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Sep 6, 2022 at 13:26 comment added Timothy Chow @MattF. Hmmm...area calculations in analytical geometry wouldn't necessarily have been thought of as "calculus" back then. But maybe I should re-read Russell.
Sep 6, 2022 at 2:27 comment added user44143 @TimothyChow, the book is online — Russell explicitly included analytical geometry in traditional pure mathematics, which would include plenty of area calculations and therefore plenty of calculus. people.umass.edu/klement/imp/imp.html
Sep 5, 2022 at 20:54 comment added Timothy Chow It's worth noting that the term "traditional pure mathematics," as used by Russell here, probably doesn't include calculus/analysis (which is "applied") or Cantor's infinite set theory (which was not "traditional").
Sep 5, 2022 at 19:09 comment added Burak Thank you. This passage from Russell aligns with the quotation that I wrote in the OP, namely, that "In the late nineteenth century, it was a widespread idea that pure mathematics is nothing but an elaborate form of arithmetic".
Sep 5, 2022 at 15:17 history answered Ben Burns CC BY-SA 4.0