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HalMorris comments on By Which It May Be Judged - LessWrong
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Very few mathematical definitions are about General Mathematical Practice. Euclidean and Riemannian (or projective) geometry are in perfect peaceful coexistence, and in general, new forms of mathematics expand the territory rather than fight over an existing patch of territory.
I think you underestimate the generality of my claim. (Perhaps the phrase 'power grab' is poorly chosen.) Relatively egalitarian power grabs are still power grabs, inasmuch as they use the weight of consensus and tradition to marginalize non-egalitarian views. There is no proof that both geometries are equally 'true' or 'correct' or 'legitimate' or 'valid;' so we could equally well have decided that only Euclidean geometry is correct; or that only project geometry is; or that neither is. There is no proof that one of the latter options is superior; but nor is there a proof that one is inferior. It's a pragmatic and/or arbitrary choice, and settling such decisions depends on an initially minority viewpoint coming to exert its consensus-establishing authority over majority practice. Egalitarianism is about General Mathematical Practice. (And sometimes it's very clearly sociological, not logical, in character; for instance, the desire to treat conventional and intuitionistic systems as equally correct but semantically disjoint is a fine way to calm down human disagreement, but as a form of mathematical realism it is unmotivated, and in fact leads to paradox.)
That depends a great deal on how coarse-grainedly you instantiate "forms". Mathematical results get overturned all the time; not just in the form of entire fields being rejected or revised from the ground up (like the infinitesimal calculus), and not just in the discovery of internal errors in proofs past, but in the rejection of definitions and axioms for a given discourse.
I'm just a 2 year math Ph.D. program drop-out from 35 years ago, but I got quite a different take on it. As I experienced it, most mathematics is like "Let X be a G-space where G-space is defined as having <list of axioms>". and then you might spend years proving whatever those axioms imply, and defining umpteen specializations of a G-space, like a G2-space which has <G-space axioms PLUS a few more>, and teasing out and proving the consequences of having those axioms. At no point do you say these axioms are true - that's an older, non-mathematical use of the word "axiom" as something (supposedly) self-evidently true. You just say if these axioms are true for X, then this and this and this follows.
Mathematicians simply don't say that the axioms of Euclidean geometry are true. It is all about, "if an object (which is a purely mental construct) has these properties, then it most have these other properties.
By the "infinitesimal calculus", being overturned, I assume you mean dropping the use of infinitesimals in favor of delta-epsilon type definitions in calculus/real analysis, it's not such a good illustration that revision from the ground up happens all the time, since really, that goes back to the late 19th century, and I really don't think such things do happen all the time though another big redefining project happened in the early 20th century.
ZFC set theory? Peano arithmetics?