shortest math dissertation

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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. Commented 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 Commented 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 Commented 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 Commented 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 Commented 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 Commented 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 Commented 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 Commented 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 Commented Aug 19, 2011 at 18:44
• $\begingroup$ 119 typewritten lines! $\endgroup$ –  David Roberts ♦ Commented 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 Commented 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 Commented 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 Commented 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 Commented Feb 8, 2011 at 17:45
• 16 $\begingroup$ 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 Commented 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 Commented 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 Commented 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 Commented 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 Commented 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 Commented 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 Commented Feb 8, 2011 at 20:18
• $\begingroup$ (2) is a trivial corollary of Picard's little theorem. $\endgroup$ –  tst Commented 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 Commented 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 Commented 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 Commented 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 Commented 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 Commented 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 Commented Feb 8, 2011 at 16:22
• 2 $\begingroup$ Mathscinet says his thesis is 30 pages. $\endgroup$ –  Jaikrishnan Commented 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 Commented 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 Commented 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 Commented Feb 23, 2011 at 22:12

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John Nash’s Super Short PhD Thesis: 26 Pages & 2 Citations

in Math | July 9th, 2018 2 Comments

When John Nash wrote  “Non Coop­er­a­tive Games,”   his Ph.D. dis­ser­ta­tion at Prince­ton in 1950, the text of his the­sis ( read it online ) was brief. It ran only 26 pages. And more par­tic­u­lar­ly, it was light on cita­tions. Nash’s diss cit­ed two texts:  John von Neu­mann & Oskar Mor­gen­stern’s  The­o­ry of Games and Eco­nom­ic Behav­ior   (1944), which  essen­tial­ly cre­at­ed game the­o­ry and rev­o­lu­tion­ized the field of eco­nom­ics; the oth­er cit­ed text, “Equi­lib­ri­um Points in n‑Person Games,”  was an arti­cle writ­ten by Nash him­self. And it laid the foun­da­tion for his dis­ser­ta­tion, anoth­er sem­i­nal work in the devel­op­ment of game the­o­ry, for which Nash won the Nobel Prize in Eco­nom­ic Sci­ences in 1994 .

The reward of invent­ing a new field is hav­ing a slim bib­li­og­ra­phy.

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Note: An ear­li­er ver­sion of this post appeared on our site in June, 2015.

Relat­ed Con­tent:

The Short­est-Known Paper Pub­lished in a Seri­ous Math Jour­nal: Two Suc­cinct Sen­tences

The World Record for the Short­est Math Arti­cle: 2 Words

Free Online Math Cours­es

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by OC | Permalink | Comments (2) |

Related posts:

Comments (2), 2 comments so far.

Some­times doc­tor­al dis­ser­ta­tions are long on foot­notes and bib­li­og­ra­phy — and short on orig­i­nal think­ing. John Nash reversed the aca­d­e­m­ic trend. Reminds me of the Renais­sance painter who was asked for evi­dence of his abil­i­ty to draw. He drew a near-per­fect cir­cle on a can­vas, and was accept­ed by the mas­ter as an appren­tice.

Excel­lent con­cept and articles.…worth reading.…pl for­ward more read­ing

Thanks and regards

Dr B Vijay Sarthi

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Doctorandum

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: Eine neue Bestimmung der Moleküldimensionen (1905) / A New Determination of Molecular Dimensions (1906)

16 pages – Edmund Landau: Neuer Beweis der Gleichung (1899) / New Proof of the Equation (2007)

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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So Many Papers, so Little Time

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The Shortest Papers Ever Published

This blog post is about short papers. It seems out of place writing a long introduction.

If you ever wondered about the shortest papers ever published, or you just want to take the unique opportunity to read several papers in full within one minute, this post is for you.

Math can be short

Math can be hard and tedious resulting in very long papers. The 1995 proof of Fermat’s last Theorem was 108 pages long.

But math can also be short.

Lander and Parkin’s paper about a conjecture by Euler (related to Fermat’s last Theorem), is probably the dream of everyone ever written a paper: It answers an interesting and important question, it’s correct beyond any doubt,  it’s easy to understand and only two sentences long.

Is there a way to beat that? John Conway and Alexander Soifer submitted a paper in 2005 with the goal to  write the shortest math paper ever.

