4159/harvard.9780674726550 ,
ISBN
978-0-674-72500-3 ,
JSTOR
j.ctt6wpqft ,
MR
3100544 ,
Zbl
1290.01005 (
e-book :
ISBN
978-0-674-72655-0 ).
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