shortest phd thesis ever

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PhD: Been There, Done That...

• The World’s Shortest PhD Dissertations

“David Lee Rector’s Ph.D. Thesis is just nine pages long plus bio and bibliography, not to mention double-spaced.” [Source & Photo Credit: Ali Almossawi ]

You have probably seen thick dissertations, too heavy to lift with one hand… but have you ever thought of how short a PhD dissertation can possibly be?

Well, John Edensor Littlewood once famously inquired “ whether a dissertation of 2 lines could deserve and get a Fellowship ” – and he seems to have meant it.

Interestingly, some of the world’s shortest PhD theses / dissertations also count among the most famous ones at the same time. Here are the Top 5 we could identify:

24 pages – John F. Nash: Non-Cooperative Games (1950)

17 pages – Albert Einstein: A New Determination of Molecular Dimensions (1905)

16 pages – Edmund Landau: Neuer Beweis der Gleichung / New Proof of the Equation (1899)

13 pages – Burt Totaro: Milnor K-Theory is the Simplest Part of Algebraic K-Theory (1992)

9 pages – David Lee Rector: An Unstable Adams Spectral Sequence (1966)

Please drop us a line if you know any shorter dissertations than the ones above!

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What is the shortest Ph.D. thesis? [closed]

The question is self-explanatory, but I want to make some remarks in order to prevent the responses from going off into undesirable directions.

It seems that every few years I hear someone ask this question; it seems to hold a perennial fascination for research mathematicians, just as quests for short proofs do. The trouble is that it has strong urban-legend tendencies: someone will say, "So-and-so's thesis was only $\epsilon$ pages long!" where $\epsilon \ll 1$ . It will often be very difficult to confirm or disconfirm such claims, since Ph.D. theses are often not even published, let alone readily available online. If you Google around for a while, as I did, you will find many dubious leads and can easily waste a lot of time on wild goose chases. Frankly, I'm a bit fed up with this state of affairs. I am therefore asking this question on MO in the hope that doing so will put this old question to rest, or at least establish provable upper bounds.

I would therefore request that you set yourself a high standard before replying. Don't post a candidate unless you're sure your facts are correct, and please give some indication why you're so sure. Read the meta discussion before posting. (Note that the meta discussion illustrates that even a MathSciNet citation isn't always totally definitive.) Include information about the content and circumstances of the thesis if you know it, but resist the temptation to gossip or speculate.

I'm not making this question community wiki or big-list because it should ideally have a definite answer, though I grant that it's possible that there are some borderline cases out there (perhaps there are theses that were not written in scholarly good faith, or documents that some people would regard as equivalent to a Ph.D. thesis but that others would not, or theses in subjects that are strictly speaking distinct from mathematics but that are arguably indistinguishable from mathematics dissertations).

Finally, to anticipate a possible follow-up question, there is a list of short published papers here (search for "Nelson"). Note that the question of the shortest published paper is not as urban-legendy because the facts are easier to verify. I looked up the short papers listed there myself and found them to be quite interesting. So in addition to trying to settle an urban legend, I am hoping that this question will bring to light some interesting and lesser known mathematics.

• ho.history-overview
• 9 $\begingroup$ I think it really should be CW. It makes no sense to me that the shorter the proposed candidate, the more reputation the proposer will get. It will also lower the temptation for people to post gossipy stuff. $\endgroup$ –  Alex B. Feb 8, 2011 at 15:31
• 3 $\begingroup$ The only reasonable interpretation of the question is extremely short theses in general, because there is more than one measure of the length of a thesis. Moreover in some cases it's debatable whether a particular document really is a thesis or the full thesis. It realy should be CW. $\endgroup$ –  Greg Kuperberg Feb 8, 2011 at 15:40
• 3 $\begingroup$ How would you like to count? Do all the cover pages, table of contents, abstract, etc. count? How about references? Or do you begin with the introduction and only include the content? $\endgroup$ –  Noah Stein Feb 8, 2011 at 16:33
• 5 $\begingroup$ -1. This question is terrible. I'm sure I could reformat my thesis in a silly font size to make it have a ludicrously small number of pages. $\endgroup$ –  Peter McNamara Feb 8, 2011 at 19:50
• 8 $\begingroup$ @Peter McNamara: you probably could, but I'm pretty certain that this is not the issue being discussed here. Anyway, most universities have specific formatting standards and would not let you submit it in this form. $\endgroup$ –  Thierry Zell Feb 8, 2011 at 20:05

