Skip to main content
SpringerLink
Log in

The late arrival of academic applied mathematics in the United States: a paradox, theses, and literature

  • Research
  • Published:
NTM International Journal of History & Ethics of Natural Sciences, Technology & Medicine Aims and scope Submit manuscript

Abstract

The article discusses the “paradox of the late (around 1940) arrival of academic applied mathematics in the U.S.” as compared to Europe, in particular Germany. A short description of both the indigenous traditions in the U.S. and (in some more detail) of the transfer of scientific ideas, persons, and ideals originating in Europe, particularly in Germany, is given, and some theses, relevant literature, and a tentative solution of the “paradox” are provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Bayart, Denis and Pierre Crépel: “Statistical Control of Manufacture”Companion Enyclopedia of the History and Philosophy of the Mathematical Sciences, 2 Volumes. ed. Ivor Grattan-Guinness. Routledge: London/New York 1994, p. 1386–1391.

    Google Scholar 

  • Ben-David, Joseph:The scientist's role in society. A comparative study, Prentice Hall: Englewood Cliffs 1971.

    Google Scholar 

  • Bennett, Albert A., William E. Milne and Harry Bateman: “Numerical Integration of Differential Equations”. National Research Council: Washington: 1933 (=Bulletin National Research Council 92).

    Google Scholar 

  • Bledstein, B.J.:The Culture of Professionalism. The Middle Class and the Development of Higher Education in America. Norton: New York, London 1976.

    Google Scholar 

  • Brocke, Bernhard vom (ed.):Wissenschaftsgeschichte und Wissenschaftspolitik im Industriezeitalter. Das “System Althoff” in historischer Perspektive. Lax: Hildesheim 1991.

    Google Scholar 

  • Butler, Loren:Mathematical Physics and the American Mathematics Community. Ph.D. Dissertation Chicago 1992.

  • Butler, Loren: “Mathematical Physics and the Planning of American Mathematics: Ideology and Institutions”,Historia Mathematica 24 (1997), p. 66–85.

    Article  MathSciNet  MATH  Google Scholar 

  • Corry, Leo: “David Hilbert and the Axiomatization of Physics (1894–1905)”,Archive for History of Exact Sciences 51 (1997), p. 83–198.

    Article  MathSciNet  MATH  Google Scholar 

  • Courant, Richard. “Variational Methods for the Solution of Problems of Equilibrium and Vibrations”,Bulletin of the American Mathematical Society 49 (1943), p. 1–23.

    Article  MathSciNet  MATH  Google Scholar 

  • Courant, Richard and David Hilbert:Methoden der mathematischen Physik; 2 Volumes, Springer: Berlin 1924 and 1937.

    MATH  Google Scholar 

  • Courant, Richard, Friedrichs, Kurt and Hans Lewy: “Über die partiellen Differenzengleichungen der mathematischen Physik”.Mathematische Annalen 100 (1928), p. 32–74 [english in:IBM Journal of Research and Development 11 (1967), p. 214–234].

    Article  MathSciNet  MATH  Google Scholar 

  • Dahan Dalmedico, Amy: “L'essor des mathématiques appliquées aux États-Unis: l'impact de la Seconde Guerre Mondiale”.Revue d'histoire des mathématiques 2 (1996), p. 149–213.

    MathSciNet  MATH  Google Scholar 

  • Dryden, H.L., F.D. Murnaghan and H. Bateman: “Report of the Committee on Hydrodynamics”.Bulletin of the National Research Council no. 84 (1932), p. 1–634.

    Google Scholar 

  • Duren, Peter (ed.):A Century of Mathematics in America 3 volumes. American Mathematical Society: Providence 1988/89.

    MATH  Google Scholar 

  • Duren, William L.: “Mathematics in American Society 1888–1988. A Historical Commentary”. In: Duren, P. (ed.) 1988/89, vol. 2 (1989), p. 399–447.

  • Fry, Thornton: “Industrial Mathematics”.The Bell System Technical Journal 20 (1941), p. 255–292.

    MATH  Google Scholar 

  • Goldstine, Herman H.:The Computer from Pascal to von Neumann. Princeton University Press: Princeton 1972.

    MATH  Google Scholar 

  • Hanle, Paul A.:Bringing Aerodynamics to America. MIT Press: Cambridge, Mass. 1982.

    Google Scholar 

  • Harwood, Jonathan: “Institutional Innovation in fin de siècle Germany”.British Journal for History of Science 27 (1994), p. 197–211.

    Article  Google Scholar 

  • Hunsaker, J. and S. MacLane: “Edwin Bidwell Wilson (1879–1964)”.Biographical Memoirs National Academy of Sciences 43 (1973), p. 284–320.

