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I am an undergraduate student with no experience at all.

If you are writing a research paper, that you are planning to submit for publication, how do you state that a particular statement/fact is commonly known to all and it's dicoverer/inventor is not known, and that there exists no research paper that introduced the concept but there do exist various books/websites that discuss the very concepts and a few derivatives of the concept?

I am not able to cite a particular statement/bunch of statements as I am not able to find any research paper related to that at all.

The particular thing in question is: https://math.stackexchange.com/questions/161661/source-of-probably-the-most-simplest-math-trick

What should I do?

11

You don't need to cite common knowledge. If you think it is common knowledge, wait for the reviewer to ask for a reference, before going to all the trouble of sorting out the history. Often if a reviewer doesn't think the statement is common knowledge he/she will suggest a reference or provide a conflicting reference.

17

If you found a book that discusses the statement, and you really can't track down where it comes from (does the book cite anything?), then citing the book (with chapter/page numbers) is acceptable.

  • Track down as far as you can, until you get to the first study in the field ever. – Erkin Alp Güney Feb 1 '17 at 17:26
8

If the statement/concept/idea that you think you want to cite is covered (without citation) in the introductory undergraduate textbook(s) on the subject, then it is likely common knowledge in the field. This is particularly true in science and social science. For example, you should not need to cite things like the following:

  • Fluorine atoms are more electronegative than carbon atoms.
  • Asexual reproduction of eukaryotic cells usually occurs by mitosis.
  • Force is a vector quantity, while power is a scalar quantity.
  • The free market equilibrium price for a commodity is found at the intersection of the supply and demand curves for that commodity.
  • Sigmund Freud is commonly considered the founder of psychoanalysis.
  • Thanks for that but it's in the topic of recreational mathematics - and there is no undergraduate course for that at all. – user557 Jun 27 '12 at 17:01
  • 1
    Check out the references and links at the bottom of the wikipedia page on recreational mathematics. Look for the good references that those references reference. – Ben Norris Jun 27 '12 at 17:29
5

I will answer your question in a somewhat sideways manner: I think anyone who is trying to write a math research paper who does not already have a PhD in mathematics or a closely related field should do so in close consultation with an adviser who does have such a PhD. It is not practical to learn all the standards of journals and publishing on your own. Virtually every undergraduate is also in the following situation: their own perspective on mathematics is not yet mature, and thus if they submit a paper to a research journal they will be submitting their work to an audience with far more experience and background knowledge. (A few truly brilliant undergraduates do work up to the standards of other mature, professional mathematicians, but even for them the work is probably much less than what they will be capable of later on. I can't think of a single instance of a professional mathematician whose undergraduate work was in the same league as their later research.)

In fact -- and I don't mean to be discouraging by saying this -- most research done by undergraduates is not of a publishable quality. This does not mean that undergraduates should not engage in research -- I think it is very valuable and enjoyable for them to do so (if anyone cares: I did research as an undergraduate, had a blast doing it, and did not try to publish it) -- but only that formal publication should probably be a goal for later in one's career than that, especially nowadays when it is so easy to put your work on the web.

In particular, you write

a particular statement/fact is commonly known to all and its discoverer/inventor is not known, and that there exists no research paper that introduced the concept but there do exist various books/websites that discuss the very concepts and a few derivatives of the concept?

Honestly, this sounds unlikely to me. The vast majority of mathematical topics that are discussed in books are also discussed in research papers (maybe it is somewhat different in recreational mathematics, but even there I imagine it's still mostly true). How do you know that no research paper treats the concept in question? Searching the mathematical literature is itself a skill that takes both general experience and specific expertise in the subfield you're searching in: as a research mathematician it is common enough for me to come across a mathematical concept, try to find it in the literature, and only find it several weeks or months later when I have become more familiar with the local terminology and standard results. Similarly, most mathematical concepts are traceable to a specific discoverer/inventor, although admittedly the generic mathematician does not feel as honorbound to track down primary sources as academics in most other fields (in my opinion this is a rare "character flaw" of the generic mathematician!).

Even if you have done all the mathematical research yourself, consulting an experienced adviser on how to write up and submit your work could save you a lot of time and headache. Some journals/editors/referees are relatively supportive of authors writing their first paper (everyone who has published a paper was in that situation at one time!), but if your paper is, or looks to be, below the level of papers they want to publish, it will probably get bounced back to you with little constructive criticism. An adviser can be much more kind...

  • I have always felt the need of an advisor, I was in school when the idea first stuck me, I contacted my teachers in school but none of them showed any interest in helping me. Now I am in a university with Computer as my major - taking your advise I will contact math teachers in my university soon. The particular fact that I want to site is this extremely simple math Trick: math.stackexchange.com/questions/161661/… Do you have an Idea of it's source? – user557 Jul 4 '12 at 8:04
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One helpful approach can be to ask a few people that you think of as familiar with the field (in your case, this could be professors or certain other students). Even though most schools offer no class in recreational mathematics, you can ask 3 or 4 people who you see as at least "intermediate" level (whatever that means) in recreational math. If all of them immediately recall the information in question, then it's a good bet that you don't have to cite it. Alternatively, if most of them don't know it, then perhaps you should cite it.

Specifically for recreational math, I recommend that you ask around on the website Art of Problem Solving: http://www.artofproblemsolving.com/ (from the front page, click on "online community"). This site is focused on contest mathematics, which is distinct from recreational math, but a close cousin (and many people interested in one are also interested in the other).

  • I did post it as a question: math.stackexchange.com/questions/161661/… before asking this question. – user557 Jul 4 '12 at 8:17
  • @myselfpoddar Yes, that post of yours looks fine. For this particular fact, I agree with the answers you received: you really don't need to cite anything. I say that because your trick is an immediate consequence of algebra (by that I mean "college algebra" that is taught in grade 9 or earlier). – Dan C Jul 4 '12 at 14:03

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