9 Answers 9

David Rector's thesis ("An Unstable Adams Spectral Sequence", MIT 1966) is 9 pages, according to the record at the MIT library . I haven't seen the actual thesis for many years, but I'm pretty the actual mathematical content takes about 3 pages total, and is largely identical to the published version in Topology (1966, same title, doi link: https://doi.org/10.1016/0040-9383(66)90025-5 ), which is 3 pages plus bibliography. (Dan Kan, his advisor, likes short papers.)

• 2 $\begingroup$ Probably not a coincidence. $\endgroup$ –  Tyler Lawson Feb 8, 2011 at 20:25
• 3 $\begingroup$ Accepted provisionally. Enough people seem instinctively annoyed at this question that it seems likely to be closed soon (despite the fact that I'm asking it on MO in order to prevent its proliferation elsewhere). It doesn't seem likely that a stronger candidate will emerge before then. Ideally I'd like to examine the thesis myself before accepting the answer but I don't feel like purchasing it and it may be a while before my next trip to Boston. $\endgroup$ –  Timothy Chow Feb 9, 2011 at 15:56
• 4 $\begingroup$ Aside from the library copy, there should be a slightly more accessible copy in the MIT Math reading room. (They used to keep copies of theses there, and I assume they still do.) Maybe somebody reading this could wander down the hall and take a look. :) $\endgroup$ –  Charles Rezk Feb 9, 2011 at 18:55
• 31 $\begingroup$ I'm in the reading room now. Rector's thesis comprises a title page, an abstract page, a table of contents page, 7 pages of math, a bibliography page (8 refs.), and a biographical note page. The MIT library record's "9 leaves" exclude the title/abstract/contents, which are not numbered. Except for some trivial changes in wording in the intro, the mathematical part is indeed identical to the 4-page Topology paper, vol. 5 (1966), 343-346. The thesis occupies more space since it's manually typed; not including section titles, the 4 sections are respectively 18, 23, 42, and 36 typewritten lines. $\endgroup$ –  Timothy Chow Aug 19, 2011 at 18:44
• $\begingroup$ 119 typewritten lines! $\endgroup$ –  David Roberts ♦ Oct 14, 2022 at 10:53

John Nash's thesis was 26 pages, and had two references in the bibliography.

Edmund Landau's thesis was 13 pages long.

• $\begingroup$ There is an English translation here: arxiv.org/PS_cache/arxiv/pdf/0803/0803.3787v2.pdf That document is 17 pages (including title page, etc.). $\endgroup$ –  Zach N Feb 8, 2011 at 18:06
• 2 $\begingroup$ For a link to a scanned version of Landau's thesis see here gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN317979566 The document has 18 pages, of which 2 are completely empty, indeed the catalogue of the libraries of Berlin gives 16 pages as lengths. (the French national library catalogue gives 18). Moreover, one page is a title page, one is a dedication, and one is a vita. So, depending on what one actually counts, 18, 16, or 13. According to library catalogues 16 or 18. $\endgroup$ –  user9072 Feb 8, 2011 at 18:15

I believe the shortest PhD thesis is of Burt Totaro "Milnor K-theory is the simplest part of algebraic K-theory", 12 pages.

Milnor K-theory is the simplest part of algebraic K-theory, Ph.D. thesis, University of California, Berkeley, 1989; published as: K-Theory 6 (1992), 177-189 ( Portico archived version ).

