The Diversity of Mathematical Cultures: One Past and Some Possible Futures

[摘要] For a long time now, as a historian as well as an observerof contemporary mathematical practices, I have beenstruck by the diversity of ways of doing mathematics. I am not speaking here of the variety of individual styles, which has already been the subject of manyworks, but rather the diversity of collectively sharedways of practising mathematics. I feel this phenomenondeserves more attention than it has received to date. Inthis article, I would like to explain some of the reasonsthat convince me of the value that could be representedby the description of these social and cultural realities– realities that it seems to me appropriate to understand as different “mathematical cultures”. I have hadthe opportunity to clarify, with the help of an exampledeveloped at length, what I mean by this last expression[1] and I will return to this question below. However,before I go any further, I must rule out one possiblesource of misunderstanding. While I propose speakingabout ‘mathematical cultures’, this is totally unrelatedto another, all-too-common interpretation of the sameexpression that seems to me meaningless and, what ismore, dangerous.