With Picard's Theorem it could be literally 2, one of statement, one of proof. The last bracket is needed solely because of the trivial accident that the function Omega, unlike its inverse k^2(tau), happens to have no unmistakable name. I'm also not sure that I agree with you that a short dissertation is not 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.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 Regarding the OP's query, I find this question to be very interesting. I downloaded the document you found and I am puzzled.Having said that, I generally prefer fewer such questions (i.e., nontechnical) on MO. It's possible that this is not the thesis but a longer document. I am not going to buy the Pro Quest version of the thesis, linked from Math Sci Net just to figure out what's going on.I had heard the story that Martens had written an unusually short thesis (don't recall if an actual page count was mentioned) from someone who was in NY at the time and knew Martens. @Voloch: I think that you are right about the document that I linked not being the thesis after all.Recently I was asked what the shortest mathematics Ph. Googling around produces a lot of dubious leads that are sometimes difficult to confirm or disconfirm, since Ph. 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. 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. MO seems like a good place to answer such a question definitively.Anyway, my rationale for saying that this question is appropriate for MO is that it's part of mathematical culture.Mathematics dissertations tend to run short even on average, and I have trouble coming up with other disciplines in whichsuch low outliers might even happen.Moreover, this appears like a slippery slope: eventually we'll be comparing how many papers different mathematicans have in the Annals, how many grad students people have had, how many of them got jobs at Harvard, Oxford, Stanford, etc...Moreover, although a short dissertation is kind of a novelty, it's not really all that interesting.