The Mathematical and the Mythical:
A Phenomenological Exploration
Delhi School of Economics, New Delhi
In this paper I want to highlight and delineate the presence of the mythical in the mathematical discourse through the technique of phenomenological description pioneered, amongst others, by the French Phenomenologist Maurice Merleau Ponty. Using Merleau Ponty’s cue that, “Rationality is precisely proportioned to the experiences in which it is disclosed”, I want to demonstrate how the mythical keeps surfacing in the mathematical discourse, suggesting that these two registers often overlap and protrude into each other as against their commonly perceived exclusiveness (Merleau Ponty 2007: 67). The myths I have chosen are the Amerindian myths analysed by Claude Levi Strauss dealing with the origin of societies and hence with the transition from the confused (nature) to the discrete (culture). I have tried to describe in this paper how the themes related to these origin myths emerged in the classroom discourse when the all the important mathematical distinction between density and continuity was introduced to the students by the teacher during a lecture on partial derivatives as part of the course on advanced calculus. One would note that this distinction between density and continuity which is so important for mathematics has no meaning phenomenologically. This point has been well argued by Franz Brentano (considered as a major influence on Husserl) in his essay ‘On what is Continuous’ (Brentano 1988: 1-45). I would show through my description that how this tension between the mathematical mode of thinking and the phenomenological one, brought to the fore the aforementioned mythical themes in the on-going classroom discussion.
My argument is based on the fieldwork I conducted in two colleges of University of Delhi for almost a period of three months from June to September, 2015. To substantiate the overriding concern of this paper I’ll also add to the ethnographic narrative inputs drawn from the interviews of mathematicians I took at ISI Delhi, HRI Allahabad and IIT Delhi, conducted at various points in the period between July to December 2015 as well as the few classes I attended at HRI Allahabad as part of the Summer Programme in Mathematics held between, 8th to 26th June 2015. I hope this description, offered here as a mode of argument, would also help me in weakening the problem; what does one do when one does mathematics? To be sure there are and there have been numerous responses to this question all seeking to underline the essence of mathematical practice in one way or the other. To be precise these answers refer not to the nature of mathematical practice as such but to the attributes of mathematical objects like, lines, numbers, sets, etc. Practice, if at all it is dealt with, is seen as a murky space through which one has to steer her way to witness the incontestable truths of the subject. Even if practice is given a more benign treatment, the matter is left in the lurch by declaring to the nth degree that mathematical truths, like all others, are performative. Well the answer not only strikes one as repetitive but also fails to provide any understanding of what it seeks to describe!
Here I seek, less to answer the question for good but to beseech various responses from the field in order to tease out the many dimensions of the problem itself. In doing so, ethnography remains for me a particular mode of reflecting on the manner in which a problem rather than being a self-contained whole becomes problematising in all its respects. Lastly, an attempt will also be made in this paper to demonstrate the affinities between Levi Strauss’s structural analysis of myths and phenomenology, two intellectual approaches which are commonly perceived as being radically different from each other.