The American Mathematical Society and Applied Mathematics from the 1920s to the 1950s: A Revisionist Account

Parshall, Karen

doi:10.1090/bull/1754

The American Mathematical Society and Applied Mathematics from the 1920s to the 1950s: A Revisionist Account
HTML articles powered by AMS MathViewer

by Karen Hunger Parshall;

Bull. Amer. Math. Soc. 59 (2022), 405-427

DOI: https://doi.org/10.1090/bull/1754

Published electronically: March 24, 2022

HTML | PDF | Request permission

Abstract:

The “standard” historical narrative has it that: 1) applied mathematics emerged as an academic discipline in the United States only after, and as a result of, World War II; and 2) a major factor in this emergence was the presence of European émigré mathematicians. While this standard narrative is not wrong, it masks a key part of the picture, namely, the foundation for this development was laid within the context of the American Mathematical Society in the 1920s, 1930s, and 1940s.

References

Ellen MacPhee Abrams, Making Mathematics American: Gender, Professionalization, and Abstraction during the Growth of Mathematics in the United States, 1890–1945, ProQuest LLC, Ann Arbor, MI, 2020. Thesis (Ph.D.)–Cornell University. MR 4172100
Donald J. Albers, Freeman Dyson: Mathematician, Physicist, and Writer, The College Mathematics Journal 25 (1994), 2–21.
Anonymous, The National Research Council, Science 49 (16 May 1919), 458–462.
Raymond C. Archibald, Semicentennial History of the American Mathematical Society, American Mathematical Society, New York, 1938.
W. L. Ayres, The annual meeting of the Society, Bull. Amer. Math. Soc. 46 (1940), no. 3, 187–201. MR 1564093, DOI 10.1090/S0002-9904-1940-07158-7
W. L. Ayres, The annual meeting of the Society, Bull. Amer. Math. Soc. 47 (1941), no. 3, 175–187. MR 1564224, DOI 10.1090/S0002-9904-1941-07400-8
W. L. Ayres, The annual meeting of the Society, Bull. Amer. Math. Soc. 50 (1944), no. 1, 23–36. MR 1564576, DOI 10.1090/S0002-9904-1944-08047-6
June Barrow-Green and Reinhard Siegmund-Schultze, “The History of Applied Mathematics,” in The Princeton Companion to Applied Mathematics, (Nicholas J. Higham, ed.), 55–79, Princeton University Press, Princeton, 2015.
Albert L. Barrows, “General Organization and Activities”, in A History of the National Research Council, 1919-1933, 7–11, National Research Council, Washington, DC, 1933.
Martina Bečvářová, Saly Ruth Struik, 1894–1993, Math. Intelligencer 40 (2018), no. 4, 79–85. MR 3870113, DOI 10.1007/s00283-018-9835-1
George Birkhoff and Rudolph Langer, Relativity and Modern Physics, Harvard University Press, Cambridge, MA, 1923.
P. W. Bridgman, Statistical mechanics and the second law of thermodynamics, Bull. Amer. Math. Soc. 38 (1932), no. 4, 225–245. MR 1562366, DOI 10.1090/S0002-9904-1932-05355-1
E. W. Brown, The relations of mathematics to the natural sciences, Bull. Amer. Math. Soc. 23 (1917), no. 5, 213–230. MR 1559923, DOI 10.1090/S0002-9904-1917-02922-9
R. H. Bruck, The annual meeting of the Society, Bull. Amer. Math. Soc. 52 (1946), no. 1, 35–47. MR 1564788, DOI 10.1090/S0002-9904-1946-08493-1
L. W. Cohen, The annual meeting of the Society, Bull. Amer. Math. Soc. 58 (1952), no. 2, 157–216. MR 1565375, DOI 10.1090/S0002-9904-1952-09585-9
L. W. Cohen, The October meeting in New York, Bull. Amer. Math. Soc. 60 (1954), no. 1, 20–37. MR 1565545, DOI 10.1090/S0002-9904-1954-09753-7