    Google Scholar 

  • Hunter, Patti W.: “Drawing the Boundaries: Mathematical Statistics in 20th-Century America”.Historia Mathematica 23 (1996), p. 7–30.

    Article  MathSciNet  MATH  Google Scholar 

  • Jammer, Max:The Conceptual Development of Quantum Mechanics. 2. ed., Tomash Publishers: New York 1989.

    Google Scholar 

  • Kármán, Theodor von: “Mathematik und technische Wissenschaften”.Die Naturwissenschaften 18 (1930), p. 12–16.

    Article  Google Scholar 

  • Korn, Arthur: “Teaching of Mathematics in the United States and in Germany”.Journal of Engineering Education 35 (1945), p. 407–413.

    Google Scholar 

  • Lax, Peter: “Hyperbolic Difference Equations: A Review of the Courant-Friedrichs-Lewy Paper in The Light of Recent Developments”.IBM Journal for Research and Development 11 (1967), p. 235–238.

    Article  MathSciNet  MATH  Google Scholar 

  • Lax, Peter: “The Flowering of Applied Mathematics in America”. In: Duren, P. (ed.), vol. 2 (1989), p. 455–466.

  • Levine, Lawrence W.:Highbrow/Lowbrow. The Emergence of Cultural Hierarchy in America. Harvard University Press: Cambridge, Mass. 1988.

    Google Scholar 

  • Lundgreen, Peter: “Engineering Education in Europe and the U.S.A., 1750–1930: The Rise to Dominance of School Culture and the Engineering Professions”.Annals of Science 47 (1990), p. 33–75.

    Article  Google Scholar 

  • Mehrtens, Herbert:Moderne, Sprache, Mathematik. Suhrkamp: Frankfurt 1990.

    MATH  Google Scholar 

  • Millman, S. (ed.):A History of Engineering and Science in the Bell System. Communication Sciences (1925–1980). AT&T Bell Laboratories: New York 1984.

    Google Scholar 

  • Mises, Richard von: “Pflege der angewandten Mathematik in Deutschland”.Die Naturwissenschaften 15 (1927), p. 473.

    Article  Google Scholar 

  • Moore, Eliakim H.: “On the Foundations of Mathematics”.Science 17 (1903), p. 401–416.

    Article  Google Scholar 

  • Owens, Larry: “Vannevar Bush and the Differential Analyzer: The Text and Context of an Early Computer”.Technology & Culture 27 (1986), p. 63–95.

    Article  Google Scholar 

  • Owens, Larry: “Mathematics and War. Warren Weaver and the Applied Mathematics Panel 1942–1945”. In Rowe/McCleary 1989, Vol. II, p. 287–305.

  • Parshall, Karen H.; David E. Rowe:The Emergence of the American Mathematical Research Community 1876–1900: J.J. Sylvester, Felix Klein, and E.H. Moore. American Mathematical Society: Providence 1994.

    MATH  Google Scholar 

  • Puchta, Susann: “Why and How American Electrical Engineers Developed ‘Heaviside's Operational Calculus’”.Archives Internationales d'Histoire des Sciences 47 (1997), no. 138, p. 57–107.

    MathSciNet  MATH  Google Scholar 

  • Pyenson, Lewis: “Mathematics, Education, and the Göttingen Approach to Physical Reality, 1890–1914”.Europa, A Journal of Interdisciplinary Studies 2 (1979), 2, p. 91–127.

    Google Scholar 

  • Reich, Karin: “The American Contribution to the Theory of Differential Invariants, 1900–1916”.The Attraction of Gravitation: New Studies in the History of General Relativity. ed. Earman, J. et al., Birkhäuser: Boston, Basel 1993, p. 225–247.

    Google Scholar 

  • Reid, Constance:Courant in Göttingen and New York. The Story of an Improbable Mathematician. Springer: New York etc. 1976.

  • Reingold, Nathan: “Refugee Mathematicians in the United States of America 1933–1941”.Annals of Science 38 (1981), p. 313–338.

    Article  MathSciNet  MATH  Google Scholar 

  • Richardson, Roland G.D.: “Applied Mathematics and the Present Crisis”.American Mathematical Monthly 50 (1943), p. 415–423.

    Article  MathSciNet  MATH  Google Scholar 

  • Rowe, David E.: “Klein, Hilbert, and the Göttingen Tradition”.Osiris (2) 5 (1989), p. 186–213.

    Article  MathSciNet  MATH  Google Scholar 

  • Rowe, David and John McCleary (eds.):The History of Modern Mathematics. Volume II: Institutions and Applications. Academic Press: Boston etc 1989.