It is only two words long and contains two distinct proofs of their problem in two figures.

The editors were a bit surprised: “The Monthly publishes exposition of mathematics at many levels, and it contains articles both long and short. Your article, however, is a bit too short to be a good Monthly article. . . A line or two of explanation would really help.”

The authors did not give up and could convince the editors: “I respectfully disagree […] What else is there to explain?” Read the full story .

Empty pages

Can you  write a meaningful paper shorter than 2 words? Probably not. Still, I want to mention the following case report of severe writer’s block, which contribute important zero words to the literature:

Also the following zero-word paper (excluding the abstract) makes an important point. Originally submitted to Nature Chemistry it did not make the cut for publication. But the editors liked it so much that they covered it in their blog  and their production team produced a print PDF for it. It finally appeared in 2016  in the journal “ Chemie in unserer Zeit ” (50(2), 144–145)  published by Wiley. It’s a German journal but don’t worry. The empty pages should be easy to read even in German…

Short abstracts

Abstracts should be short by definition. But some are shorter than others. These are the shortest we could find:

Enough already

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Short but Substantial Math Papers [closed]

I am looking for short papers that made a significant impact on the mathematics community. I have already seen: interesting-but-short-math-papers and, What is the Shortest Ph.D. Thesis? on math overflow, but these weren't quite what I was looking for (although the intersection of the set of answers to this question with the set of answers to either of the above links is likely to be non-trivial)

I am more interested in short and important works of mathematics, not necessarily Ph.D.s (but not necessarily not Ph.D.s either). Things that changed the course of mathematical history, that sort of thing.

Any suggested readings would be very much appreciated.

I realize I was not clear on what I meant by short. around the 20 page or less mark. If it goes higher, but is really something for its size then that is acceptable too.

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• 3 $\begingroup$ A classic in short papers is John Nash's Equilibrium Points in N-Person Games with $1$ page(something which today would maybe not be considered a paper anymore). With $26$ pages a little over, but compensating this through its impact, could be Goedel's Ueber formal Unentscheidbare Saetze der Principia Mathematica und verwandter System, I. $\endgroup$ –  blub Commented Aug 31, 2018 at 13:14
• 3 $\begingroup$ This MO question could also be of interest : mathoverflow.net/questions/7330/… (the first two answers there are the paper by Riemann in Barry Cipra's answer and the Nash one in the comment above). $\endgroup$ –  Arnaud D. Commented Aug 31, 2018 at 13:19
• $\begingroup$ Levin's paper on universal search problems was only 2 pages long, but introduced the idea of NP-completeness in complexity theory (which might stretch your definition of mathematics a bit). $\endgroup$ –  chepner Commented Aug 31, 2018 at 15:19
• $\begingroup$ @chepner: Why is it stretching? P=NP is still an open problem that can be written as an arithmetical sentence (namely one that only quantifies over natural numbers), and even got chosen by the Clay Mathematics Institute as 1 of only 7 Millenium Prize Problems. =) $\endgroup$ –  user21820 Commented Aug 31, 2018 at 16:48
• 1 $\begingroup$ If Riemann hypothesis is wrong and a counterexample is found, the corresponding paper would be pivotal and extremely short : "BTW, here's a non-trivial zero for Riemann zeta function which is outside the critical line : $a+bi$. kthxbye". $\endgroup$ –  Eric Duminil Commented Aug 31, 2018 at 21:40

7 Answers 7

Riemann's short paper, "Über die Anzahl der Primzahlen unter einer gegebenen Grösse," surely qualifies.

• 1 $\begingroup$ I've made this answer community wiki so that upvotes can indicate agreement rather than reward. $\endgroup$ –  Barry Cipra Commented Aug 31, 2018 at 13:36

Not a paper, but definitely significant, is Russell's paradoxical letter to Frege.

• $\begingroup$ I've made this answer community wiki so that upvotes can indicate agreement rather than reward. $\endgroup$ –  Barry Cipra Commented Aug 31, 2018 at 13:36

I would recommend Classics of Mathematics , ed. Ronald Calinger. It's got articles from a very broad range of mathematical history, all the way from the Stone Age through 1932 (includes Gödel). Naturally, it does not include later works. Most of the most important ideas in modern mathematics will be found in here somewhere. For more modern topics, I found Love and Math by Edward Frenkel to be excellent.