Cecil C. Craig, “Early Days in Statistics at Michigan”, in A Century of American Mathematics: Part III (Peter L. Duren et al., eds.), History of Mathematics, vol. 3, 573–576, American Mathematical Society, Providence, RI, and London Mathematical Society, London, 1989.
Amy Dahan Dalmedico, L’essor des mathématiques appliquées aux États-Unis: l’impact de la seconde guerre mondiale, Rev. Histoire Math. 2 (1996), no. 2, 149–213 (French, with English and French summaries). MR 1438748
Arnold Dresden, The thirty-fourth annual meeting of the American Mathematical Society, Bull. Amer. Math. Soc. 34 (1928), no. 2, 129–154. MR 1561524, DOI 10.1090/S0002-9904-1928-04500-7
Albert Einstein, Elementary derivation of the equivalence of mass and energy, Bull. Amer. Math. Soc. 41 (1935), no. 4, 223–230. MR 1563062, DOI 10.1090/S0002-9904-1935-06046-X
Loren Butler Feffer, Mathematical physics and the planning of American mathematics: ideology and institutions, Historia Math. 24 (1997), no. 1, 66–85 (English, with English, French and German summaries). MR 1433922, DOI 10.1006/hmat.1997.2124
Loren Butler Feffer, Oswald Veblen and the capitalization of American mathematics. Raising money for research, 1923–1928, Isis 89 (1998), no. 3, 474–497. MR 1647005, DOI 10.1086/384074
Irving Fisher, The application of mathematics to the social sciences, Bull. Amer. Math. Soc. 36 (1930), no. 4, 225–243. MR 1561927, DOI 10.1090/S0002-9904-1930-04919-8
Alan Gluchoff, Pure mathematics applied in early twentieth-century America: the case of T. H. Gronwall, consulting mathematician, Historia Math. 32 (2005), no. 3, 312–357 (English, with English and German summaries). MR 2159515, DOI 10.1016/j.hm.2004.05.002
Kurt Gödel, “Some Basic Theorems on the Foundations of Mathematics and Their Implications,” in Collected Works, (Solomon Feferman, et al., eds.), 5 vols., Clarendon Press, Oxford, 1986–2003.
John L. Greenberg and Judith R. Goodstein, Theodore von Kármán and applied mathematics in America, Science 222 (1983), no. 4630, 1300–1304. MR 729487, DOI 10.1126/science.222.4630.1300
G. H. Hardy, An introduction to the theory of numbers, Bull. Amer. Math. Soc. 35 (1929), no. 6, 778–818. MR 1561815, DOI 10.1090/S0002-9904-1929-04793-1
E. R. Hedrick, A proposed journal of applied mathematics, Bull. Amer. Math. Soc. 48 (1942), no. 11, 791. MR 1564436, DOI 10.1090/S0002-9904-1942-07787-1
Robert Henderson, Life insurance as a social service and as a mathematical problem, Bull. Amer. Math. Soc. 31 (1925), no. 5-6, 227–252. MR 1561032, DOI 10.1090/S0002-9904-1925-04040-9
G. W. Hill, Remarks on the progress of celestial mechanics since the middle of the century, Bull. Amer. Math. Soc. 2 (1896), no. 5, 125–136. MR 1557428, DOI 10.1090/S0002-9904-1896-00325-6
T. R. Hollcroft, The annual meeting of the Society, Bull. Amer. Math. Soc. 45 (1939), no. 3, 197–208. MR 1563942, DOI 10.1090/S0002-9904-1939-06943-7
T. R. Hollcroft, The annual meeting of the Society, Bull. Amer. Math. Soc. 48 (1942), no. 3, 183–198. MR 1564347, DOI 10.1090/S0002-9904-1942-07636-1
T. R. Hollcroft, The annual meeting of the Society, Bull. Amer. Math. Soc. 51 (1945), no. 1, 25–38. MR 1564680, DOI 10.1090/S0002-9904-1945-08278-0
T. R. Hollcroft, The annual meeting of the Society, Bull. Amer. Math. Soc. 53 (1947), no. 3, 240–260. MR 1564922, DOI 10.1090/S0002-9904-1947-08747-4
