Connecting Humans to Equations pp 137-149 | Cite as

# Beyond the Isolation of Mathematics

## 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.

## Keywords

Computer-based investigations in mathematics Costa’s minimal surface Differential equation Euclid’s*Elements*Four colour theorem Fourier transformations Intertwined Mechanical worldview Wavelet

## References

- Appel, K., & Haken, W. (1976). Every planar map is four colorable.
*Bulletin of the American Mathematical Society, 82*, 711–712.CrossRefGoogle Scholar - Fourier, J. (2009).
*The analytical theory of heat*. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar - Gibbons, M., et al. (1994).
*The new production of knowledge: The dynamics of science and research in contemporary societies*. London, UK: Sage Publications.Google Scholar - Hoffman, D. (1987). The computer-aided discovery of new embedded minimal surfaces.
*The Mathematical Intelligencer, 9*(3), 8–21.CrossRefGoogle Scholar - Lakatos, I. (1976).
*Proofs and refutations*. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar - Newton, I. (1999).
*The principia: Mathematical principles of natural philosophy*. Berkeley, CA: University of California Press.Google Scholar - Prigogine, I., & Stengers, I. (1984).
*Order out of chaos: Man’s new dialogue with nature*. Toronto, Canada: Bantam Books.Google Scholar - Tymoczko, T. (1979). The four-color problem and its philosophical significance.
*The Journal of Philosophy, 76*(2), 57–83.CrossRefGoogle Scholar - Tymoczko, T. (Ed.). (1986).
*New directions in the philosophy of mathematics*. Boston, MA: Birkhäuser.Google Scholar - Wolfram, S. (2011). Costa minimal surface. Retrieved from http://mathworld.wolfram.com/LagrangesEquation.html