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The popular MO question "Famous mathematical quotes" has turned up many examples of witty, insightful, and humorous writing by mathematicians. Yet, with a few exceptions such as Weyl's "angel of topology," the language used in these quotes gets the message across without fancy metaphors or what-have-you. That's probably the style of most mathematicians.

Occasionally, however, one is surprised by unexpectedly colorful language in a mathematics paper. If I remember correctly, a paper of Gerald Sacks once described a distinction as being

as sharp as the edge of a pastrami slicer in a New York delicatessen.

Another nice one, due to Wilfred Hodges, came up on MO here.

The reader may well feel he could have bought Corollary 10 cheaper in another bazaar.

What other examples of colorful language in mathematical papers have you enjoyed?

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    $\begingroup$ Latest paper, my co-author put in "but we will choose a more painful way, because there is nothing like pain for feeling alive" but the referee jumped on it. $\endgroup$
    – Will Jagy
    Apr 23, 2010 at 5:09
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    $\begingroup$ Maybe I should expand the question to include colorful language cut from serious mathematics papers :) $\endgroup$ Apr 23, 2010 at 5:18
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    $\begingroup$ By the way, your remark reminds me of another in a similar spirit that made it into the Princeton Companion. In his article on algebraic geometry, János Kollár says of stacks: "Their study is strongly recommended to people who would have been flagellants in earlier times." $\endgroup$ Apr 23, 2010 at 7:49
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    $\begingroup$ I was actually rather surprised recently by a referee who did not know the phrase “red herring”, and had to look it up. He insisted that we change it to something more understandable. It makes me wonder how much “colourful” language is weeded out by referees, and whether the mathematical literature is poorer for it. $\endgroup$ Apr 24, 2010 at 2:31
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    $\begingroup$ @Harald: If you intend your mathematical papers to be read by a wide range of readers, then write them in simple language, suitable for those who are relative beginners in English. I remember reading long ago some metaphoric phrase in a mathematics research paper, then imagining students all over the world getting out their English dictionaries, looking it up, and still not understanding what it meant. (I no longer remember what the phrase was, just this reaction to it.) $\endgroup$ Apr 24, 2010 at 15:43

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Here are several colourfully named concepts:

  • perverse sheafs
  • transgression
  • schizophrenic objects

Errett Bishop wrote a paper on constructive mathematics which is titled Schizophrenic Mathematics and begins with a polemic against formalism in mathematics:

One could probably make a long list of schizophrenic attributes of contemporary mathematics, but I think the following short list covers most of the ground: rejection of common sense in davour of formalism; debasement of meaning by wilful refusal to accomodate certain aspects of reality; inappropriateness of means to ends; the esoteric quality of the communication; and fragmentation.

David Mumford wrote that algebraic geometry:

seems to have acquired the reputation of being esoteric, exclusive and very abstract with adherents secretly plotting to take over the rest of mathematics! In one respect, the last point is accurate ...

To which Vakil added in his book, The Foundations of Algebraic Geometry:

The revolution has fully come to pass ...

But warned:

Do not be seduced by the lotus-eaters into infatuation with untethered abstraction ...

And also quotes Atiyah:

"Should you just be an algebraist or a geometer?" is a bit like saying "should you rather be blind or deaf?"

Atiyah also calls spinors "the square root of geometry", which, though not colourful, is certainly esoteric.

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An excerpt from E. C. Zeeman. Seminar on combinatorial topology:

... choose a spine in the interior; expand each edge like a banana and collapse from one side; then expand each vertex like a pineapple and collapse from one face.

I find this a very good specimen of colourful language: the colourfulness is used to convey an idea in an elegant yet precise way. Halmos wrote `Clarity is what’s wanted, not pedantry; understanding, not fuss'. Zeeman's excerpt is a good example to go with Halmos' advise.

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From one of the papers on integrable systems

"The authors X.X and Y.Y took only a small peace of the integrability cake...."

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    $\begingroup$ peace or piece? $\endgroup$
    – David Roberts
    Apr 6, 2011 at 6:01
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I like "Let's take this guy" (in German: Bursche) when a Graph theorist picks a vertex. (it's not colourful at first sight, but think about it)

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  • $\begingroup$ Brazilians say "a gente pega um cara" (more or less literally: let us take a guy) $\endgroup$ Jan 19, 2011 at 23:43
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    $\begingroup$ My Intention was to say that (among others) mathematicians tend to anthropomorphize their subjects. $\endgroup$ Jan 20, 2011 at 0:08
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    $\begingroup$ @Hans: Really? anthropomorphize? When I look at how many "monsters", "beast" etc. are out there, then I tend to think that at least the "official" termininology is more animalistic. $\endgroup$ Jan 20, 2011 at 10:56
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    $\begingroup$ I once followed a lecture of David Goss where he started calling his objects "guy", passed on to something like "unpleasant fellow" (when he was revealing some undesired properties of that object) and ended up calling it "sucker" - repeatedly and emotionally. $\endgroup$ Oct 22, 2011 at 20:12
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    $\begingroup$ "Sucker" reminds me inevitably of Chuck Weibel, who used to say this all the time. $\endgroup$
    – Todd Trimble
    Dec 13, 2011 at 12:29
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This reminds me of the little blue book by Swan... It must be "Theory of Sheaves", I don't have it on my shelf here. But I remember clever chapter titles. Maybe someone else here can tell us.

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  • $\begingroup$ I've just thumbed through The Theory of Sheaves, and I saw nothing in the titles (or in anything else there) that applies. The cover is blue all right, but I imagine you're thinking of something else. $\endgroup$
    – Todd Trimble
    Mar 2, 2011 at 2:15
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