Burt Totaro's webpage at Cambridge , including a pdf of the published version .

• 1 $\begingroup$ its complete thesis. I gave two references here, Milnor K-theory is the simplest part of algebraic K-theory, Ph.D. thesis, University of California, Berkeley, 1989 and K-Theory 6 (1992), 177-189 $\endgroup$ –  J Verma Feb 8, 2011 at 17:43
• 2 $\begingroup$ I noticed, but the reference to the actual thesis does not have a page numbers (and it is somewhat surprising that the number of pages did not change from the thesis to K-theory's format) :) $\endgroup$ –  Mariano Suárez-Álvarez Feb 8, 2011 at 17:45
• 15 $\begingroup$ Totaro's 1989 thesis is titled "K-theory and algebraic cycles" and, according to ProQuest, is 20 pages. If your university library subscribes to ProQuest, you can see a PDF preview of the thesis by searching for "Totaro, Burt" in the Dissertations and Theses database. $\endgroup$ –  Zach N Feb 8, 2011 at 18:02
• 4 $\begingroup$ You can download it on mathscinet. It has 16 numbered pages, incl. 1 page of bibliography. Definitions start on page 1 though, not much of an introduction. $\endgroup$ –  fherzig Feb 9, 2011 at 2:58
• 1 $\begingroup$ I downloaded the thesis from ProQuest. It comprises a signature page, a title page, an abstract page, an epigram page, 15 pages of (TeXed) math, and a bibliography page. Short, but not as short as David Rector's thesis. $\endgroup$ –  Timothy Chow Aug 19, 2011 at 19:00

This is not really an answer because these PhD's were never actually written, but anyway: in his book A mathematicians miscellany (in the chapter on math with minimum raw material) Littlewood gave 2 examples that could have been 2-line PhDs:

(1) Cayley's projective definition of length

(2)Theorem: An integral function never 0 or 1 is a constant. Proof: $\exp(i\Omega(f(z)))$ is a bounded integral function. ($\Omega$ is inverse to the elliptic modular function.)

• 3 $\begingroup$ Richard, perhaps you overlooked that Gerry Myerson already gave this example on the meta discussion? $\endgroup$ –  Timothy Chow Feb 8, 2011 at 15:53
• 19 $\begingroup$ I don't think it is reasonable to expect people to have read all the meta discussion before posting on a regular thread. This is a sort of fluff question, so it doesn't matter much, but in general I think it should be fine to repost answers from meta, so that the main thread has the most complete record of answers to the question. $\endgroup$ –  David E Speyer Feb 8, 2011 at 16:52
• 7 $\begingroup$ While I agree with David Speyer in general, I also do not think this should have been posted as an answer to this particular question, given the questioner's emphasis on restricting the scope of the question. $\endgroup$ –  Charles Staats Feb 8, 2011 at 17:27
• 6 $\begingroup$ @David: I too would agree that in general it’s not reasonable to expect people to read meta discussions on questions before answering them. But this question specifically asks us to, and gives good reasons for it. $\endgroup$ –  Peter LeFanu Lumsdaine Feb 8, 2011 at 20:18
• $\begingroup$ (2) is a trivial corollary of Picard's little theorem. $\endgroup$ –  tst Jun 13, 2017 at 3:06

I already posted this on meta where there was some discussion of whether the page count was correct. My guess is that it is, so I will post it here too:

MR2615548 Martens, Henrik Herman Buvik A NEW PROOF OF TORELLI'S THEOREM. Thesis (Ph.D.)–New York University. 1962. 12 pp.

• 8 $\begingroup$ Compared to that, the thesis of his student Kristian Seip was a massive tome, weighing in at 30 pages. $\endgroup$ –  Harald Hanche-Olsen Feb 9, 2011 at 7:56

Kurt Gödel seems to be a good candidate for this "prize".

