Just as people tend to follow particular trends in the way they dress, Professor Rabouin puts forth the idea that mathematicians too adopt “theories”, “concepts” and “objects” that are in trend or in circulation. However, unlike fashion trends, these “theories” and “concepts” seem to show signs of stability: they cannot be wiped out like a fashion trend. We know that 11th standard CBSE maths textbooks continue to describe parabolas as Descartes first did while there are other ways to do so. The question that becomes important at this juncture is why Descartes’ “mechanical” method still persists.
More pointedly, mathematical “concepts” and “theories” seem to stabilize over time despite being interpreted or given new meanings. Historians of science, in particular those focused on mathematics, seem to describe mathematical activity as the circulation of “concepts” and “theories” across “national cultures”, specific “schools” of thought, or more generally, across different contexts. How do they then maintain the epistemic integrity of the “concepts” and “theories” they describe across different contexts? In other words, how would they know whether these epistemic entities are being interpreted or given the same “meaning” across different contexts?
The description of mathematical activity, unlike other sciences, lacks the material surroundings of, say, physical instruments, or any sort of experimental setup. According to Rabouin, the analysis of “styles” may provide a solution to this problem as well as to problems related to epistemic integrity. Mathematical activity can then be seen as a “way of writing.” He goes on to describe how “styles of writing” can be relatively independent from the different contexts in which they are used, and how they can possibly have more epistemic significance than the “mathematical concepts” themselves. Especially since, according to Rabouin, it is the way of writing that is stable, while the variable element is the understanding of the “concept.” In other words, the concept itself may change, but the way it is spoken about remains fixed. That said, Rabouin does not do away with “concepts” or epistemic entities completely. The Professor concludes by describing the cognitive value of styles of writing, which is tied to the notion of “material anchors” as first propounded by Edwin Hutchins.