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I am writing a paper on a big theorem in Algebra. But in order to supply as many proofs as I find interesting, I have to mention the theorems used to prove this Big Theorem. Do I have to include all the proofs of all the theorems I mentioned as well as relevant lemmas, even if they take me away from my topic for some time?

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    It is very difficult for undergraduates to write mathematics papers without the assistance of a faculty mentor to help them out (at least) with the conventions and mechanics of mathematical writing. If you don't have a faculty mentor, it is extremely unlikely that you can get your paper into a form in which it will be seriously considered by a reputable journal. (Maybe that's not your goal. But if not, you have to tell us what it is, because the conventions depend upon the form.) I hope you have a faculty mentor. You should ask her about this. – Pete L. Clark Apr 26 '15 at 21:40
  • Hey, @PeteL.Clark! Thank you for your thoughtful answer. To answer your implied questions: 1. My paper is simply a final year project to be read and graded by only my professors. I think the idea is to teach us how to write papers or something. 2. I do have a mentor, but I left this project to almost the last moment and after looking through my first draft she assured me all was well. I, however, have decided to try to shape it into a better form. And it's midnight where I am right now, and a cruel hour to contact one's professor. – Siyanda Apr 26 '15 at 21:46
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Generally speaking, every statement in a published mathematics paper needs to have a proof somewhere that the reader can find it. (If this paper is for a class assignment rather than for publication, ask your instructor. The rules are also a little different for "expository" papers which are mainly intended to discuss previous work, rather than to present new results.)

  • If you use a result that is well known, you can mention it by name. It is not necessary to include a formal statement or proof, nor a reference. This would apply to results that are found in most standard textbooks in your area, and that most people reading the paper would be familiar with.

  • If you use a result previously proved by someone else, give a reference to the paper containing their proof. It is often also helpful to give a formal statement of their theorem. You do not need to include the proof in your paper unless you think it will be specifically helpful to the reader (for instance, if you are planning to extend the same ideas yourself).

  • For an original theorem, not previously proved by anyone else, give a complete and careful proof.

  • This is a great comment! Thank you for taking the time to type this all out. I have another question: because I am doing almost a collection of proofs, do you think including the original proof and published critique of it, is necessary? (eg. Gauss's 1799 proof for FTA, in a paper on FTA proofs) – Siyanda Apr 26 '15 at 22:34
  • I haven't ever written a historical survey, but I think you have to make your own judgment about what historical material is relevant. – Nate Eldredge Apr 26 '15 at 23:33
  • Thanks for your prompt response! I've been considering it all day and have since decided against it. – Siyanda Apr 26 '15 at 23:46

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