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I am in the process of writing a paper which proves some conjecture.

What I want to know is: Is it standard practice to include general commentary on the conjecture and other research around it as references, even when I didn't need any of it to come up with the proof?

If it is standard, accepted practice, what would be the implications of not including it anyway and trying to publish?

Daniel
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    "I didn't need any of it to come up with the proof?" How do you know the conjecture exists? How do you know the conjecture has not been proven? Don't you need reference to answer these two questions? – Nobody Dec 07 '22 at 07:04
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    Well, someone told me the conjecture and that it hadn't been proven. I then checked wikipedia that indicated it hadn't been proven. Then I discovered a proof for it. I've already referenced the conjecture itself. I can talk about current research on the problem fairly easily afaik, but wasn't sure how important it was in this scenario. – Daniel Dec 07 '22 at 10:13
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    I think your question is essentially answered in the one I linked above, so I voted to mark it as a duplicate, but if that doesn't answer your question, please say why. – Kimball Dec 07 '22 at 12:14
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    The paper will almost certainly be rejected if you do not provide some context of other work on the problem. You have to explain why your work is new and what it provides which is not provided by existing works. Why would anyone care about your proof? You must explain this in the article. – Tom Dec 07 '22 at 13:28
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    I would imagine the Wikipedia page you checked references a paper that posed the conjecture in the first place: you should too. – chepner Dec 07 '22 at 14:27
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    You can't provide a solution without describing the problem first, and you can't describe a problem you didn't formulate without citing whoever did formulate the problem. – chepner Dec 07 '22 at 14:32
  • Is this paper being written for self-glorification or to add to the overall body of knowledge? References aren't 100% related to credit for credit's sake. A lot of referencing is to provide a roadmap to the ideas that led to the conclusion. – David S Dec 07 '22 at 16:50
  • In addition to all good answers, let me just add that there are also political reasons. People who feel they did something related and are deserved to be cited will not like it that you did not cite them. (Note also that the other extreme where you cite too many people just so is also a bad practice) – Yanko Dec 08 '22 at 04:52
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    If the conjecture is famous enough to be mentioned on Wikipedia, then there is no way to prove it without heavily building on previous work. – Tobias Kildetoft Dec 08 '22 at 08:22
  • I highly recommend reading more papers, as I will gently suggest that you haven't read that many. I don't know of any field in which the standard isn't to list many references in the Introduction that give context and background to the problem, and this introduction style should be second nature to you long before you begin writing your own paper. – Jerome Dec 08 '22 at 22:20
  • For fun, I was looking at articles being famous for being very short, like this counter-example to a conjecture by Euler (https://www.openculture.com/2015/04/shortest-known-paper-in-a-serious-math-journal.html) or this short proof of a theorem by Fermat (https://people.mpim-bonn.mpg.de/zagier/files/doi/10.2307/2323918/fulltext.pdf) but even those ones refer previous work – Taladris Dec 08 '22 at 23:25
  • So sum up a number of these questions. I'm not referring to referencing the original conjecture. That one seems like a given. I was more considering additional works and papers that advance the knowledge. Seeing as my proof didn't use any previous work to build upon, I wasn't sure the expectation of referencing this material. I also wasn't sure if there was a difference between a proof paper and research paper. In seems that I should read more papers on the topic and reference these papers to highlighted how my proof is different from exisisting research and how it can benefit the field. – Daniel Dec 10 '22 at 09:25

2 Answers2

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An academic paper is not used as evidence that you can do something so you can be judged on it, like a paper for a course might be. It's meant to advance knowledge in some area. You don't get "points" only by making no mistakes in your proof.

If you haven't shown the current state of knowledge, you've failed to demonstrate how the paper advances knowledge. Your proof might be valid, but you haven't shown why anyone should care, and you haven't demonstrated that you have done something new that no one else did before you. References to other work positions your work relative to the field as a whole.

Bryan Krause
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If you cannot provide context to your problem, who will be interested? You also want to show how your proof differs from or builds on the work of others.

Both of these are reasons for desk rejection; in fact one question that is often asked of referees is if the manuscript refers to most recent work on the topic.

ZeroTheHero
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  • I don't disagree, but if I was to, for example, come up with a proof for P=NP, would not the subject itself bare enough interest for people to read? That eing said, how would I determine what references should be added if there is a lot of work on the topic but not related to my proof? – Daniel Dec 07 '22 at 10:15
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    Yes it would be interesting enough, but even then you need to place your work in proper context citing appropriate references. If there is a lot of prior work, you can choose a sample representing the most important developments and the current state-of-the-art. – Kimball Dec 07 '22 at 12:11
  • @Daniel your paper would rather soon become the most cited paper on the planet. I think you might want to make sure that it is 101% perfect – SirHawrk Dec 07 '22 at 12:58
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    @Daniel: if there is a lot of work on the topic but not related to my proof -- Perhaps I'm missing something, or perhaps you haven't given enough context, but to get an idea of how background stuff is handled in your subfield it seems to me that you could look at how these other papers on the topic handle their background stuff. Also, you could quickly glance at how background stuff is handled in a few dozen randomly selected papers in a generalist mathematics journal (example 1 and example 2). – Dave L Renfro Dec 07 '22 at 13:30
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    @Daniel If you claim to solve a big open problem it's probably even more important that you reference other work to demonstrate your understanding of the situation of the field, otherwise you'll clearly appear as a crank. It's really common in crankery that someone claims to solve a problem and their error isn't that they made some stepwise error in their proof but that they never understood the nature of the problem in the first place, so they've instead proven something trivial and unrelated to the actual problem. – Bryan Krause Dec 07 '22 at 14:27
  • @Daniel - Take your example, you'd still want to cite the papers that show why P=NP is an interesting problem and how your proof actually relates to the problem – ScottishTapWater Dec 07 '22 at 14:53
  • @BryanKrause: For the specific case of P≠NP, it also helps to be aware of how not to prove it (although I'm not suggesting anyone should cite that page!). – Kevin Dec 07 '22 at 18:39
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    @BryanKrause You raise a good point. As much as I believe I've solved this problem, I would prefer to be correct and not come across as a crank. It seems I'll need to prioritise further research in the field. – Daniel Dec 10 '22 at 09:27