Accueil > Archives > Ancients projets de recherche > Anthropologie des mathématiques > Version anglaise > Our project > Introduction

## Introduction

This is a translation of the “official” project, that we wrote last year, and which enabled us to get the money.

I think that Eric and me have some what advanced from here, since.

How is it recognized that an activity is "mathematical" when it is not identified as such by those who practise it ? What criteria should we use ? We also want to understand how does a mathematical activity becomes a "knowledge".

When does mathematics become a field of specialised knowledge ? How is erudite mathematics worked out ?

Our aim is thsu to link the two different trends that the word ethnomathematics contains : a mathematical point of view on objects we deem mathematical, and the study of mathematica activities before they are recongized as « knowledge » by institutions. In all cases our focus in also on using sound antropological methods.

As a group we are currently funded on a three year project by the french minsitry of research. You can find bellow, the texts of projects for which we have sought funding, this will give you an idea of our working philosophy.

### B - Description of the Project

B1 – Aims and context

We are used to think of mathematics as an intellectual and scholarly activity practiced within institutions. This is probably why so little research has been produced in the field of ethnomathematics, especially in France. Our project would like to overcome our ignorance in this field by creating a group involving anthropologists, mathematicians, historians and historians of mathematics to explore mathematical practices observed outside of the field of scholarly and institutional activity, and outside of the much studied territories of Europe and the United States. We intend to do field work on specific localized territories, with well defined themes.

B2 – Description of the project

Indeed, our proposal involves the study of mathematical activities in New Guinea, Arctic and India. These activities (cat’s cradles, mathematical riddles…) represent aspects of mathematical activities that are not written down, but transmitted orally or with body language.

The identification of such activities as being mathematical is of course at the source of our investigation. Indeed, when activities are not identified as such by those who practice them – which is the case with cat’s cradles in New Guinea and in Arctic- how do we recognize them as belonging to the field of mathematics ? What criteria should we apply ?

These fundamental questions have seldom been probed into until now. Let us mention the work of Marcia Ascher, whose first book [Ascher 1991] was translated in French by Karine Chemla and Serge Pahaut (see also the postface which discusses these questions in the French version, pp. 259-278). Marcia Ascher suggest a methodological approach which enables the study of activities that seem mathematical (drawings on the sand, orientations, games, geometrical patterns in house hold decorations) by a structural analysis of these activities, rewritten in our own symbolical language. This work, according to Marcia Ascher, can help us understand the structures of these activities and reveal their mathematical character.

On the other hand, ethnolinguists and ethnomusicologists have been for several years thinking on the possibilities of developing a multi-disciplinary research on similar terms. Certain ethnomusicologists such as Simha Arom have questions similar to ours : identifying, studying and defining a musical system also raises questions of criterias. Linguists and ethnolinguists have the same problem. A colaboration with researchers of these disciplines, used to such trans-disciplinary work might enable us to dynamise our research.

This is why wee have seaked the collaboration of Frank Alvarez-Pereyre (linguist and ethnologist, Research Director in the Language-Music-Societies laboratory of the CNRS), who has been concentrating on multidisciplinary projects ( [Alvarez-Pereyre, Frank 2003].) [2]

We will also focus on the circulations between activities considered as mathematical by those who practice them and the literary corpus of scholarly mathematics. Some of the activities practiced today have a long hisstory. To study them offers precious openings with the History of Mathematics. For instance, mathematical riddles practiced today in “illiterate” villages of Tamil Nadu, in South India, can be also found in XVIIth century scholarly texts. What then was the link between mathematical activities practiced in day day to life and scholarly mathematics ?

Our research would thus investigate localized field work how does mathematics become a form of “knowledge” ? How does it become a scholarly knowledge ? How does it interact with activities that aren’t part of the scholarly realm ? This is a reflexion on the nature of mathematics, between knowledge and activity, that we intend to explore by confronting anthropological, historical and mathematical approaches.

Our project is modest and small, because little attention has been devoted to ethnomathematics in France. We will concentrate on two fields of research. One will concern string games in Arctic and in New Guinea, the other on mathematical activities in Tamil Nadu. These field works will be associated with a research seminar which will last the three years of the project and which will lead to the interaction between members of anthropological laboratories with historians of science and mathematicians. Bibliographical seminar the first year, with guests the second year (we thus hope to invite Marcia Ascher if we can), the last year will be devoted to research discussions, ending in a common publication. We hope to arise the curiosity of anthropologists in mathematical activities and reciprocally we hope that we can invite historians of mathematics to think of the larger context in which the texts and the disciplines they work on arose and developed.

We have contacted several documentary makers. We hope to elaborate with them a project which will enable us to produce radio and movie documentaries. The aim will be to give to a large public a new vision of mathematics, with a more “play-like” atmosphere to it.