Short does not mean a lot of things for me. A paper may be short, but to understand it you may have to read a lot of books. You can read the work of Milnor, he is very well-known for is concise papers which are very well written. Look for example his work on exotic spheres.

Milnor, John W. (1959), "Differentiable structures on spheres", American Journal of Mathematics, 81 (4): 962–972

There is a proof of the non-existence of vector fields on spheres by (Adams and Atiyah ?) that was famously said, could fit on a post card. There is an Indian mathematician named C.P. Ramanujan who wrote a number of very important papers in algebraic geometry and number theory. To the best of my recollection, none of his papers is over 20 pages.

The Proceedings of the AMS is all about short papers. You could probably search MathSciNet for publications in the Proceedings and sort by citation number to find some winners.

I'd do this myself, but I don't have a login right now :c

The Noah Sheets helped me a lot in contest math.

• 1 $\begingroup$ I don't think this qualifies as an answer to the question : it seems to me that OP asks about articles that have had a lot of influence on mathematical research by introducing new ideas. Your link is just a list of known formulae. $\endgroup$ –  Arnaud D. Commented Sep 3, 2018 at 11:49
• $\begingroup$ Oh... well then I guess I can't contribute... $\endgroup$ –  Jason Kim Commented Sep 3, 2018 at 16:08

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Mathematics PhD dissertations that opened a new field of research

I propose this as a companion wiki page to the one about PhD dissertations which contain a solution to an open problem in the style of big-list questions, thinking in terms of the well-known paradigm that splits mathematical research into problem solving and theory building . Theories are at times developed to solve famous open problems, but sometimes the concrete problems they solve are quickly dwarfed by the possibilities that a new theory opens.

Can you name modern mathematicians who already in their PhD theses (or earlier in their career) developed a substantial new theory or laid the foundations of a new field of research?

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• 9 $\begingroup$ The list will be too long. $\endgroup$ –  Alexandre Eremenko Commented Apr 24, 2018 at 12:11
• 6 $\begingroup$ en.wikipedia.org/wiki/Tate%27s_thesis $\endgroup$ –  Steve Huntsman Commented Apr 24, 2018 at 12:14
• 2 $\begingroup$ en.wikipedia.org/wiki/… $\endgroup$ –  Steve Huntsman Commented Apr 24, 2018 at 12:15
• 2 $\begingroup$ Perhaps Scholze's Perfectoid spaces ? $\endgroup$ –  TKe Commented Apr 24, 2018 at 14:25
• 2 $\begingroup$ @Steve Huntsman: Shannon's thesis does not qualify: it was a master thesis:-) $\endgroup$ –  Alexandre Eremenko Commented Apr 25, 2018 at 2:52

5 Answers 5

John Forbes Nash Jr. got a Nobel Prize for his.

Nash earned a Ph.D. degree in 1950 with a 28-page dissertation on non-cooperative games. The thesis, written under the supervision of doctoral advisor Albert W. Tucker, contained the definition and properties of the Nash equilibrium, a crucial concept in non-cooperative games. It won Nash the Nobel Memorial Prize in Economic Sciences in 1994.

There are many examples. Here are a few that come to mind:

Simon Donaldson's thesis The Yang-Mills equations on Kahler manifolds contains the first major steps in his work on the differential topology of four manifolds. The following paraphrases its abstract. He gave a new proof of a theorem of Narasimhan and Seshadri characterizing those holomorphic bundles over a projective curve that admit a flat connection and used it to prove the simplest interesting case of the conjecture of Hitchin and Kobayashi. He studied the moduli space of self-dual connections on a simply-connected four manifold and used it to deduce obstructions to the realization of a matrix as the intersection pairing on the second cohomology of such a manifold.

John Tate's thesis is another well known example, although I'm not competent even to summarize it. It has its own wikipedia page .

Mikio Sato's doctoral thesis (based on some already published work) introduced the theory of hyperfunctions as boundary values of holomorphic functions. See this survey by P. Schapira and this interview with Sato. (Nothing about Sato's education is standard.)

