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From the War Against Errors to Mathematics After the War: Public Discourses on a New Mathematical Dictionary

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Mathematical Communities in the Reconstruction After the Great War 1918–1928

Part of the book series: Trends in the History of Science ((TRENDSHISTORYSCIENCE))

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Abstract

In 1917 George Abram Miller proposed to the Mathematical Association of America (MAA) the creation and publication of a mathematical dictionary. By then, American mathematics had a history of contributions to celebrate and important prospects for the future on the national scale and beyond, though critical infrastructural aspects were lacking. Although the project was never realized, the context and discussions surrounding it highlight not only calls to “warfare against mathematical errors” but the nationalism underlying the desire of key MAA members to serve the development of mathematics, bolster research activity, and transfer aspects of the “apparatus of research” to American soil.

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Notes

  1. 1.

    The MAA was to function alongside the AMS, devoting itself to the pedagogical discussions and activities its sister organization largely eschewed (Parshall 2015). Its mission “to assist in promoting the interests of mathematics in America, especially in the collegiate field” (Cairns 1916) resonated with a broad class of professionals, including instructors at universities, colleges, normal schools, and high schools; engineers; and actuaries (Mathematical Association of America 1916).

  2. 2.

    In the preface to the volume the editors objected to existing dictionaries of suitable size “arising from their price, but more especially from their want of delicacy, and chastity of language”; see Steger (1913).

  3. 3.

    While Webster’s proposal for a “Nue Merrykin Dikshunary” was mocked by many of his contemporaries (Lepore 2006), its nationalistic undertones and Johnson and Elliott’s belief in the necessity of creating a volume sensitive to the American sense of decorum underscore the critical role of the nation in shaping the content and form of popular works of reference in America already at this early stage.

  4. 4.

    The publishers indicated in an advertisement that the editors attempted to retain the essential features of the German edition, but the presentation accounted for “des traditions et des habitudes françaises”.

  5. 5.

    These included Charles Hutton’s Mathematical and Philosophical Dictionary (1795) and Philosophical and Mathematical Dictionary (1815) and Peter Barlow’s New Mathematical and Philosophical Dictionary (1814). Both Hutton and Barlow were English.

  6. 6.

    Davies and Peck’s Mathematical Dictionary and Cyclopedia of Mathematical Science, for instance, appeared in 1855.

  7. 7.

    Somewhat ironically, not all of Miller’s criticisms passed muster. Louis Karpinski (1878–1956) would find it “unfortunate, in view of the general worthlessness of the historical passages [cited in Miller (1911a)], that Professor Miller has incidentally chosen for criticism one of the few correct statements” concerning the origins of the decimal system; see Karpinski (1912).

  8. 8.

    This is very similar to a statement made in Collins (1910) in the same journal one year prior.

  9. 9.

    In spite of the generally positive reception of the dictionary project, to be discussed in what follows, not all of Miller’s contemporaries viewed his criticism of scholarly sources favourably, and some seem to have privately questioned his position to criticize in the first place. In this vein, the author would like to thank Frédéric Brechenmacher for drawing attention to unpublished letters between David Eugene Smith and James McKeen Cattell dated 7, 13, and 16 November 1925 located in the David Eugene Smith professional papers collection at Columbia University. Such opinions did not appear to affect the public discourse on the subject.

  10. 10.

    In response, Parshall (2017) has raised the questions of exactly what it is and how it is measured.

  11. 11.

    One sees an affirmation of this sentiment elsewhere; in the words of Dauben (1977), “Mathematicians in America could blame their lack of status on apathy and indifference” during the late nineteenth century.

  12. 12.

    As pointed out in Siegmund-Schultze (1997), this was never realized.

  13. 13.

    Collins admonished the “pomposity and verbosity” of Webster’s definition of number and the definition of a perpendicular in terms of a right angle and a right angle in terms of a perpendicular. “If a pupil in a geometry class were to do this”, he pointed out, “the teacher, metaphorically at least, would box his ears”.

  14. 14.

    Karpinski, for instance, spurred in part by Miller (1911a), pointed to a number of historical errors in the Encyclopaedia Britannica, remarking that certain articles “contain so many inaccuracies and so much misinformation that selection becomes difficult” (Karpinski 1912).

  15. 15.

    For further debate of this issue, see Rothrock (1918) and Jourdain (1919).

  16. 16.

