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A Multiple Perspective Approach to History of Mathematics: Mathematical Programming and Rashevsky’s Early Development of Mathematical Biology in the Twentieth Century

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Interfaces between Mathematical Practices and Mathematical Education

Abstract

A multiple perspective approach to history of mathematics is introduced. It is discussed how such an approach can be used to explore and shed light on relationships between developments in mathematics and the conditions of those developments. The approach will be illustrated by two episodes from the history of applied mathematics from the twentieth century: the development of mathematical programming and the significance of World War II, and Nicolas Rashevsky’s early attempts to develop mathematical biology in the 1930s in the USA and issues of engagement with interdisciplinary research. The importance that the historical actors attached to education and teaching for the development of these new fields is discussed, drawing attention to education and teaching as relevant and significant perspectives for understanding historical developments in mathematics.

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Notes

  1. 1.

    I have borrowed and translated the term “a multiple perspective approach” from the historian Bernard Eric Jensen’s term “en flerperspektivist tilgang” from his book “historie—livsverden og fag” (History—lifeworld and discipline), Jensen (2003). I have also discussed this in Kjeldsen (2009, 2012).

  2. 2.

    The conference took place in Salvador, Brazil in October 2017, http://www.philmathpractice.org/2016/06/11/fourth-meeting-of-the-apmp-october-23-27-2017-salvador-da-bahia-brazil/

  3. 3.

    https://mathscinet.ams.org/msc/pdfs/classifications2010.pdf

  4. 4.

    Mathematical programming is dealing with finite dimensional optimization under inequality constraints.

  5. 5.

    The Russian mathematician and economist Leonid V. Kantorovich published the paper Mathematical Methods of Organizing and Planning Production containing similar ideas in 1939. For an English translation, see Kantorovich (1960). See also Leifman (1990).

  6. 6.

    von Neumann (1928, p. 295).

  7. 7.

    von Neumann (1928, p. 295, note 2).

  8. 8.

    For an analysis of von Neumann’s work and encounter with the minimax theorem in different contexts, see Kjeldsen (2001).

  9. 9.

    Heims (1980, p. 91).

  10. 10.

    von Neumann (1937). An English translation was published in 1945 under the title “Model of General economic equilibrium.”

  11. 11.

    See Kuhn and Tucker (1958, p. 116) and Rellstab (1992, p. 87). For an analysis of Ville’s proof, see Kjeldsen (2001).

  12. 12.

    von Neumann and Fréchet (1953, pp. 124–125).

  13. 13.

    See Kjeldsen (2000).

  14. 14.

    See Kjeldsen and Blomhøj (2013) and Kjeldsen (2017) where Rashevsky’s early work on cell division is discussed in relation to its value for teaching students to reflect upon mathematical modeling and the modeling process.

  15. 15.

    For Rashevsky’s career at the University of Chicago and his relationship with the Rockefeller Foundation, see Abraham (2004). For a scientific biography of Rashevsky, see Shmailov (2016).

  16. 16.

    The Rockefeller Foundation, President’s Review and Annual Report, 1958.

  17. 17.

    In her book Making Sense of Life, Evelyne Fox Keller (2002, p. 96) evaluated this to be one of the major problems, “a clash in scientific culture” between Rashevsky and the biologists.

  18. 18.

    See also Rau (1999).

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  1. Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

    Tinne Hoff Kjeldsen

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  1. Department of Mathematics, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Gert Schubring

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Kjeldsen, T.H. (2019). A Multiple Perspective Approach to History of Mathematics: Mathematical Programming and Rashevsky’s Early Development of Mathematical Biology in the Twentieth Century. In: Schubring, G. (eds) Interfaces between Mathematical Practices and Mathematical Education. International Studies in the History of Mathematics and its Teaching. Springer, Cham. https://doi.org/10.1007/978-3-030-01617-3_6

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