• $\begingroup$ I read that article my Mikio Sato. I thought it very interesting. Too bad most famous mathematicians seem to be as unforthcoming as Sato in describing their formative influences. $\endgroup$ –  Mozibur Ullah Commented May 3, 2018 at 4:51

I’ll pick Philippe Delsarte’s 1973 thesis “An algebraic approach to the association schemes of coding theory” which basically expressed classical extremal problems in designs and codes as algebraic questions involving eigenspaces of related association schemes.

Here is a link to a talk on what is now known as “ Delsarte Theory ”.

Maybe not up to the Nash standard, but pretty good for a PhD!

Thomas G. Kurtz ' PhD dissertation at Stanford University (1967) was titled Convergence of operator semigroups with applications to Markov processes . He went on to write with his PhD student Stewart N. Ethier the book Markov Processes: Characterization and Convergence (John Wiley & Sons Inc., 1986), which is "the standard reference for the advanced theory of Markov processes". Its first chapter is Operator semigroups . He made a stellar research career on these foundations. Much of the modern theory of stochastic processes is variations of what he pioneered: "establishing the convergence of Markov processes and characterising the limiting process" (quotes from the Wikipedia page). I do not claim that he single-handedly created the area, but his contribution is immense.

There has been a similar question here: https://www.quora.com/Which-are-the-best-PhD-theses-ever-in-pure-mathematics

I would suggest Kurt Godel. His doctorate thesis proved the completeness theorem, and a year later he published his incompleteness theorems.

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The Dramatic and Ultimate Shortening of a Doctoral Dissertation in Mathematics

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Length of the average dissertation

On R is My Friend, as a way to procrastinate on his own dissertation, beckmw took a look at dissertation length via the digital archives at the University of Minnesota.

I’ve selected the top fifty majors with the highest number of dissertations and created boxplots to show relative distributions. Not many differences are observed among the majors, although some exceptions are apparent. Economics, mathematics, and biostatistics had the lowest median page lengths, whereas anthropology, history, and political science had the highest median page lengths. This distinction makes sense given the nature of the disciplines.

I was on the long end of the statistics distribution, around 180 pages. Probably because I had a lot of pictures.

As I was working on my dissertation, people often asked me how many pages I had written and how many pages I had left to write. I never had a good answer, because there’s no page limit or required page count. It’s just whenever you (and your adviser) feel like there’s enough to get a point across. Sometimes that takes 50 pages. Other times it takes 200.

So for those who get that dreaded page-count question, you can wave your finger at this chart and tell people you’re somewhere in the distribution.

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13 Comments

As a student at Minnesota, I’m not sure our digital archive is representative, as it is optional, and and certain fields are more or less likely (either due to subject matter, or internal politics) to include their works within the archive. Other than that, this is neat!

what do the colors mean? at first glance I thought the colors had to do with subject area, but on closer examination that are same colored major that are very different (i.e. anthropology/aerospace engineering,

The colors look like they are reverse alphabetical.

Kyle, thanks – I figured I was missing something super simple – its been a long day. So the colors are meaningless then?

Yes, the colors are useless. They convey no information that is not already transparently conveyed.

For that matter, the box plot itself is thoroughly obsolete. Read Edward Tufte’s books, specifically chapter 6 of “The Visual Display of Quantitative Information” for the description of the successor to the box plot.

As for the topic of the post, my math dissertation was 88 pages. My advisor’s was (not a typo) 23 pages, double-spaced, including front matter and references.

And Presburger’s was 19 pages or so. But his supervisor, Tarski, would not give him his PhD. He thought the thesis was too short. So there is a lower bound.

would be interesting to see if they have been getting longer over time and by how much by subject

The chart would be more useful if the majors were ordered by median or average dissertatin length. But it is interesting to note that the more mathematical and objective the mayor, the less pages needed. Llongest dissertations: sociology and anthropology. Shortest: biostatistics.

Out of curiosity, Nathan, what was your dissertation on? (Not that I’d understand it anyway!)

Then, there are the departments’ or universities’ format standards. Single spaced? Double spaced? That, of course doubles the plage length. Better, what was the word count in the dissertations?

