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Maybe because the title of the book this is a review of is “Reactionary Mathematics: A Genealogy of Purity”. This does not mean that coordinate free geometry i

• zozbot234 9mo ago
  > considering the coordinate system as spoiling the purity Isn't that one of the main arguments for "coordinate free" or "synthetic" anything? It's about a pursuit of elegance and increased generality, not necessarily of obnoxious real-world politics; so it seems especially weird to inherently conflate these things.
  • freehorse 9mo ago
    Depends way you look at it. In some ways, analytic geometry generalises a set of algebraic tools to geometric problems. Eg from the text > For the analysts, this was irrelevant: algebra captured the essential relations expressed by the terms of the problem, which then served to guide the mathematician toward the solution. For the synthetics, by contrast, a solution to the original geometrical problem could only be geometrical in nature; and so, what the analysts were offering were not solutions but meaningless numbers. > While the analysts strove for maximum generality, the synthetics argued for the specificity and locality of all mathematical methods. […] [For the synthetics] even more misleading would be to believe that there is a single universal method that can be applied to all kinds of problems.