    MATH  Google Scholar 

  • Schubring, Gert: “Changing Cultural and Epistemological Views on Mathematics and Differenti Institutional Contexts in Nineteenth-century Europe”.L'Europe mathématique, ed. C. Goldstein, J. Gray and J. Ritter, Editions de la Maison des sciences de l'homme, Paris 1996, p. 361–388.

    Google Scholar 

  • Schweber, Silvan S.: “The Empiricist Temper Regnant: Theoretical physics in the United States 1920–1950”.Historical Studies Physical Sciences 17 (1986), 1, p. 55–98.

    Google Scholar 

  • Servos, John: “Mathematics and the Physical Sciences in America, 1880–1930”.ISIS 77 (1986), p. 611–629.

    Article  MathSciNet  MATH  Google Scholar 

  • Siegmund-Schultze, Reinhard: “Las frustradas tentativas de reforma de la formación matemática de los ingenieros en los Estados Unidos de América en torno a 1900 sobre el trasfondo de similares reformas en Alemania”.Llull 18 (1995), p. 619–652.

    Google Scholar 

  • Siegmund-Schultze, R.: “The Emancipation of Mathematical Research Publishing in the United States from German Dominance (1878–1945)”.Historia Mathematica 24 (1997a), p. 135–166.

    Article  MathSciNet  MATH  Google Scholar 

  • Siegmund-Schultze, R.: “Ein Bericht Felix Kleins aus dem Jahre 1902 über seine mathematischen Vorträge in den Vereinigten Staaten 1893 und 1896”.NTM (N.S.) 5 (1997b), 228–235.

    Google Scholar 

  • Siegmund-Schultze, R.: “Felix Kleins Beziehungen zu den Vereinigten Staaten, die Anfänge deutscher auswärtiger Wissenschaftspolitik und die Reform um 1900”.Sudhoffs Archiv 81 (1997c), p. 21–38.

    MathSciNet  MATH  Google Scholar 

  • Siegmund-Schultze, R.:Mathematiker auf der Flucht vor Hitler. Quellen und Studien zur Emigration einer Wissenschaft. Vieweg: Braunschweig/Wiesbaden 1998.

    MATH  Google Scholar 

  • Siegmund-Schultze, R.:Rockefeller and the Internationalization of Mathematics Between the Two World Wars. Documents and Studies for the Social History of Mathematics in the 20th century. Birkhäuser: Basel etc. 2001.

    MATH  Google Scholar 

  • Tobies, Renate: “Wissenschaftliche Schwerpunktbildung: der Ausbau Göttingens zum Zentrum der Mathematik und Naturwissenschaften”, in: Brocke 1991 (ed.), p. 87–108.

  • Truesdell; Clifford:An Idiot's Fugitive Essays on Science. Springer: New York, Berlin 1984.

    MATH  Google Scholar 

  • Truesdell, Clifford: “Genius and the Establishment of a Polite Standstill in the Modern University: Bateman”. in: Truesdell 1984, p. 403–438.

  • Wehler, Hans-Ulrich:Der Aufstieg des amerikanischen Imperialismus. Vandenhoeck & Ruprecht: Göttingen 1974.

    Google Scholar 

  • Weyl, Hermann: “Courant and Hilbert on Partial Differential Equations (Review)”.Bulletin American Mathematical Society 44 (1938), p. 602–604.

    Article  MathSciNet  Google Scholar 

  • Williamson, Frank: “Richard Courant and the Finite Element Method: A Further Look”.Historia Mathematica 7 (1980), p. 369–378.

    Article  MathSciNet  Google Scholar 

  • Wilson, Edwin B.:Vector Analysis: A Text Book for the Use of Students of Mathematics and Physics Founded upon the Lectures of J. Willard Gibbs. New York/London 1901.

  • Zienkiewicz, O.C.: “Achievements and some unsolved problems of the finite element method”.International Journal for Numerical Methods in Engineering 47 (2000), p. 9–28.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Agder University College, Serviceboks 422, 4604, Kristiansand, Norway

    Reinhard Siegmund-Schultze

Authors
  1. Reinhard Siegmund-Schultze
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

To Menso Folkerts, the meticulous historian sine ira et studio, on the occasion of his 60th birthday!

Rights and permissions

Reprints and permissions

About this article

Cite this article

Siegmund-Schultze, R. The late arrival of academic applied mathematics in the United States: a paradox, theses, and literature. NTM N.S. 11, 116–127 (2003). https://doi.org/10.1007/BF02908592

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02908592

Keywords

Search

Navigation