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Perhaps under the influence of a recent question on perverse sheaves, in conjunction with the impending $\pi$-day (3/14/15 at 9:26:53), I recalled a long-ago parody of abstruse mathematical language that I can no longer remember in detail nor find by searching.

I am not seeking merely "examples of colorful language," as in that earlier MO question, but rather parodies almost in the Alan Sokal Fashionable Nonsense sense (although I don't think he parodied abstract mathematics directly).

I am partly motivated by the possible educational advantage of self-mockery (or self-awareness), tangentially related to an MESE question, "Wonder as Motivation." But I ask here to tap into the likely greater density of mathematicians working in abstract fields ripe for parody.

Q. Can you provide examples of (or pointers to) intentionally comic parodies of abstruse mathematical language, written by knowledgeable mathematicians so that they could (in another universe) make mathematical sense.

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    $\begingroup$ The Sokal hoax was meant to expose actual intellectual bankruptcy in certain academic circles, where nonsense dressed up in jargon could pass muster. I can't think of examples where "abstruse" fields of mathematics are ripe for a similar kind of parodizing, since we make a point of being careful and at least somewhat rigorous, unless we're talking about the output of outright incompetents. And I confess that I don't understand the boxed question; what is meant by "(in another universe) make mathematical sense"? Could you give an example of what you mean? $\endgroup$
    – Todd Trimble ♦
    Mar 14, 2015 at 0:58
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    $\begingroup$ I really find the suggested likening to a Sokal-type hoax perplexing, since (again) the parody in that case was meant to expose outright nonsense and lack of real intellectual standards. Do you think this parody you're trying to recall was likewise parodizing abstract fields as relative nonsense? What I'm trying to press you on is whether the comparison to Sokal is at all apt for what you want. $\endgroup$
    – Todd Trimble ♦
    Mar 14, 2015 at 1:13
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    $\begingroup$ Simplest example to illustrate Todd's "just about all": Hitler Learns Topology on YouTube. $\endgroup$
    – Tom Copeland
    Mar 14, 2015 at 3:05
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    $\begingroup$ Not quite writing per se, but perhaps relevant. $\endgroup$
    – Zhen Lin
    Mar 14, 2015 at 8:35
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    $\begingroup$ Many of the examples here are cerebral. You smirk if anyone is around just so they understand you get the inside joke, but the Hitler parody is visceral, with the roles of authority reversed between the student and teachers, and had me ROTFL. I think disenchanted students can relate more to it than the insider jokes that are intended more to embarrass the pretentious than as a self-parody. $\endgroup$
    – Tom Copeland
    Mar 17, 2015 at 23:29

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In a spirit similar to MathGen, there is The proof is trivial!, a small website which randomly generates short snippets along the lines of:

The proof is trivial! Just biject it to a

Lebesgue-measurable variety

whose elements are

orientable generating functions

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Meta variant: Does the Euler-Diderot incident count? E.g. here Because it is made-up?

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A lovely example of this genre is Burritos for the hungry mathematician by Ed Morehouse, which includes such lines as "To wit, a burrito is just a strong monad in the symmetric monoidal category of food."

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    $\begingroup$ One of the references therein deserves separate mention in fact - F. William Lawvere. “Display of Graphics and their Applications, as Exemplified by 2-Categories and the Hegelian Taco”. In: Proceedings of the First International Conference on Algebraic Methodology and Software Technology. 1989. As nLab puts it, "The Hegelian taco is food for thought from William Lawvere's kitchen." $\endgroup$
    – მამუკა ჯიბლაძე
    Mar 7, 2020 at 16:37
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