Mathematics and Culture

March 6, 2009

This post  is actually a slightly revised version of a short article written years ago.  It originally appeared on the Vanier College  Mathematics Department website.  Its purpose was polemical. I include it here because it is, in some sense, complementary to the previous post.

A somewhat prevalent image of mathematics relates it to calculation and situates it against a purely empirical background. There is a certain orthodoxy dominant in some academic circles,  an orthodoxy which insists that mathematical conceptualization must be linked uniquely to modeling  and problem solving.  But this orthodoxy, by placing maximum value on performance with respect to technology and economics, itself confirms the hypothesis that mathematics is deeply linked to culture  and that this link cannot be considered in isolation from the factors which determine the evolution of thought in general.

It is undoubtedly possible to anchor the point of view which places prime importance on the integration of mathematics into general culture by going back to Pythagoras to demonstrate how mathematics was once long ago a vibrant part of an inclusive world view.  It is also commonplace to underline the importance of Descartes in the articulation of  the fundamental relation between mathematics and the rationalism which many see as the defining property of Western civilization.  Philosophers also understand how Leibniz’s thought was integrated into a complex philosophical system which has a significance rarely captured by cute biographical notes found in collegiate level mathematical textbooks.  These three well-known examples indicate that it is possible to believe that mathematics could be related to world view and not simply confined (as it often is now) to a narrowly defined realm of  “mathematical science”.

There is also a relation between mathematics and certain types of  literature.  The mathematical appropriation of Pascal often ignores that he is equally the author of Les Pensées. Yet writers such as Borges and M. Serres have led us to re-think Pascal in a way that emphasizes the practice of metaphorization based on mathematics.  For example, Pascal resurrected the ancient metaphor of God as a sphere whose center is everywhere but whose circumference is nowhere.  M. Serres has shown the exact manner in which this metaphor is incorporated into the logical structure of Pascal’s writings.  Borges, whose literary universe is in part structured around a constellation of these kinds of  “metaphors”, conjectures that universal history may perhaps be conceived as a juxtaposition of metaphors whose natures  resemble that of the “frightful sphere of Pascal”.   In a more contemporary example , the reading of  Gravity’s Rainbow demands a certain familiarity with a number of mathematical concepts which are integrated into the text as metaphors and assumed to be recognized as common culture by the reader.  Pynchon’s Mason and Dixon is even more demanding in terms of  what it assumes in terms of the knowledge of mathematical ideas.

Post-modernism has also incorporated (sometimes poorly as in the case of Jean-François Lyotard) mathematical conceptualization in its preferred topoi. Catastrophe theory and fractal geometry have already been interpreted as fundamental structural models with the same reverence  that older generations of scholars reserved for the supposed purity of Euclidean geometry.  Post-modernism has also led us to re-think mathematics in terms of the relation of logic and rhetoric, thus causing a certain unhappiness among practitioners of mathematics who feel uncomfortable with the idea that their “science” could have a strong rhetorical component.

It would then be futile to ignore the complex relations that mathematics has with “non-scientific” disciplines.  To do so would not only deny the evolution of general culture, but also reduce mathematical thought to a commodity status in which knowledge of techniques and algorithms would be brokered like any other consumer good.  The foundation for the authentic reception and appropriation of mathematics obviously begins with those of us who teach the basics of the discipline.