T. R. Hollcroft, The annual meeting of the Society, Bull. Amer. Math. Soc. 56 (1950), no. 2, 140–190. MR 1565186, DOI 10.1090/S0002-9904-1950-09372-0
Patti W. Hunter, Drawing the boundaries: mathematical statistics in 20th-century America, Historia Math. 23 (1996), no. 1, 7–30 (English, with English, French and German summaries). MR 1375744, DOI 10.1006/hmat.1996.0002
M. H. Ingraham, The annual meeting in St. Louis, Bull. Amer. Math. Soc. 42 (1936), no. 3, 150–162. MR 1563260, DOI 10.1090/S0002-9904-1936-06261-0
Wilfred Kaplan, “Mathematics at the University of Michigan”, in A Century of American Mathematics: Part III (Peter L. Duren et al., eds.), History of Mathematics, vol. 3, 179–189, American Mathematical Society, Providence, RI, and London Mathematical Society, London, 1989.
J. R. Kline, The annual meeting in Pittsburgh, Bull. Amer. Math. Soc. 41 (1935), no. 3, 150–161. MR 1563042, DOI 10.1090/S0002-9904-1935-06045-8
J. R. Kline, The annual meeting of the Society, Bull. Amer. Math. Soc. 49 (1943), no. 3, 195–204. MR 1564479, DOI 10.1090/S0002-9904-1943-07858-5
J. R. Kline, The annual meeting of the Society, Bull. Amer. Math. Soc. 54 (1948), no. 3, 260–297. MR 1565047, DOI 10.1090/S0002-9904-1948-08967-4
Peter Lax, “The Flowering of Applied Mathematics in America,” in A Century of American Mathematics: Part II (Peter L. Duren et al., eds.), History of Mathematics, vol. 3, 455–466, American Mathematical Society, Providence, RI, and London Mathematical Society, London, 1989.
Wassily Leontief, Mathematics in economics, Bull. Amer. Math. Soc. 60 (1954), 215–233. MR 61351, DOI 10.1090/S0002-9904-1954-09791-4
Joseph Lipka, Graphical and Mechanical Computation, 2 vols., John Wiley & Sons, Inc., New York, and Chapman & Hall, Ltd., London, 1918.
Emory McClintock, The past and future of the Society, Bull. Amer. Math. Soc. 1 (1895), no. 4, 85–94. MR 1557358, DOI 10.1090/S0002-9904-1895-00251-7
A. D. Michal, The April meeting in Berkeley, Bull. Amer. Math. Soc. 50 (1944), no. 7, 476–477. MR 1564625, DOI 10.1090/S0002-9904-1944-08148-2
Eliakim Hastings Moore, On the foundations of mathematics, Bull. Amer. Math. Soc. 9 (1903), no. 8, 402–424. MR 1558011, DOI 10.1090/S0002-9904-1903-01007-6
Notes, Bull. Amer. Math. Soc. 47 (1941), no. 7, 548–552. MR 1564275, DOI 10.1090/S0002-9904-1941-07486-0
Rufus Oldenburger, Pure and applied mathematics, J. Engrg. Education 33 (1943), 432–437. MR 9771
Karen Hunger Parshall, The New Era in American Mathematics, 1920–1950, Princeton University Press, Princeton, 2022.
Karen Hunger Parshall, “ ‘A New Era in the Development of Our Science’: The American Mathematical Research Community, 1920–1950”. in A Delicate Balance: Global Perspectives on Innovation and Tradition in the History of Mathematics: A Festschrift in Honor of Joseph W. Dauben, (David E. Rowe and Wann-Sheng Horng, eds.), 275–308, Birkhäuser Verlag, Berlin, 2015.
Karen Hunger Parshall, Perspectives on American mathematics, Bull. Amer. Math. Soc. (N.S.) 37 (2000), no. 4, 381–405. MR 1779411, DOI 10.1090/S0273-0979-00-00873-9
Karen Hunger Parshall and David E. Rowe, The emergence of the American mathematical research community, 1876–1900: J. J. Sylvester, Felix Klein, and E. H. Moore, History of Mathematics, vol. 8, American Mathematical Society, Providence, RI; London Mathematical Society, London, 1994. MR 1290994, DOI 10.1090/hmath/008
