*(Theorem.) An integral function never 0 or 1 is constant. Littlewood goes on to explain the k^2(tau) is the modular function etc., etc. And don't most of us feel that short proofs are interesting?*@Ryan: Questions like that are unlikely to appear on MO because they are readily answerable via the Mathematics Genealogy Project or Math Sci Net. For example, the short papers listed here (search for "Nelson" to get to the list) are all pretty interesting in my mind.

For what it's worth, my thesis was 29 pages (according to ; I don't have a copy of it).

The published version was either 13 pages or 131 pages, depending on how you count it.

The Fary-Milnor theorem is an interesting bit of mathematics and its history is significant. On the question of how short a math dissertation could, theoretically, be, we have Littlewood, pages 39-40 of the Miscellany: The question recently arose in conversation whether a dissertation of 2 lines could deserve and get a Fellowship.

I had answered this for myself long before; in mathematics the answer is yes.

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.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.The official thesis corresponds to Chapter 5 (13 pages) of the monograph (131 pages) that was eventually published.Since that chapter was largely independent of the rest of the work, I thought it would be less hassle to just turn that section in as my thesis.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.(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. Having said all that, I'll refrain from posing the question if a couple other people say they don't like it. The problem with the question is that we can always give examples but, unless someone presents us with an empty thesis, we can't guarantee it is an absolute minimum.(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...

## Comments Shortest Phd Thesis In History

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