Let me quote from this review (see Page 74) of Kurt Gödel Collected Works.

The first three works of Godel in this volume are his dissertation of 1929 ( twenty-one pages in English ), a revised and substantially abbreviated version (eleven pages in English) published in 1930, and a brief abstract based on a presentation of Godel's results in Konigsberg on 6 September 1930. Of all of Godel's longer, published writings, his dissertation has been, until now, the most difficult to obtain, and is here translated for the first time into English, by Stefan Bauer-Mengelberg and van Heijenoort.

• 3 $\begingroup$ The original version of his thesis seems to have 33 pages; see permalink.obvsg.at/AC05181322 (the number next to "Umfangsangabe") $\endgroup$ –  user9072 Feb 8, 2011 at 16:59
• 2 $\begingroup$ I cannot say anything about the original version (my German skills are null, not almost null). But I have just checked my copy of the Collected Works (unfortunately I have not found any online library to link), and in pages 60-101 we can find Godel's dissertation (even pages match German, while odd ones match English). Thus, the description "21 pages in English" is accurate. $\endgroup$ –  boumol Feb 8, 2011 at 17:14
• 1 $\begingroup$ I did not want to imply your claim was not accurate. Only, as I understand the question, it is about the actual document the person submitted as a thesis. Thus, I supplemented this information, documenting it by the link to the entry of Goedels thesis in the joint library catalogue of Austrian (academic) libraries. It specifies title, author, year, lengths (that's the Umfangsangabe, S. abbreviates 'Seiten' i.e. pages), the type of document (thesis of University of Vienna (Wien)), and finally the specific libraries where it can be found. $\endgroup$ –  user9072 Feb 8, 2011 at 17:48

According to mathscinet, Eva Kallin's thesis was 14 pages.

• 3 $\begingroup$ This is promising, but as the question mentions and the meta thread shows, MathSciNet alone is not an authoritative reference. More documentation? $\endgroup$ –  Peter LeFanu Lumsdaine Feb 8, 2011 at 20:12

Barry Mazur's thesis on the proof of the Schoenflies conjecture (and introducing the method of infinite repetition in topology) is 5 pages long.

• 4 $\begingroup$ According to "Mathematical apocrypha redux" by Krantz, Mazur's thesis was 26 pages long. $\endgroup$ –  Michael Greinecker Feb 8, 2011 at 16:22
• 2 $\begingroup$ Mathscinet says his thesis is 30 pages. $\endgroup$ –  Jaikrishnan Feb 8, 2011 at 16:26
• 70 $\begingroup$ Well, it may not be the shortest but it surelyt appears to have the most variable number of pages! $\endgroup$ –  Mariano Suárez-Álvarez Feb 8, 2011 at 16:42
• 17 $\begingroup$ Let's please heed Timothy's call to do one's homework carefully. "Don't post a candidate unless you're sure your facts are correct, and please give some indication why you're so sure. Read the meta discussion before posting." $\endgroup$ –  Todd Trimble ♦ Feb 8, 2011 at 16:47
• $\begingroup$ Yikes. I had never looked at the thesis, but just the published version in the Bulletin of the AMS which is 5 pages long. $\endgroup$ –  Victor Miller Feb 23, 2011 at 22:12

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Very short PhD Thesis by famous people [closed]

I read that John Nash had a very short PhD Dissertation. A mere 27 pages. See this link:

http://www.princeton.edu/mudd/news/faq/topics/Non-Cooperative_Games_Nash.pdf

Are there other famous people with such short PhD theses? Anyone breaks this 27 page record?