James Pierpont, Some modern views of space, Bull. Amer. Math. Soc. 32 (1926), no. 3, 225–258. MR 1561200, DOI 10.1090/S0002-9904-1926-04201-4
Everett Pitcher retires as AMS secretary, Notices Amer. Math. Soc. 35 (1988), no. 10, 1463–1466. MR 969001
William Prager and T. R. Hollcroft, First Symposium in Applied Mathematics, Bull. Amer. Math. Soc. 53 (1947), no. 9, 878–881. MR 1564975, DOI 10.1090/S0002-9904-1947-08872-8
Michael Pupin, From Chaos to Cosmos, Scribner’s Magazine 76 (July 1924), 3–10.
Michael Pupin, From Immigrant to Inventor Charles Scribner’s Sons, New York, 1923.
Nathan Reingold, Refugee Mathematicians in the U.S.A., Annals of Science 38 (1981), 313–338; reprinted in A Century of Mathematics in America: Part I (Peter L. Duren et al., eds.), History of Mathematics, vol. 1, 175–200, American Mathematical Society, Providence, RI, and London Mathematical Society, London, 1988.
Eric Reissner, William Prager, and James Stoker, eds., Nonlinear Problems in Mechanics of Continua, Proceedings of Symposia in Applied Mathematics, vol. 1, American Mathematical Society, New York, 1949.
R. G. D. Richardson, The annual meeting in Atlantic city and Princeton, Bull. Amer. Math. Soc. 39 (1933), no. 3, 161–170. MR 1562573, DOI 10.1090/S0002-9904-1933-05558-1
R. G. D. Richardson, The annual meeting in Bethlehem, Bull. Amer. Math. Soc. 36 (1930), no. 3, 145–155. MR 1561909, DOI 10.1090/S0002-9904-1930-04906-X
R. G. D. Richardson, The annual meeting in Cambridge, Bull. Amer. Math. Soc. 40 (1934), no. 3, 177–188. MR 1562816, DOI 10.1090/S0002-9904-1934-05799-9
R. G. D. Richardson, The annual meeting in New York, Bull. Amer. Math. Soc. 35 (1929), no. 2, 156–190. MR 1561707, DOI 10.1090/S0002-9904-1929-04691-3
R. G. D. Richardson, The first Josiah Willard Gibbs Lecture, Bull. Amer. Math. Soc. 30 (1924), no. 7, 289–291. MR 1560904, DOI 10.1090/S0002-9904-1924-03881-6
Roland Richardson, The Mathematics of Engineering, Science 70 (30 August 1929) (1929), 211.
R. G. D. Richardson, The twenty-seventh annual meeting of the American Mathematical Society, Bull. Amer. Math. Soc. 27 (1921), no. 6, 245–265. MR 1560413, DOI 10.1090/S0002-9904-1921-03403-3
Arnold Dresden and R. G. D. Richardson, The twenty-eighth annual meeting of the American Mathematical Society, Bull. Amer. Math. Soc. 28 (1922), no. 4, 148–164. MR 1560533, DOI 10.1090/S0002-9904-1922-03536-7
R. G. D. Richardson, The twenty-ninth annual meeting of the Society, Bull. Amer. Math. Soc. 29 (1923), no. 3, 97–116. MR 1560681, DOI 10.1090/S0002-9904-1923-03671-9
R. G. D. Richardson, Applied mathematics and the present crisis, Amer. Math. Monthly 50 (1943), 415–423. MR 9005, DOI 10.2307/2303664
Jim Ritter, “Geometry as Physics: Oswald Veblen and the Princeton School”, in Mathematics Meets Physics: A Contribution to Their Interaction in the 19th and the First Half of the 20th Century (Karl-Heinz Schlote and Martina Schneider, eds.), 146–179, Verlag Harri Deutsch, Frankfurt, 2011.
Bruce Seely, Research, Engineering, and Science in American Engineering Colleges: 1900–1960, Technology and Culture 34 (1993), 344–386.
Reinhard Siegmund-Schultze, The ideology of applied mathematics within mathematics in Germany and the U.S. until the end of World War II, LLULL 27 (2004), no. 60, 791–811 (2005) (English, with English and Spanish summaries). MR 2156708
