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I don't understand how you got that at all. The impression I got was the synthetic mathematicians were wary of applying the new "analysis" methods because lack

I don't understand how you got that at all. The impression I got was the synthetic mathematicians were wary of applying the new "analysis" methods because lack of rigor made them question how safe and valid it was to use. > Using another set of metaphors: Analysts followed the fast flights of their feverish and uncontrolled imagination, while synthetics kept their feet on the ground. Their procedures were slow but safe.

zozbot234 9mo ago
> I don't understand how you got that at all. The word "reactionary" appears multiple times on that page, in association with either synthetic mathematics itself or the politics that's said to be closely connected to it. I'd say that's by far the most unambiguous part of my argument about this text.
- freehorse 9mo ago
  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 is reactionary per se, but considering the coordinate system as spoiling the purity of geometry is.
  - 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.

zozbot234 9mo ago

> I don't understand how you got that at all. The word "reactionary" appears multiple times on that page, in association with either synthetic mathematics itself or the politics that's said to be closely connected to it. I'd say that's by far the most unambiguous part of my argument about this text.

freehorse 9mo ago
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 is reactionary per se, but considering the coordinate system as spoiling the purity of geometry is.
- 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.