• 1 I can't for the life of me find a reference at this point, but I remember reading that Alzheimer's thesis was 11 pages. (but, you know, different times and such) –  xLeitix May 26, 2015 at 7:58
• 2 Assuming it is a math thesis, this has been answered at mathoverflow.net/questions/54775/… . There is a reference in that question to a 9 page thesis. –  StrongBad May 26, 2015 at 8:00
• 2 I do not see how this is going to be anything but a random list of short theses with little value to anyone. –  StrongBad May 26, 2015 at 8:03
• @StrongBad: I agree, asking for the shortest PhD thesis would be a way to limit the list, as only answers beating the current leader would be acceptable (and such questions do work on many Stack Exchanges), however things get problematic here as there is the another diffuse criterion of fame (unless one argues that having the shortest PhD thesis in history alone suffices to make you famous). –  Wrzlprmft ♦ May 26, 2015 at 9:42
• 2 @curious_cat no, the theses have value, what I do not see is the value of listing them. –  StrongBad May 26, 2015 at 9:51

Barry Mazur's thesis "On Embeddings of Spheres" runs 17 pages, as far as I can tell from the paywalled source here: http://link.springer.com/article/10.1007%2FBF02559532

• 3 There is some debate about that over at MO.SE with a page count as low as 5 and as high as 30. –  StrongBad May 26, 2015 at 8:01

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What was the shortest PhD thesis in physics? [closed]

When I took freshman physics in 1983, my professor made an off-handed comment that Louis de Broglie's PhD thesis on the matter wave was only 3 pages long, and that it was the shortest PhD thesis ever in physics.

For some time now I've been trying to find a PhD of the thesis, which I presume is in German. I can't find it.

I have found the proper reference to his doctoral thesis, though. It appears to be:

L. de Broglie, “Recherches sur la théorie des quanta”, Thèse de doctorat soutenue à Paris, le 25 novembre 1924, Annales de Physique (10e série) III (1925) 22. Reproduced in: L. de Broglie, Recherches sur la théorie des quanta (Fondation Louis de Broglie, Paris, 1992).

I've searched online for that document, and I can't find it. I can find another publication with the same title , but it appears to be a book based on the PhD thesis, and not the thesis itself.

So what is the shortest PhD thesis in physics, and if it is de Broglie's, where can I find it?

• soft-question

• 2 $\begingroup$ I'm voting to close this question as off-topic because it's about publication lengths rather than physics. $\endgroup$ –  Qmechanic ♦ Dec 25, 2019 at 15:04
• 3 $\begingroup$ It does not look like de Broglie's thesis was 3 page long. According to American Journal of Physics 44, 1047 (1976), "De Broglie's thesis was published in its entirety in Ann. Phys. (Paris) 3, 22 ( 1925)." This publication's reprint can be found at tel.archives-ouvertes.fr/tel-00006807/document and it is about 80 page long. $\endgroup$ –  akhmeteli Dec 25, 2019 at 15:17
• $\begingroup$ @Qmechanic, this question is about the practice of physics. There is no physics without scientific publications. $\endgroup$ –  vy32 Dec 26, 2019 at 10:50

Not really answering your question but perhaps you'll find this amusing: In 1951, a two-sentence, three-line paper was published in Physical Review by Friedrich Lenz who simply noticed that the (present) proton-electron mass ratio of $1836.12\pm 0.05$ happened to coincide with $6\pi^5=1836.12.$ You can find the article here , or for those without access here is a screenshot .

• 1 $\begingroup$ Thanks for such an informative answer. It has given me so much hope that Physics and Maths aren't just for geniuses. I'm really grateful to you. $\endgroup$ –  user240696 Dec 25, 2019 at 15:05
• $\begingroup$ The Lenz case shows that some physicists, and journal editors, find numerology irresistible. Lens had absolutely no reason for thinking this ratio ought to be that value, and it isn’t. $\endgroup$ –  G. Smith Dec 26, 2019 at 1:15
• $\begingroup$ That is totally cool. Thanks. $\endgroup$ –  vy32 Dec 26, 2019 at 10:50
• $\begingroup$ The Lenz article was fun, but the relationship no longer holds. Alas. $\endgroup$ –  vy32 Dec 27, 2019 at 9:40

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