## Samenvatting

A major issue in the field of the philosophy of mathematical practices is to better understand how far mathematical practices are related to the cultural contexts within which they are developed. In this paper, we bring together two complementary directions of research to tackle this issue. First, we show how Wittgenstein’s philosophy affords conceptual tools to discuss the possibility of simultaneous existence of culturally different mathematical practices. Wittgenstein abandons the essentialist concept of language and therefore denies the existence of a universal language. Languages—or ‘language games’ as Wittgenstein calls them—immerse in a form of life, in a cultural or social formation and are embedded in a totality of communal activities. This idea gave rise to the notion of understanding rationality as an invention or as a construct that emerges in specific local contexts. Relaying on the later work of Wittgenstein and his concept of ‘family resemblance’ (Familienähnlichkeit), we will give meaning to the existence of different kinds of mathematical knowledge and the coexistence of ethnomathematical practices.

Throughout the last decades, many activities practiced in non-western cultures (and in societies with an oral tradition in particular) have been analyzed by ethnomathematicians as related to mathematics. These activities still need to be further compared to one another, in an attempt to bring to light invariant and distinguishing features from one cultural context to another, and in order to better characterize mathematical practices (including Western ones) in sociological and epistemological terms. In that perspective, we draw on recent studies in ethnomathematics—integrating anthropological approaches and using ethnographical methods—which analyze data about ‘geometrical’ activities involved in the creation of artefacts (such as string figures, sand drawings, textile production…). These studies contribute to reaching a better understanding of the cognitive acts that underlie these activities, as well as the ways they are embedded into a cultural environment. We suggest that these works in ethnomathematics afford both new materials and fundamental outcomes worth analyzing in a comparative way to reflect on the forms of interrelations between mathematics and cultures.

Throughout the last decades, many activities practiced in non-western cultures (and in societies with an oral tradition in particular) have been analyzed by ethnomathematicians as related to mathematics. These activities still need to be further compared to one another, in an attempt to bring to light invariant and distinguishing features from one cultural context to another, and in order to better characterize mathematical practices (including Western ones) in sociological and epistemological terms. In that perspective, we draw on recent studies in ethnomathematics—integrating anthropological approaches and using ethnographical methods—which analyze data about ‘geometrical’ activities involved in the creation of artefacts (such as string figures, sand drawings, textile production…). These studies contribute to reaching a better understanding of the cognitive acts that underlie these activities, as well as the ways they are embedded into a cultural environment. We suggest that these works in ethnomathematics afford both new materials and fundamental outcomes worth analyzing in a comparative way to reflect on the forms of interrelations between mathematics and cultures.

Originele taal-2 | English |
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Titel | Conference Cultures of Mathematics IV |

Plaats van productie | New Delhi |

Status | Published - 2015 |

Evenement | Conference Cultures of Mathematics IV - Indian National Science Academy (INSA), New Delhi, India Duur: 22 mrt 2015 → 25 mrt 2015 |

### Conference

Conference | Conference Cultures of Mathematics IV |
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Land/Regio | India |

Stad | New Delhi |

Periode | 22/03/15 → 25/03/15 |

### Bibliografische nota

Cultures of Mathematics IV22-25 March 2015

New Delhi, India

http://www.math.uni-hamburg.de/spag/ml/Delhi2015/

Keynote speakers.

Tom Archibald (Simon Fraser University, Vancouver BC, Canada) Jessica Carter (University of Southern Denmark, Odense, Denmark) JosÃ© Ferreiros(Universidad de Sevilla, Seville, Spain) Karen FranÃ§ois (Vrije Universiteit Brussel, Brussels, Belgium) Albrecht Heeffer (Universiteit Gent, Gent, Belgium) Matthew Inglis (Loughborough University, Loughborough, England) Brendan Larvor (University of Hertfordshire, Hatfield, England) Madeline Muntersbjorn (University of Toledo, Toledo OH, U.S.A.) Alison Pease (Imperial College, London, England) Emil Simeonov (Fachhochschule Technikum Wien, Vienna, Austria) Keith Weber (Rutgers University, Piscataway NJ, U.S.A.)

A research community that could be described with the phrase "Practice and Cultures of Mathematics" has studied mathematics as a human subject with different practices and cultures in recent years. This research has been closely linked to the Philosophy of Mathematical Practice community and its Association for the Philosophy of Mathematical Practice, but is broader in the sense that it is interested in the study of mathematical practices and cultures independently of whether there is an interaction with traditional philosophical questions (such as epistemology or ontology).