Abstract
This chapter considers what it means if one move beyond the thesis of isolation, which assumes that mathematics operates and develops according to its own intrinsic priorities. In general, it is important to considered to what extent mathematics becomes formed through worldviews, metaphysical assumptions, ideologies, political priorities, economic conditions and technologies. The chapter addresses such social structurings of mathematics, and concentrates on metaphysics, technology and the market.
First, it is exemplified how general worldviews can shape mathematics. It becomes illustrated how mathematical disciplines become structured by contemporary ideas and social trends. This is exemplified with reference the change in priorities with respect to research in differential equations, which in turn reflects the rise and fall of the mechanical worldview. Second, the importance of technological tools for the development of mathematics becomes addressed. In particular, it becomes illustrated how the computer is shaping mathematics: not only by changing features of the mathematical research practice, but also by changing conceptions of what counts as a mathematical proof. Finally, the chapter considers the commodification of knowledge that has taken place and the impact this has on the formation of mathematics. In brief, one finds market values in the shaping of mathematical research priorities. These observations all challenge the thesis of isolation.
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Notes
- 1.
See Chapter 1, for a presentation of Euclid’s axiomatics.
- 2.
It should be noted be noted that in Principia, Newton did not use any differential calculus in order to present his mechanical interpretation of nature. The use of differential calculus, however, was the next consequential step in the development of the insight presented in Principia.
- 3.
Source: MathSciNets database (Full search+Review Text). American Mathematical Society (2009).
- 4.
For more abort minimal surfaces, see, for instance, Wolfram (2011).
- 5.
However, it is no easy matter to go through the original proof presented by Appel and Haken, an outline of more than 700 pages containing the details of the proof.
- 6.
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Ravn, O., Skovsmose, O. (2019). Beyond the Isolation of Mathematics. In: Connecting Humans to Equations . History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-01337-0_10
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DOI: https://doi.org/10.1007/978-3-030-01337-0_10
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