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Marston Morse

August 29, 2023

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.

H. C. Marston Morse
Morse in 1965 (courtesy MFO)
Born(1892-03-24)March 24, 1892
Waterville, Maine, U.S.
DiedJune 22, 1977(1977-06-22) (aged 85)
Princeton, New Jersey, U.S.
NationalityAmerican
Alma materColby College
Harvard University
Known forMorse theory
AwardsBôcher Memorial Prize (1933)
National Medal of Science (1964)
Scientific career
FieldsMathematics
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

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 Edit

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 2009.

Marston Morse should not be confused with either his 5th cousin twice removed Samuel Morse,[9][10][11]: 183 (Entry 2696), 217 (Entry 3297) [12][13] famous for Morse code, nor Anthony Morse, famous for the Morse–Sard theorem.

Selected publications Edit

Articles Edit

  • 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 Edit

  • Calculus of variations in the large, American Mathematical Society, 1934[14]
  • Topological methods in the theory of functions of a complex variable, Princeton University Press, 1947[15]
  • 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[16]
  • 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 Edit

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

Notes Edit

  1. ^ "Marston Morse". American Academy of Arts & Sciences. February 9, 2023. Retrieved June 1, 2023.
  2. ^ "H. Marston Morse". www.nasonline.org. Retrieved June 1, 2023.
  3. ^ "APS Member History". search.amphilsoc.org. Retrieved June 1, 2023.
  4. ^ A Conversation with J. Robert Oppenheimer on YouTube
  5. ^ "Marston Morse - Scholars | Institute for Advanced Study". www.ias.edu. December 9, 2019. Retrieved December 26, 2021.
  6. ^ Marston Morse at the Mathematics Genealogy Project
  7. ^ O'Connor, John J.; Robertson, Edmund F., "Marston Morse", MacTutor History of Mathematics Archive, University of St Andrews
  8. ^ "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.
  9. ^ National Academy of Sciences (1994). "Marston Morse". Biographical Memoirs: Volume 65. Washington, DC: The National Academies Press. ISBN 978-0-309-07359-2.
  10. ^ "Noteworthy Morses". Morse Society. Retrieved June 5, 2022.
  11. ^ 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.
  12. ^ "Howard Calvin MORSE". Pilgrim Edward Doty Society: A Family History Society. Retrieved June 5, 2022.
  13. ^ Grimaud, Jessica (July 23, 2019). "Cousin Chart—Family Relationships Explained". FamilySearch. Retrieved June 5, 2022.
  14. ^ 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.
  15. ^ 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.
  16. ^ 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 Edit

References Edit

 
Wikiquote has quotations related to Marston Morse.

August 29, 2023
marston, morse, harold, calvin, march, 1892, june, 1977, american, mathematician, best, known, work, calculus, variations, large, subject, where, introduced, technique, differential, topology, known, morse, theory, morse, palais, lemma, results, morse, theory,. 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 H C Marston MorseMorse in 1965 courtesy MFO Born 1892 03 24 March 24 1892Waterville Maine U S DiedJune 22 1977 1977 06 22 aged 85 Princeton New Jersey U S NationalityAmericanAlma materColby CollegeHarvard UniversityKnown forMorse theoryAwardsBocher Memorial Prize 1933 National Medal of Science 1964 Scientific careerFieldsMathematicsInstitutionsCornell UniversityBrown UniversityHarvard UniversityInstitute for Advanced StudyThesisCertain Types of Geodesic Motion of a Surface of Negative Curvature 1917 Doctoral advisorGeorge David BirkhoffDoctoral studentsEmilio Baiada Nancy Cole Gustav Hedlund Sumner Myers Everett Pitcher Arthur SardHe 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 Bocher Memorial Prize for his work in mathematical analysis J Robert Oppenheimer described Morse as almost a statesman of mathematics 4 Contents 1 Biography 2 Selected publications 2 1 Articles 2 2 Books 2 3 Film 3 Notes 4 Biographical references 5 ReferencesBiography EditHe 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 2009 Marston Morse should not be confused with either his 5th cousin twice removed Samuel Morse 9 10 11 183 Entry 2696 217 Entry 3297 12 13 famous for Morse code nor Anthony Morse famous for the Morse Sard theorem Selected publications EditArticles Edit 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 Edit Calculus of variations in the large American Mathematical Society 1934 14 Topological methods in the theory of functions of a complex variable Princeton University Press 1947 15 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 a href Template Citation html title Template Citation citation a CS1 maint postscript link Global variational analysis Weierstrass integrals on a Riemannian manifold Princeton University Press 1976 16 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 0889255Film Edit Pits Peaks and Passes A Lecture on Critical Point Theory Mathematical Association of America Lecture Films 1966Notes Edit Marston Morse American Academy of Arts amp 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 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 EditPitcher 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 EditBott 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 Wikiquote has quotations related to Marston Morse Retrieved from https en wikipedia org w index php title Marston Morse amp oldid 1170869242, wikipedia, wiki, book, books, library,

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