    By 1922 the figure had risen to $100,000 “or of $20,000 per year for five years”; see Slaught (1922).

  17. 17.

    The NRC was fairly new at that time; see Archibald et al. (2014).

  18. 18.

    This metaphor also took root in other sciences. In a 1908 lecture to the Scientific Society of the University of Colorado Professor Theodore Dru Alison Cockerell (1866–1948) claimed that the growth of science made specialization necessary and desirable, yet “as time went on and zoology not only grew apart from botany, but the various branches of zoology seemed to have different languages, it appeared as if a tower of Babel would result.” (Cockerell 1908). See, too, the remarks of Henry Bower (1833–1896), a pioneer of the Philadelphia chemical industry and member of the American Chemical Society (Bower 1893).

  19. 19.

    These include The Mathematical Correspondent, published from 1804 to 1806, and the ill-fated New York Mathematical Society, founded in 1817, as well as The Analyst or Mathematical Museum, The Mathematical Diary (Parshall and Rowe 1994), and The Mathematical Miscellany (Kent 2008).

  20. 20.

    On the distinction between images and identities of mathematics, see Turner (2012).

  21. 21.

    Siegmund-Schultze (1997) has described how “a growing independence from Europe in research” and a “need to gain independence with respect to the publication system as well” in America were accompanied by “nationalistic emotions”.

  22. 22.

    While the members represented disciplines ranging from Latin to political science to entomology to dentistry, Hedrick was among their ranks (American Association of University Professors 1918).

  23. 23.

    This seems to have been the same body as the Committee on Apparatus for Productive Scholarship, which was also referred to as the Committee on the Apparatus of Scholarship; see Teggart (1919).

  24. 24.

    These included the presentation, discussion, and publication of papers stimulating general mathematical interest and “professional esprit de corps” or the planning or reworking of instructional courses, and investigations and reports of committees including “the Committee on Mathematical Dictionary which desires to see in the hands of every teacher and student of mathematics a source of information giving in clear, compact, and scientific form an explanatory definition of every mathematical term which is likely to be found in their reading or study” (Slaught 1920).

  25. 25.

    The Carus Monographs were published under the auspices of the MAA through a gift to the Association by Mary Hegeler Carus in the amount of $1,500, and the support to increase the Annals from 200 to 300 pages annually (Parshall 2015) totaled between $100 and $375 annually. The Chauvenet Prize for Mathematical Exposition was less demanding still. Sanctioned by the Trustees in 1925, it was to be awarded every five years at an amount of $100 (Mathematical Association of America 1925).

  26. 26.

    See, for instance (Cairns 1918, 1921). In 1921 the Association had “just been able to match expenditures with income” Cairns (1922). The following two years saw slightly better reports.

  27. 27.

    Miller, whose yearly salary never totaled more than $6,000, had been quietly investing large portions of his earnings in stocks and bonds. He died a millionaire in 1951, bequeathing his riches to the University of Illinois, leading one to wonder why he did not sponsor his pet project. By the estimate of one friend and financial advisor, however, his net worth upon retirement in 1932 was $25,000. The reasons for which he did not make smaller contributions are yet unclear, but his attorney later indicated that Miller wanted to ensure his wife (whom he believed would outlive him) wanted for nothing after he passed (Fay 1951). It is also possible that by the time he had amassed a reasonable sum the momentum of the project had petered out, or that he began to question the feasibility of the undertaking.

  28. 28.

    Woodward was also the AMS President from 1898–1900 and the AAAS President immediately thereafter.

  29. 29.

    Cattell (1927) indicated that the MacMillan Company was poised to undertake the publication 20 years prior, but balked at the proposed structure, preferring a standard 10-volume series arranged alphabetically.

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  1. Monmouth University (USA), West Long Branch, NJ, USA

    Laura E. Turner

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  1. Sorbonne Université, LPSM, CNRS, UMR 8001, Paris, France

    Laurent Mazliak

  2. Université de Lille CNRS, UMR 8524, Laboratoire Paul Painlevé, Villeneuve d’Ascq, France

    Rossana Tazzioli

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Turner, L.E. (2021). From the War Against Errors to Mathematics After the War: Public Discourses on a New Mathematical Dictionary. In: Mazliak, L., Tazzioli, R. (eds) Mathematical Communities in the Reconstruction After the Great War 1918–1928. Trends in the History of Science. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-61683-0_5

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