How has one, and How could have one approached the diversity of mathematical cultures?

Abstract

This contribution argues that history of mathematics should take as its object not only knowledge, but also ways of doing mathematics that are collectively shared (what I call “mathematical cultures”), and additionally the connections between the two. I provide evidence showing that there is a history of ways of doing mathematics, and this history suggests that mathematical knowledge takes shape at the same time as practices do. Indeed, ways of doing mathematics do not fall out of the sky. They are shaped and transformed by actors in the process of working out some problems and addressing some issues. They represent one of the outcomes of mathematical research. I further argue that attending to the mathematical culture in the context of which actors worked is essential for interpreting their writings.