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Recently I was asked what the shortest mathematics Ph.D. thesis on record is. This is not the first time I have encountered this question—it seems to be perennially fascinating to research mathematicians—but as you can imagine, finding the answer to such an urban-legendy question is not easy. Googling around produces a lot of dubious leads that are sometimes difficult to confirm or disconfirm, since Ph.D. theses are often not published.
MO seems like a good place to answer such a question definitively. It is similar in genre to a question recently asked by Greg Kuperberg that tries to straighten out the facts about a particular widely circulated urban legend.
However, after seeing several discussions here on meta about non-technical questions, I get the impression that a sizable number of regular participants don't want questions like this on MO. Should I pose it or not?
@Ryan: Questions like that are unlikely to appear on MO because they are readily answerable via the Mathematics Genealogy Project or MathSciNet. The short Ph.D. thesis question is not so easy to answer reliably.
I'm also not sure that I agree with you that a short dissertation is not interesting. It's true that it isn't necessarily interesting. However, provided that the dissertation was produced in good faith (as opposed to being a publicity stunt or a mere formality or something), it is about as interesting as a "short proof" is. And don't most of us feel that short proofs are interesting? For example, the short papers listed here (search for "Nelson" to get to the list) are all pretty interesting in my mind. (By the way, note that the "shortest paper" question doesn't have the same urban-legend tendencies because it's much easier to verify the facts.)
But let me state explicitly my main reason for wanting to ask this question on MO: I'm kind of sick of hearing this question asked yet again and having no rebuttal to urban-legendy responses of the form, "So-and-so's dissertation was only epsilon pages long!" where epsilon is a positive real much less than 1. It would be nice to put this question to rest.
Having said all that, I'll refrain from posing the question if a couple other people say they don't like it.
I think the question is fine. It is soft, but it is closely linked to the culture of mathematics, and I think it will be of interest to many.
(It is certainly at least as good as a previous question of mine, "Which pair of mathematicians has the most joint papers?")
@Voloch: When I look at Martens' thesis (it is freely available online), it seems longer than 12 pages to me... 32 leaves seems to be about right to me based on the scanned pdf I downloaded (this includes introduction, appendix, bibliography, etc). I downloaded it from http://www.archive.org/details/newproofoftorell00mart
Regarding the OP's query, I find this question to be very interesting. Having said that, I generally prefer fewer such questions (i.e., nontechnical) on MO. So I will sit on the fence.
@Voloch: I think that you are right about the document that I linked not being the thesis after all. Besides the fact that it actually says that it is a report (which I obviously didn't look at closely enough the first time!), it is lacking other things that one might expect to find in a dissertation (acknowledgements, declaration of originality, etc).
I apologize for any confusion brought about by my earlier claim that it was Martens' thesis.
I'd always heard that David Rector's thesis (at MIT) was remarkably short, but I can't seem to access it from the web. The publication based on it (Rector, David L. An unstable Adams spectral sequence. Topology 5 1966 343–346) could only be called 4 pages if one was generous.
@David: Regarding your question about the longest thesis, wasn't Jacob Lurie's somewhere in the neighborhood of 1000?
To bring the conversation back to the original purpose: I don't think that this is a suitable MO question. The Milnor legend is not a suitable case to base an argument on, and even if that was considered passable (I didn't see it until the matter had actually been resolved so please don't read anything into my not voting to close) then it was barely so. This question is considerably looser, considerably more pointless, and considerably harder to verify an answer to.
If this question appears on MO, I will vote to close.
@Andrew Stacey: the question has already appeared on MO.
... as has my vote to close.
(I tend to check meta before MO and as there wasn't a comment here saying that the question had been posted then I assumed that it hadn't yet appeared on MO and so left my comment. I do think that if a question that has been discussed in advance on meta is posted then a link should be given here. As no one else did so, here it is.)