Math SE references in thesis

Question

I am writing my bachelor's degree thesis and have used a number of Math SE (and a Physics SE) question as references. My thesis supervisor is a bit unsure how appropriate this is. I used them mainly not to find other (maybe printed) references for the proofs I wanted references for. So I was wondering: how common is it for math papers/books to use SE references? Is it appropriate for my thesis?

Update

Some examples: [1], [2], [3], [4], [5], [6]. [1] is one I may decide not to include because it might happen that the part where it is cited is cut out of the thesis. [2] (spectral theorem) is a typical example of what I mean: I wouldn't include that in the thesis, since it should be known from Linear Algebra (isn't to me, but anyways), and my thesis is a Geometry thesis. [3] (closed unit ball of Hilbert space is weakly sequentially compact) is another typical "immense" proof which I surely wouldn't include in the thesis, because of its length, and because my thesis is about symplectic geometry and only uses this to prove an existence result for periodic orbits of Hamiltonian fields on strictly convex hypersurfaces of $\mathbb{R}^{2n}$. Still, I would like to reference a proof of these. I could reference a book, but it would have the disadvantage that the proof has bits spread out over various chapters for [2], and that some results are in another book for [3]. I might well include [4]. I believe I will find [5] in Rudin, it's bound to be there somewhere after all. As for [6], the only reason I have that reference is that my supervisor told me not to make the thesis too "heavy" and to remove that proof (and those of 4 other related results, plus another proposition that says a bilinear form induces an isomorphism from the space to the dual).

Update 2

The above are all my Math SE citations. There is also a Physics SE citation which is a self-answer about the physical meaning of the Lagrangian -- well, the action actually. This in turn contains a link to a Feynman pdf, which is very authoritative. However, I would like to keep the citation to the self-answer and the other answers.

Update 3

Just replaced [5] with Rudin, with precise reference to theorem 3.11 on pp. 67-68. Saving all other links as htmls on my computer in a sec.

Update 4

[1] integrated into thesis; [2] turned to appendix; [3] is too long to turn into an appendix, and no book has such completeness on this, so finding references in books would require tons of references and require the reader to have 3-4 books and look for the results in each of them to piece the proof together, absolutely unacceptable; [5] cfr [1]; [6] removed from thesis because the part that called it has been removed. A few others also removed and integrated into thesis or made to vanish completely. Physics.SE reference kept, I do not know where to look to find what those answers contain. This is my "compromise", let's see what my supervisor says.

Answer 1

[H]ow common is it for math papers/books to use SE references?

I don't think this is common.

Is it appropriate for my thesis?

I would ask your advisor. Ok, so you already did that. And I think this will be dependent on personal opinions. But I would say that this is up to the advisor (and/or committee). You might even ask your (graduate) college about their guide lines for using online sources (yes, they probably wouldn't know anything about Math.SE).

If I was the advisor, I would say that you shouldn't do this. Usually I would think of citations as being to things that are published (and maybe even peer reviewed) in authoritative publications. This is certainly not always the case, but it should be the general rule. It is easy to find all kinds of stuff online that you could cite in support of pretty much anything. But it is harder to support something if you rely on only published results.

Also, I would like to be able to read your thesis in 20 years and be able to check your sources. There is not guarantee that Math.Se exists in 20 years. And there is no guarantee that links are the same as they are today. If you do decide to cite Math.SE then I would at least print out the pages and maybe include them as appendices in your thesis.

Because of this, I would also, in general, also advice against citing Wikipedia in a thesis.

A thesis is a formal document. With a homework assignment or even a semester project, I wouldn't care.

Now, I don't know your specific situation and exactly what our thesis covers and I could maybe see a situation where references to Math.SE would be appropriate, but, again, in general I would say no. I wonder, for example, if you can't just include the proofs in your thesis. In this case it doesn't mean that you shouldn't cite where you found the proof, but I wouldn't cite Math.SE as an authoritative source.

Answer 2

Not all references are the same. Very roughly, some references are there to establish what is true and others are there to establish who is to get the credit. (Of course some will serve both purposes.)

For the latter, references to math.SE, MO etc. are good. It is not uncommon to even reference inaccessible sources to this end, as "private communications" or something.

For the former, I would recommend more caution, since the credibility of the source might not be considered as high enough for that end, especially not when you quote yourself. Instead you should either dig up sources with more credibility or make your work more self-contained. The proposal in Thomas's answer to include the information as appendix seems good to me: I would even go for a traditional appendix, not a reproduction of the pages. You can and like should still mention if math.SE was helpful, but I think you should not use it to outsource part of your work.