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Grattan-Guinness’s work on classical mechanics

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Research in History and Philosophy of Mathematics

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Abstract

Throughout a career spanning nearly half a century Grattan-Guinness evinced an interest in nearly everything in the universe that had even the remotest connection with mathematics: philosophy (especially epistemology), logic, physics, religion, music, art, education, economics, psychology, and much more. Although it could be said that his strongest area was logic and its history, his contributions to our understanding of the history of classical physics are a recurring theme. His earliest publication (Lanczos, J Frankl Inst 292(4):308, 1966) was a review of a book on Fourier series. It was followed a few years later by a longer paper (Grattan-Guinness, J Inst Math Appl 5:230–253, 1969) on the general impact of Fourier’s work, and the next year by a short paper (Grattan-Guinness, Oper Res Q 21:361–364, 1970) discussing Fourier’s possible anticipation of linear programming. Two years later came the magisterial monograph (Grattan-Guinness, Joseph Fourier, 1768–1830. A survey of his life and work, based on a critical edition of his monograph on the propagation of heat. MIT Press, Cambridge/London, 1972) on Fourier’s life and work, written jointly with J. R. Ravets, which established him as one of the leading lights among historians of mathematics. He devoted nearly a decade to Fourier, crowning the work with a final summary (Grattan-Guinness, Ann Sci 32:503–524, 1975) of what he had discovered. From this root, he branched out into a general study of nineteenth-century French mathematicians, culminating in 1990 with the publication of his definitive three-volume masterpiece (Grattan-Guinness, Convolutions in French Mathematics, 1800–1840: from the calculus and mechanics to mathematical analysis and mathematical physics. Vol. I. The settings, Science networks. Historical studies, vol 2, Birkhäuser Verlag, Basel, 1990a; Grattan-Guinness, Convolutions in French Mathematics, 1800–1840: from the calculus and mechanics to mathematical analysis and mathematical physics. Vol. II. The turns, Science networks. Historical studies, vol 2. Birkhäuser Verlag, Basel, 1990b; Grattan-Guinness, Convolutions in French Mathematics, 1800–1840: from the calculus and mechanics to mathematical analysis and mathematical physics. Vol. III. The data, Science networks. Historical studies, vol 2. Birkhäuser Verlag, Basel, 1990c). His interest in this area never left him, and the last of the 154 papers by him that were reviewed or indexed in Mathematical Reviews—117 were given full reviews and they amount to about 7000 pages of publication—was a review (Grattan-Guinness, Hist Math 42:223–229, 2015) of a book on a 19th-century French mathematical physicist (Coriolis), thereby putting a right book-end on the long shelf of his publications that matched the one on the left.

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Notes

  1. 1.

    The word play on groß and klein is purely coincidental.

  2. 2.

    In his 1968 book The Role of Mathematics in the Rise of Science (Princeton University Press), my adviser Salomon Bochner noted that Poisson might well have been the best French mathematician of the early nineteenth century, except that there was no edition of his collected works available to support that judgment. As I found when I visited the Institut Mittag-Leffler in 1981, Mittag-Leffler had attempted to assemble Poisson’s works in a number of volumes. I showed these to Pierre Dugac, who was also visiting there at the time. He looked them over and said, “Il y manque beaucoup.” I duly wrote to Bochner about this, but he unfortunately died a few months later, not having responded to my letter.

  3. 3.

    And perhaps after all the earlier debate over infinitesimals fits the same pattern. After Abraham Robinson’s work, it is now agreed that you may have infinitesimals or not. It’s a matter of taste, not a matter of being right or wrong.

  4. 4.

    This is the popular version of the aphorism, slightly misleading. Hilbert made the statement in an address to the Westphalian Mathematical Society in Münster on 5 June 1925, at a meeting dedicated to the memory of Weierstrass. After saying that Weierstrass had banished infinitesimals and the infinite number ∞ from analysis by defining these concepts in terms of finite quantities, he added that the problem of infinite collections remained, especially in set theory, where ordinal and cardinal numbers are actually rather than potentially infinite. Weierstrass had merely displaced the problem of the infinite one step farther away by talking about “every” ɛ > 0, thereby replacing the infinitesimal with an infinite collection of propositions. (Euclid did the same when he “defined” a ratio in Book V.) Hilbert proposed to solve that problem by defending set theory and the axiom of choice against the criticism of the intuitionists. To that end, he attempted to axiomatize it. In connection with those axioms, he listed two desiderata that were to be guiding principles. First, that the amazing results one can prove using set theory and the axiom of choice should be preserved. It was in that connection that he said the axioms should be so well formulated that “No one will be able to drive us from the paradise Cantor created for us.” (“Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben können.”) The second desideratum was that the system should be as transparent as elementary number theory, “which no one doubts and where contradictions and paradoxes arise only through our own carelessness.” That statement seems almost prophetic, considering what Gödel was to do with elementary number theory five years later. Hilbert’s address was reprinted as “Über das Unendliche” in Mathematische Annalen, 95 (1926), 161–190. See p. 170 for the quotations above.

  5. 5.

    Professor Ky Fan, who taught me linear algebra in 1961–62, alerted the class to this distinction when we discussed inner product spaces, saying that those who preferred the Spectral Theorem to the Jordan Canonical Form were probably inclined to be analysts, whereas those who had the opposite preference should probably specialize in algebra.

  6. 6.

    I have in mind particularly his tabloidization of the relationship between Kovalevskaya and Weierstrass and his outrageous dismissal of the work of Legendre on elliptic functions.

  7. 7.

    “…but I have to say, I found my true schoolmaster on the dust jacket of the treatise on algebra by M. Garnier. That dust jacket consisted of a single printed page on the outside of which a piece of blue paper had been stuck. Reading the side of the page that wasn’t covered inspired in me a curiosity to know what the blue paper was hiding from me. I steamed it off with great care and was able to read underneath it the following advice given by d’Alembert to a young man who was telling him about the trouble he was having in school. ‘Persevere, Sir, persevere, and faith will come to you.’ ” (François Arago, Histoire de ma jeunesse, in Œuvres Complètes, t. 1, p. iv.)

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  1. Department of Mathematics, University of Vermont, Burlington, VT, 05401, USA

    Roger Cooke

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  1. Roger Cooke
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Correspondence to Roger Cooke .

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  1. Mathematical Information and Computer Sciences, Point Loma Nazarene University, San Diego, California, USA

    Maria Zack

  2. Department of Philosophy, University of California, Davis, Davis, California, USA

    Elaine Landry

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Cooke, R. (2016). Grattan-Guinness’s work on classical mechanics. In: Zack, M., Landry, E. (eds) Research in History and Philosophy of Mathematics. Proceedings of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-46615-6_10

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