I am writing my PhD thesis in mathematics.

It happens frequently that I use results that I don't have a reference for except

  • textbooks stating "it is easily seen that ..." or "it is well-known that..."
  • it is stated on Wikipedia (without proof)
  • I have derived it with colleagues or people from Q&A sites

Then I try to find a source for some time, before I write down a proof by myself. However, most probably, there has been an earlier mention of this result that I could reference instead.

How should I proceed in such cases?

  • 1
    Do the textbooks give a name for the base equation? or at least the context it is written for? That could be a more effective way to search for a citation. I encountered this with field darkening equations, where I had to search out synonyms of the contexts involved. – user7130 Sep 13 '13 at 14:31
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    Whatever you do, DO NOT cite Wikipedia as an authority! The reader might wonder whether you added it to Wikipedia yourself in order to cite it. (But that's no reason not to cite Wikipedia for reasons other than using it as an authoritative source. But remember that Wikipedia articles can change at any time.) – Michael Hardy Sep 13 '13 at 14:53
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    @UV-D True. I was more about what to do instead of giving a straight reference. – Jan Sep 13 '13 at 15:06
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    Wikipedia is the best place to start a search and the worst place to end it. If you cannot prove such "it is easily seen..." results, don't use them unless you can find a scientific reference. If you can prove it, just say also "it is easily seen that..." -because if anybody challenges you, you will be able to prove it to him. – Alecos Papadopoulos Sep 14 '13 at 3:44
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    @jakebeal this question mentions Wikipedia, but it's not really about Wikipedia, so I think the tag is misplaced here. – ff524 Dec 24 '14 at 15:46

If it's a textbook-level result, you could just cite a textbook. Otherwise, if you derived it yourself or with colleagues, no citation is required unless you published that proof earlier (not likely if it's a minor one). But you should definitely thank the people who helped in acknowledgments.

Finally, note that there is a threshold for citation: if a result is trivial, and as such is likely to have been independently demonstrated by many people over time, with no clear historical/seminal work, then you do not need to cite it.

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    Ok, good points. I would of course cite a textbook if the result is proven there (and not left as an exercise). I see the threshold you mention. But it's rather fuzzy. – Jan Sep 13 '13 at 15:04
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    If something is left as an exercise in a textbook you can still cite that textbook as evidence that it's a standard result. If the exercise is tricky you may want to include a proof though. – Noah Snyder Sep 13 '13 at 15:49

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