Abstract
This book argues that we can only understand the transformations of nature studies in the early modern period, often called the Scientific Revolution, if we take seriously the interaction between those who know by doing (practitioners or craftsmen) and those who know by thinking (scholars or philosophers). Mathematical practitioners played an essential role in this transformation; this book examines the role of mathematics and mathematical practice on the changing ideology and methodology of science. We first set out the problematic, examining the argument from both sides: articulating Zilsel, Cormack identifies those dimensions of practical mathematics that showed up as important aspects of ‘the new science’; Schuster focuses on the new scientists as selective appropriators of ideas, values and practices originally embedded in practical mathematics. This book furthers the debate about the role of mathematical practice in the scientific revolution in four ways. First, it demonstrates the variability of practical mathematicians and of their practices. Second, it argues that in spite of this variability, participants were able to recognize the family resemblance between the different types. Third, differences and nuances in practical mathematics typically depended on the different contexts in which it was practiced. Fourth, this book shows that diverse and new historiographical approaches to the study of practical mathematics should be considered.
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Notes
- 1.
Alexandre Koyré, From a Closed World to an Infinite Universe (Baltimore: Johns Hopkins University Press, 1957).
- 2.
Geoffrey Gorham and Benjamin Hill (eds.), The Language of Nature: Reassessing the Mathematization of Natural Philosophy (Minneapolis: University of Minnesota Press, 2015) provides an interesting philosophical discussion of this issue. See also Lesley B. Cormack, “The Grounde of Artes: Robert Recorde and the Role of the Muscovy Company in the English Mathematical Renaissance,” Proceedings of the Canadian Society for the History and Philosophy of Mathematics 16 (2003): 132–138.
- 3.
E.G.R. Taylor, The Mathematical Practitioners of Tudor and Stuart England (Cambridge, Cambridge University Press, 1954). Taylor completed a second volume, Mathematical Practitioners of Hanoverian England, 1714–1840 (Cambridge: Cambridge University Press, 1966), published just after her death, and bringing the number of mathematical practitioners she identified to 2500.
- 4.
Katherine Neal, “The Rhetoric of Utility: Avoiding Occult Associations for Mathematics through Profitability and Pleasure,” History of Science 37 (1999): 151–178 discusses some attempts to make mathematics appear useful.
- 5.
Thomas Hood’s lecture, A Copie of the Speache made by the Mathematicall Lecturer, unto the Worshipfull Companye present . . . in Gracious Street: the 4 of November 1588 (n.p. 1588) is a good example. See Deborah Harkness, The Jewel House. Elizabethan London and the Scientific Revolution (New Haven: Yale University Press, 2007) for a discussion of the complex interactions among London merchants, artisans and scholars.
- 6.
Of course, once Galileo successfully gained a patronage position, particularly with the Florentine Medici court, he left his mathematical practitioner roots behind and became a much higher status natural philosopher. Mario Biagioli, Galileo, Courtier: The Practice of Science in the Culture of Absolutism. (Chicago: University of Chicago Press, 1993). Matteo Valeriani, Galileo Engineer (Dordrecht: Springer, 2010).
- 7.
Mario Biagioli, “The Social Status of Italian Mathematicians, 1450–1600,” History of Science 27 (1989): 41–95, and his Galileo Courtier (n.6, above).
- 8.
Stephen Johnston, Making Mathematical Practice: Gentlemen, practitioners and artisans in Elizabethan England, PhD dissertation, Cambridge University, 1994, and “Mathematical Practitioners and Instruments in Elizabethan England,” Annals of Science 48.4 (1991): 319–44.
- 9.
James A. Bennett, “The Mechanics’ Philosophy and the Mechanical Philosophy,” History of Science 24 (1986): 1–28, and “The Challenge of Practical Mathematics,” pp. 176–190 in S. Pumfrey, P.L. Rossi and M. Slawinski (eds.), Science, Culture and Popular Belief in Renaissance Europe (Manchester: Manchester University Press, 1991).
- 10.
Peter Dear, Discipline and Experience: The Mathematical Way in the Scientific Revolution (Chicago: University of Chicago Press, 1995). See Schuster, Chap. 3, for a critique of Dear’s argument.
- 11.
Eric Ash (ed.), Expertise: Practical Knowledge and the Early Modern State, Osiris 25 (2010); Power, Knowledge and Expertise in Elizabethan England (Baltimore: Johns Hopkins University Press, 2004).
- 12.
In certain ways, this approach was long ago championed by Edwin T. Layton, “Mirror-Image Twins: The Communities of Science and Technology in Nineteenth-Century America,” Technology & Culture 12 (1971): 562–580.
- 13.
Harkness, The Jewel House (n.5, above).
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Cormack, L.B. (2017). Introduction: Practical Mathematics, Practical Mathematicians, and the Case for Transforming the Study of Nature. In: Cormack, L., Walton, S., Schuster, J. (eds) Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe. Studies in History and Philosophy of Science, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-319-49430-2_1
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