I have questions on how to properly cite a mathematical theorem in order to use it in a paper.

For example, assume that I need to apply an existing theorem from a published book 1.

Theorem 1 [book 1]. statements...

Proof: Refer to [book 1]

My supervisor suggested that if I put the citation remark after Theorem 1, then all my writing and wordings have to be identical to the original one in [book 1]. However, if I state this theorem by my own words, with possible changes of notations or similar things, then I cannot put the citation remark after Theorem 1. In that case, I should refer it at the beginning of the proof of this theorem as I have shown above.

So what is the proper way to cite a theorem in a situation like this? I personally prefer to state an exiting theorem in my own words. This is because formulations of theorems are not always optimal, and also the notations generally have to be changed in accordance with my writings.

Note that I need to apply the equations in Theorem 1 in my subsequent writings, so simply quoting this theorem and applying its conclusions may not be a good choice.

Thanks a lot!


On the one hand, you sort of don't need to worry about it, but it's best to make your advisor happy (especially if they are a co-author). Here are my thoughts.

  1. Your advisor ought to have experience with this sort of thing in general. So as a rule, it's good to take their opinion into consideration.

  2. The journal you ultimately submit to will have people whose job is to make sure you use any nuanced writing rules like this correctly. And the formatting and such that you choose will probably be changed by the journal any way.

  3. I've never heard of any rule like you mention, and I don't think there's any expectation in the community about this. Citations in math papers are always weird. They have no standard format (the journal will do the format they like for you), and you don't have to worry so much about exactly quoting somebody per se.

  4. My rule of thumb is that when I cite something, I always try to credit previous literature for everything I can. I ask myself "is what I'm writing obviously equivalent to or implied by the theorem they wrote?" If so, I would simply phrase the result in my own words and credit them for the theorem. You can do this easily, and you don't have to mention a proof at all unless it's unclear how their result implies your statement.

For example, I would write something like:

We recall the following theorem due to Smith [4].

Theorem 3: All objects have property.

And the theorem number is just whatever number would be next in your paper. Or you could do

The problem was originally asked by Smith [4], who addressed the situation when things are nice. In particular, she proved.

Theorem 3 (Smith [4]): All objects have property.

Or if it's very hard to find where in [4] Smith wrote that theorem, you could say

Smith proved the following, which appears as theorem 13.b of [4]

Theorem 3: All objects have property.

Or if you want to emphasize that what you're stating is easily implied by Smith, I might say something like

We now use a special case of a theorem of Smith [4] recalling here only what we need.

Theorem 3: The objects I like have property.

Note that in all of the above cases, it wouldn't be appropriate to cite a proof or anything after the theorem statement. The result should either be very obviously the same as the paper you cite, or it should be very obviously implied by it. If you want to use something similar to Smith's theorem, but it's not obviously the same or implied, then I suggest something like the following.

We now appeal to a general theorem of Smith [4], which states

Theorem 3: All objects have property.

By regarding her (thing) in (our setting), we obtain (by this hint of a proof sketch)

Corollary 4: The things we care about do the thing we care about.

If needed, then say more about why this follows from Smith's result. If this connection (and stating Smith's result in the first place) is too much, then you might want to consider putting that part in an appendix and just saying something like "the following is obtained from a theorem of Smith [4], but for ease of reading this connection is discussed in appendix A."

One final piece of advice would be to simply read a lot of well-written papers and see what they do. Look in places that have good exposition even if it's not in your area. It's not important to understand the math in those articles so much as how they write and how they handle these nuances.

You have a lot of freedom, and any choice you make is likely going to be fine as long as you thoroughly credit previous authors and you make your paper easy to read.

  • 8
    In your third example I would remove the consideration that the result is hard to find. Unless the paper has only one result, it is always good practice to refer to the precise part used. Nov 30 '16 at 7:32
  • Thank you very much for your detailed answer Pat. I am a little bit confusion about your statement ''I've never heard of any rule like you mention''. Are you referring to the rules which my supervisors suggested, or the rules I stated that ''if I state this theorem by my own words, with possible changes of notations or similar things, then I cannot put the citation remark after Theorem 1, but only refer it at the beginning of the proof of this theorem as I have shown above''. Thanks again for your help !
    – Johannes
    Nov 30 '16 at 12:28
  • 4
    I'm referring to the second thing you mention in this comment. I've certainly never heard of anything like that. I would add that when I read papers, I always assume the results are restated in the author's own words.
    – Pat Devlin
    Nov 30 '16 at 13:08
  • 1
    @TobiasKildetoft I wonder to what extent this changes by discipline. I do combinatorics, where many papers are short and self-contained. And most of the time the paper has only one or two results. I think I would say this: if the result appears in the abstract or introduction, you don't have to say where in the paper it came from, but otherwise you should.
    – Pat Devlin
    Nov 30 '16 at 13:12
  • 3
    I would simplify Smith proved the following, which appears as theorem 13.b of [4] as Smith proved the following [Theorem 13.b, 4], which you can do in LaTeX using \cite[Theorem 13.b]{X}.
    – user2768
    Aug 1 '17 at 15:18

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