Beyond the Isolation of Mathematics
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.
KeywordsComputer-based investigations in mathematics Costa’s minimal surface Differential equation Euclid’s Elements Four colour theorem Fourier transformations Intertwined Mechanical worldview Wavelet
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