Just as the title says: do you spell out Thm., Prop., Eq., Ch. and comparable abbreviations in a mathematical paper?

I suppose that, if in doubt, it is always best to stay consistent (in whatever way) throughout ones writing for the least. Do journals have (different) policies on this, or is there a prefered style when in doubt?

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    My personal favorite is people writing "Ass" for "Assumption". – Federico Poloni Jun 13 '13 at 17:30
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    Use macros for them in the document markup; then you can later decide whether or not to expand them without doing tedious search and replace. – Kaz Jun 13 '13 at 18:48
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    Assuming you're using LaTeX to typeset your papers, you can use the cleveref package to help ease this kind of thing :) – cmhughes Jun 13 '13 at 23:47
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    @Kaz: even if you use the macros consistently, you will still have to make a decision sooner or later. – Lie Ryan Jun 14 '13 at 2:31
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    @LieRyan Later later, just not now! ;) – Kaz Jun 14 '13 at 2:32

It is a matter of style. I would say yes, expand them. In my opinion, authors tend to over-abbreviate making documents harder to read. For instance, I can't work out what you mean by Ch. (Conjechure?)

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    Chapter, likely. – Federico Poloni Jun 13 '13 at 17:29
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    The word you want is spelled conjecture so like Federico said, most likely Ch. means chapter. – Fixed Point Jun 13 '13 at 20:39
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    This was a joke. As a mathematics paper rarely has Chapters, but they do often contain conjectures, all I could imagine was that it was an abbreviation for a misspelled conjecture. – Dave Clarke Jun 14 '13 at 7:18

In my experience, authors almost always spell out words like "Theorem", "Proposition", and so on. I expect that journal styles will generally require this. I can't remember the last time I saw a published paper that abbreviated them.

But if you're writing a paper, you must have read a lot of other people's published papers. Surely by now you've formed your own opinion of the consensus?

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    Equation and Figure frequently get abbreviated in journals, but those are about the only examples I can think of. – aeismail Jun 13 '13 at 22:23
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    A few times I've also seen section abbreviated with the section sign §. – Willie Wong Jun 14 '13 at 12:12

To expand on Dave's answer slightly, abbreviations should follow the guidelines of the specific venue to which you are sending a paper. If they expect no abbreviations, don't use them. If they have standard ones specified, use those as appropriate. Typically, I would only use something like "Prop." for "proposition" when it's referring to something with a specific number, and that's what the style guide calls for.

Other abbreviations should be used to improve readability: for instance writing out "fast Fourier transform" one hundred times during a paper can start to get more tedious than using "FFT" as an abbreviation. But shortening individual words should only be done if it makes reading the paper easier, not simply to shorten it.

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    "To make it easier" - thanks for reminding me of that essential principle. One cannot repeat too much. – Ambicion Jun 13 '13 at 15:37
  • writing out "fast Fourier transform" one hundred times during a paper can start to get more tedious than using "FFT" as an abbreviation — Says you. – JeffE Jun 14 '13 at 3:53
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    So also says the American Chemical Society and a number of other publishers. – aeismail Jun 14 '13 at 6:16
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    In contemporary math writing, this is not quite right: it would be silly to modify the style of your paper to match the journal you're submitting to, since you have no idea whether it'll be accepted. Moreover, once it is accepted, the journal's copy editors will do the work of converting these things to house style (and will do a much better job than you would). – Tom Church Sep 18 '17 at 22:25

One heuristic is to write things as you would read them out loud. In other words, don't try to save space in print unless you would use the same abbreviation in speech.

For example, I'm happy to say "i.e." or "e.g." orally in certain situations, so those abbreviations can be fine (indeed, it would sound really weird if you wrote "id est" or "exempli gratia"), but I would never refer to "Sec. 5" or "Eq. 3" when speaking. Trying to pronounce "Ch. 2" as written would be even worse. By this standard, abbreviations like NASA or FFT are OK, although they can of course be overused and they may be more cryptic than the writer intends.

This principle extends beyond abbreviations: try not to write anything that would be awkward to read aloud. (For example, mathematicians sometimes violate this by juxtaposing formulas with no words in between them.) Of course this is not an absolute rule, but following it will generally make your papers easier and more pleasant to read. The effects are admittedly small, but if you are explaining complicated or subtle ideas, you shouldn't add to the difficulties with clumsy writing.

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  • Stylistically, I find that e.g., only really works for me when it proceeds a list of items, but not when it is used, for example, in the middle of a larger sentence (such as this one). – Dave Clarke Jun 14 '13 at 13:50
  • I agree. For example, I wouldn't write "E.g., I wouldn't write...". By expanding "e.g.", I meant as "exempli gratia", not "for example". I'll edit to clarify. – Anonymous Mathematician Jun 14 '13 at 13:53
  • I never speak Latin. – Dave Clarke Jun 14 '13 at 14:12
  • The bits about "Sec." and "Eq." probably need to follow the journal you've decided to submit to. Even if you prefer something else, they'll likely adjust it during final processing! – aeismail Jun 14 '13 at 18:25
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    @aeismail The experience seems to be that if you are self-consistent, the copy eds are more tolerant to style differences. – yo' Sep 18 '17 at 14:30

Well, yes, you in general spell out these words. However, there are basically three types of their usage and you can draw the line between Abbr./Spell-out any where between them.

  1. In-text usage at the beginning of a sentence. Theorem 3.5 clearly shows that Foo is actually a Bar of chocolate. Equation 3.17 confirms this. Equation (3.18) is irrelevant.

  2. In-text usage in the middle of a sentence. We see in Thm. 3.5 that Foo is actually a Bar of chocolate, which is confirmed by Eq. (3.17), noting that (3.18) is irrelevant.

  3. Parenthesized usage. We see that Foo is actually a Bar of chocolate (Thm. 3.5).

(I personally prefer no abbreviation for any references, and omitting the word "Equation" whenever possible, but that's not the point.) The point is that you should draw the line somewhere and be consistent throughout your document, and especially be consistent with "Fig." vs. "Table" etc. The exceptional things are:

  • Equations with 5 (five!!!) possible styles: Equation (3.18), Equation 3.18, Eq. (3.18), Eq. 3.18, (3.18).
  • Bibliographic citations which usually have a prescribed style and you should only be consistent in whether they can be a grammatical object in the sentence or not.
  • Chapters/sections, where: first you don't need to follow the LaTeX's terminology, and second you can use the sign "§" for them.
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  • Some journal guidelines specify whether references should be spelled out in full, abbreviated or omitted (for equations). And the typesetter will likely change the author's choice to comply with the guidelines anyway. – Massimo Ortolano Sep 18 '17 at 15:09
  • @MassimoOrtolano Concerning some of the mentioned points, not all journals/publishers have a prescribed style, so if you're consistent, there is a significant chance they'll preserve the style. – yo' Sep 18 '17 at 15:30

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