Reinhard Siegmund-Schultze, The late arrival of academic applied mathematics in the United States: a paradox, theses, and literature, NTM (N.S.) 11 (2003), no. 2, 116–127. MR 1979079, DOI 10.1007/BF02908592
J. C. Slater, Physics and the wave equation, Bull. Amer. Math. Soc. 52 (1946), 392–400. MR 15639, DOI 10.1090/S0002-9904-1946-08558-4
The Special Committee on Applied Mathematics, Instruction and research in Applied Mathematics, Bull. Amer. Math. Soc. 53 (1947), no. 7, 639–640. MR 1564957, DOI 10.1090/S0002-9904-1947-08822-4
Dirk Struik, “The MIT Department of Mathematics During Its First Seventy-Five Years: Some Recollections,” in A Century of American Mathematics: Part III, ed. Peter L. Duren et al, History of Mathematics, vol. 3, 163–177, American Mathematical Society, Providence, RI, and London Mathematical Society, London, 1989.
James Henry Taylor, A generalization of Levi-Civita’s parallelism and the Frenet formulas, Trans. Amer. Math. Soc. 27 (1925), no. 2, 246–264. MR 1501309, DOI 10.1090/S0002-9947-1925-1501309-9
R. C. Tolman, Thermodynamics and relativity, Bull. Amer. Math. Soc. 39 (1933), no. 2, 49–74. MR 1562556, DOI 10.1090/S0002-9904-1933-05559-3
Oswald Veblen, Remarks on the foundations of geometry, Bull. Amer. Math. Soc. 31 (1925), no. 3-4, 121–141. MR 1561010, DOI 10.1090/S0002-9904-1925-03992-0
Hermann Weyl, Ramifications, old and new, of the eigenvalue problem, Bull. Amer. Math. Soc. 56 (1950), 115–139. MR 34940, DOI 10.1090/S0002-9904-1950-09369-0
F. J. Weyl, Introduction and Critique, Amer. Math. Monthly 61 (1954), no. 7, 1–4. MR 1528813, DOI 10.2307/2308440
F. Joachim Weyl, The NRC-AMS conference on training in applied mathematics, Bull. Amer. Math. Soc. 60 (1954), no. 1, 38–44. MR 1565546, DOI 10.1090/S0002-9904-1954-09756-2
F. J. Weyl, Report on a survey of training and research in applied mathematics in the United States, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1956. Conducted by the National Research Council under contract with the National Science Foundation. MR 80594
F. J. Weyl and J. W. T. Youngs, The November meeting in Evanston, Bull. Amer. Math. Soc. 60 (1954), no. 1, 59–74. MR 1565548, DOI 10.1090/S0002-9904-1954-09758-6
W. M. Whyburn, The annual meeting of the society, Bull. Amer. Math. Soc. 57 (1951), no. 2, 109–152. MR 1565283, DOI 10.1090/S0002-9904-1951-09479-3
Norbert Wiener, In Memory of Joseph Lipka, J. Math. Phys. 3 (1924), 63–65.
Eugene Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Comm. Pure Appl. Math. 13 (1960), 1–14.
Edwin Bidwell Wilson, Reminiscences of Gibbs by a student and colleague, Bull. Amer. Math. Soc. 37 (1931), no. 6, 401–416. MR 1562161, DOI 10.1090/S0002-9904-1931-05169-7
R. S. Woodward, The century’s progress in applied mathematics, Bull. Amer. Math. Soc. 6 (1900), no. 4, 133–163. MR 1557689, DOI 10.1090/S0002-9904-1900-00681-1
J. W. T. Youngs, The annual meeting of the Society, Bull. Amer. Math. Soc. 55 (1949), no. 3, 261–311. MR 1565116, DOI 10.1090/S0002-9904-1949-09184-X

Bibliographic Information

Karen Hunger Parshall
Affiliation: Departments of History and Mathematics, University of Virginia, P. O. Box 400137, Charlottesville, Virginia 22904-4137
MR Author ID: 215967
Received by editor(s): July 23, 2021
Published electronically: March 24, 2022
Journal: Bull. Amer. Math. Soc. 59 (2022), 405-427
DOI: https://doi.org/10.1090/bull/1754
MathSciNet review: 4437803