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I'm not sure if this is the right forum for this question, in any case probably CW is appropriate?

I've been looking around the mathblogosphere for the past few weeks and ran into mathgen. It's pretty amusing, to be sure, but point 6 in the Why? section has set me to serious thinking. For those opposed to clicking links, mathgen is a random generator of math papers, and the creator give several justifications for the creation, the relevant one being:

I think this project says something about the very small and stylized subset of English used in mathematical writing. This program only knows a handful of sentence templates, and yet I think its writing style is [typical.] I think we could stand to pay more attention to our writing styles, instead of unthinkingly relying on stock phrases.

With this in mind, have any of you encountered reputable, "research-tier" papers that have a writing style dramatically or at least distinctly different from the one that seems to dominate so much of this kind of mathematical writing? I'm not really looking for expository writings, although I imagine that what I am looking for will have a similar feel to it. So I think what I'm going to mean by research-tier (for now) is simply that it proves something new and at least mildly significant.

Links, especially free ones, are appreciated.

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    $\begingroup$ @bof -- I agree that using a small subset of the language is good. Common words. Short sentences. Simple structure. I value all these things myself, even though I'm not Slobbovian. But I think math-journal English is something different (and worse). I'm looking forward to some good answers, because I don't like typical mathematical writing at all, personally. $\endgroup$ – bubba Oct 5 '13 at 4:34
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    $\begingroup$ See this Math Overflow question for a very entertaining list. $\endgroup$ – Jair Taylor Oct 8 '13 at 0:49
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    $\begingroup$ I know that this is not what you were looking for, but I would like to mention A Headache Causing Problem anyway. $\endgroup$ – user161303 Oct 15 '14 at 19:31
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    $\begingroup$ @Frank: What? Nobody is suggesting that Mathgen papers would be an example of an appropriate answer to this question. It just provided the impetus for the question... $\endgroup$ – Eric Stucky Mar 11 '16 at 1:30
  • $\begingroup$ Yes [second sentence of the introduction]. But frankly, I'm really uninterested in having that conversation (even if I were qualified to participate), which is why it is not the subject of my question. If you think I'm shutting myself off to an important component of a useful answer, let me know :) $\endgroup$ – Eric Stucky Mar 11 '16 at 9:10
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One piece that comes to mind is Gromov's "Metric structures for Riemannian and Non-riemannian spaces." Everything from the numbering - a Gromov hallmark - to some of the colorful yet sometimes remarkably illuminating language - a wonderful example is 1.25.1/2, "If one feels disgusted by the spineless flexibility of arc-wise isometric maps, ..." - is rather unique in the literature. (And still, Gromov is far more digestible in print than when speaking.)

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This is moderately common in Theoretical Computer Science. A lot of problems and algorithms in that field are posed and discussed in terms of mini stories, even in technical papers. In his celebrated paper introducing what is known as the "Arthur-Merlin Protocols", Laszlo Babai writes as if telling a fable about Camelot.

Leslie Lamport, the founder of the field of distributed systems, wrote a 33 page paper describing a protocol with the entire thing wrapped in a conceit about a fictional greek society's parliament deciding on laws to pass, which itself involves a nested conceit about a bunch of Greek priests agreeing on a decree. Three years later published a paper outlining the same protocol but in a more normal tone and it was a third the length. He even makes a quip about the fact that the original paper was Greek to many readers and was therefore inaccessible.

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The review of Perlman and Chaudhuri, Reversing the Stein effect, Statist. Sci. 27 (2012), no. 1, 135–143, MR2953500, says (in part),

"The authors make their point in a rather unorthodox way using a made-up Star Trek episode. The starship Enterprise is lost in space and unable to move. To be rescued it is necessary to send a probe close enough to the interstellar space station Delta so that it will be detected and convey the position of the Enterprise. Mr. Chekov, who studied with Admiral Emeritus Stein at the Space Academy, suggests the use of the JS plus-rule estimator to figure out where to send the probe. Different suggestions are given by the other crew members. Spock then comes forward and says "This is not logical''. He asks the computer to display the region where the JS estimator lies closer to Delta. He notes that the set of values of $\delta_0$ where use of the JS does more harm than good is quite extensive and that it is likely that JS shrinkage would move them farther away from Delta. Spock recommends that they tether the probe to the Enterprise and hope that Delta can detect their present location. Chekov is confused, and Captain Kirk asks to be beamed to the bar where perhaps he can figure things out after belting down a few drinks."

There is a link to the paper at https://projecteuclid.org/euclid.ss/1331729987. Most of the paper is in standard definition-theorem-proof style, but the Star Trek part takes up a couple of pages in the middle, and it's well worth having a look, even if you're not a Trekkie, just to see what the authors got away with!

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