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As a student working on my first academic publication, I have a ton of questions specifically about writing about math. For example:

  • When should I state the full theorem rather than just its name and a reference?
  • When I have multiple references for a theorem, should I cite the oldest one or the one that I find most helpful?
  • When should I call something a theorem, corollary, or proposition?
  • If I am using the first half of someone else's proof to prove something else, how should I credit them?

There might be some general advice on these issues on several websites, but I am looking for a place where I can give some context on my specific problem and ask those questions in that context. The answers would probably be opinion-based, but nonetheless valuable to me.

I am not sure whether to take those questions. There is writing.stackexchange.com, but the focus seems to be on writing fiction. Then there is also academia.stackexchange.com of which I haven't quite figured out its purpose. Since my questions are specifically about mathematical writing, I would think that the crowd on math.SE is the one that can offer the most helpful advice, but math.SE doesn't seem to be right platform for this.

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Regarding your third bulleted question, for example, a search on the Mathematics Stack Exchange website for the word triplet "proposition theorem lemma" brings up some useful answers here, here, and here. (I omitted "corollary" because I think that everyone would agree that it's a result which relates to a particular theorem as a special case or immediate consequence of that theorem.)

Using search terms for the other example questions didn't lead to useful answers on the same site; so I think that, in general, you may have more luck with MathOverflow regarding soft questions about mathematical writing.

In my opinion, your example questions are clear and have definite answers. For what it's worth, here are mine.

When should I state the full theorem rather than just its name and a reference ? Err on the the side of stating too much: The reader who is familiar with the result can easily skim through it, while the reader who has forgotten some of the details will find it a pain to go off and look them up. Omit the details if it's a standard result that anyone capable of reading your paper would be expected to know well.

When I have multiple references for a theorem, should I cite the oldest one or the one that I find most helpful ? Ideally both. For example, "A theorem of Smith (1923), elegantly proved by Jones (2012), states ... ". As a heading, this could be in the form "Theorem 4.1 (Smith 1923; Jones 2012)."

When should I call something a theorem, corollary, or proposition ? The term theorem should be reserved for what you consider to be the best result (or results) of the paper—the result that you would like the paper to be remembered for. Significant results that play a supporting role in the paper might be called propositions, and lemmas are the stepping-stones on the way to proving propositions and theorems. (Corollary was mentioned earlier.) If history should deem your Lemma 3.8, Corollary 4.5, or Proposition 2.7 to be the most useful result of the paper, and forget about your prized Theorem 5.1, then so be it.

If I use the first half of someone else's proof to prove something else, how should I credit them ? An example might be "Proof. Initially following the lines of Brown's (2014) proof of her Theorem 5.2, we consider ... ".

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