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Has anyone written or expressed a coherent position on how to refer to mathematical results (theorems, proofs) by past authors? Even if there are no hard and fast rules, I find it helpful to have a guide that I can follow in order to speed things along. Here are some of the issues that I regularly find myself dealing with inconsistently, even in the same article:

  • Do I refer to authors (citet, in natbib, say) or their articles (citep)? Or in what situations is one preferred? In the case of citep, is it reasonable to treat the actual reference [ABC+03] as a noun? Or is that bad style? (Perhaps some journals have specific rules on this.)
  • Do I refer to the act of proving results in the present tense or past tense?

Perhaps this relates to how one stands on the question of whether mathematical results are "discovered" or "invented". But here are five ways to say almost the same thing:

  1. [AB03] proves X.
  2. [AB03] proved X.
  3. Abacus and Bacchus [AB03] prove X.
  4. Abacus and Bacchus [AB03] proved X.
  5. A proof for XYZ appears in [AB03].

(... and perhaps the answers would be different for s/prov/show/.)

In addition to the above, what other inconsistencies have people come across and how do they address them?

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  • $\begingroup$ Hopefully there's no uniform style, just be coherent, especially as regards the use of past/present form. Of course the information is not always the same: "a proof of ... appears in" does not mean that this is the original reference, and might refer to the fact that the proof was written in detail, etc. The way to quote also depends on where it fits, for instance you can think of it historically, or as part of the present stream, etc. Also there's the possible use of "has proved that"; maybe a native or better English speaker would better describe the nuance. $\endgroup$
    – YCor
    Commented Mar 9, 2019 at 15:07

1 Answer 1

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Well, this is what the American Mathematical Society recommends:

Form I and form II refers to the different ways to present the bibliography, with numbered references (I) or with alphabetically ordered authors (II). So I would say number 4 of your options is recommended.

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  • $\begingroup$ Love it. Looking at your own writing: do you follow this? Past tense and using the humans as the noun? $\endgroup$
    – D.R.
    Commented May 3, 2016 at 17:05
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    $\begingroup$ @D.R. Of course past tense, unless you're psychic ("Roe will prove this in 2018"). $\endgroup$
    – Robert Israel
    Commented May 3, 2016 at 17:29
  • $\begingroup$ @D.R. --- In my writings your option number 5 is more customary, perhaps with "Ref. [AB03]" instead of just "[AB03]", but I'm a physicist. Typically, a proper name is only included in the main text to pay special respect: This result was first discovered by Einstein [Ein05] and later extended in Refs. [NN25,MM40,XX70]. $\endgroup$
    – Carlo Beenakker
    Commented May 3, 2016 at 19:49
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    $\begingroup$ One editor I know regards the brackets as parentheses: if the brackets (and their contents) are deleted entirely, then what remains should still be a complete sentence. Your 3 and 4 pass this test but 1, 2, and 5 fail it. I kind of like this approach in theory, but in practice it can force you to be more verbose than you might otherwise want to be. Note also that it's helpful to the reader for the reference to contain some information about the authors' identities. If you're already writing "[Roe73]" then "Roe [Roe73]" is a bit clumsy, but "Roe [1]" is more informative than simply "[1]". $\endgroup$
    – Timothy Chow
    Commented May 3, 2016 at 20:55
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    $\begingroup$ @RobertIsrael Funny, but it is already clear from 1 and 3 that the OP is considering present tense as an option, as in "In [2], Roe establishes the following statement" -- certainly not an uncommon construction. There is present perfect, as in "Roe has shown in [2] that the following holds". $\endgroup$
    – Todd Trimble
    Commented Mar 9, 2019 at 17:48

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