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elharo comments on Harry Potter and the Methods of Rationality discussion thread, part 21, chapters 91 & 92 - Less Wrong
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Both canon and HPMoR have arithmancy. In HPMoR, "Harry and Professor McGonagall had bought his textbooks from Flourish and Blotts just under the deadline. With only a slight explosion when Harry had made a beeline for the keyword 'Arithmancy' and discovered that the seventh-year textbooks invoked nothing more mathematically advanced than trigonometry." And Harry really shouldn't have exploded. Many real world Muggle schools don't get as far as trigonometry by the end of high school, and they don't have to spend any time on charms or transfiguration.
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For a professional-grade comment on "muggle math" versus "Hogwarts math", see Michael Spivak's Physics for Mathematicians: Mechanics I.
To express this point another way ... how likely is it, that Harry's final understanding of magic will be non-mathematical? What grade of mathematical abstraction capabilities will Harry need to acquire?
I can't find the particular proofs of Noether theorems that your link refers to. Can you help me find them? I see no instances of the word "muggle" in Spivak's paper - in fact no index at all. Is there a different version of it? Please help, as I would greatly appreciate reading this!
Edit: I see now that the comment was referring to a book by Spivak, and that the linked PDF is only on 'elementary mechanics.'
Edit 1: Kudos to "gjm" (see above) for pointing to Spivak's page on Amazon!
Edit 2: Spivak's Hogwarts proof implicitly uses a fundamental theorem in differential geometry that is called Cartan's Magic Formula ... this oblique magical reference is Spivak's joke ... as with many magical formulas, the origins of Cartan's formula are obscure.
Amazon UK's "look inside" feature has it. I haven't checked Amazon US. Search for "Muggles"; first result (page 576) is the one.