So with the current trend of dissertation chapters being prepared/formatted as manuscript submissions for journals up front (which have limits to the manuscript length), I would expect to see overall dissertation lengths get shorter over time (to present). Mine started out much longer, but as I started conforming to target journal format standards, I would say the overall length was reduced by a third or so. Is this true outside of ecology as well?

Oh, dear, my dissertation wouldn’t even appear on this chart, but would be off the right edge. And yes, I’m in one of the ‘runs long’ disciplines. Then again, my opus would count as short for, say, a German Habilitation or a French These d’Etat in my field, so it all depends!

This is very interesting. One variable that isn’t accounted for, but varies greatly between institutions and individual authors, is the number of words per page – determined by spacing, margins, font size, and so on. A more helpful plot would count theses by words, instead of pages, as a measure of content.

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Dissertations and Placements 2010-Present

Emily Dautenhahn Thesis: Heat kernel estimates on glued spaces Advisor: Laurent Saloff-Coste First Position:  Assistant Professor at Murray State University

Elena Hafner Thesis: Combinatorics of Vexillary Grothendieck Polynomials Advisor: Karola Meszaros First Position: NSF Postdoctoral Fellow,, at University of Washington

Sumun Iyer Thesis: Dynamics of non-locally compact topological groups Advisor: Slawomir Solecki First Position: NSF Postdoctoral Fellow at Carnegie Mellon University in Pittsburgh

Sebastian Junge Thesis: Applications of Transferring the Ramsey Property between Categories Advisor: Slawomir Solecki First Position: Lecturer at Texas State University

Nicki Magill Thesis: Infinite Staircases for Hirzebruch Surfaces Advisor: Tara Holm First Position: NSF Postdoctoral Fellow at UC Berkeley

Prairie Wentworth-Nice Thesis: Finite Groups, Polymatroids, and Error-Correcting Codes Advisor: Edward Swartz First Position: Postdoctoral Teaching Fellow at Johns Hopkins University

Fiona Young Thesis: Dissecting an Integer Polymatroid Advisor: Edward Swartz First Position: Pursuing her own start-up in the math education technology space

Kimoi Kemboi Thesis: Full exceptional collections of vector bundles on linear GIT quotients Advisor: Daniel Halpern-Leistner First Position: Postdoc at the Institution for Advanced Study and Princeton

Max Lipton Thesis: Dynamical Systems in Pure Mathematics Advisor: Steven Strogatz First Position: NSF Mathematical Sciences Postdoctoral Fellow at Massachusetts Institute of Technology

Elise McMahon Thesis: A simplicial set approach to computing the group homology of some orthogonal subgroups of the discrete group  Advisor: Inna Zakharevich First Position: Senior Research Scientist at Two Six Technologies

Andrew Melchionna Thesis: Opinion Propagation and Sandpile Models  Advisor: Lionel Levine First Position: Quantitative Researcher at Trexquant

Peter Uttenthal Thesis: Density of Selmer Ranks in Families of Even Galois Representations Advisor: Ravi Kumar Ramakrishna First Position: Visiting Assistant Professor at Cornell University

Liu Yun Thesis: Towers of Borel Fibrations and Generalized Quasi-Invariants Advisor: Yuri Berest First Position: Postdoc at Indiana University Bloomington

Romin Abdolahzadi Thesis: Anabelian model theory Advisor: Anil Nerode First Position: Quantitative Analyst, A.R.T. Advisors, LLC

Hannah Cairns Thesis: Abelian processes, and how they go to sleep Advisor: Lionel Levine First Position: Visiting Assistant Professor, Cornell University

Shiping Cao Thesis: Topics in scaling limits on some Sierpinski carpet type fractals Advisor: Robert Strichartz (Laurent Saloff-Coste in last semester) First Position: Postdoctoral Scholar, University of Washington

Andres Fernandes Herrero Thesis: On the boundedness of the moduli of logarithmic connections Advisor: Nicolas Templier First Position: Ritt Assistant Professor, Columbia University

Max Hallgren Thesis: Ricci Flow with a Lower Bound on Ricci Curvature Advisor: Xiaodong Cao First Position: NSF Postdoctoral Research Fellow, Rutgers University

Gautam Krishnan Thesis: Degenerate series representations for symplectic groups Advisor: Dan Barbasch First Position: Hill Assistant Professor, Rutgers University

Feng Liang Thesis: Mixing time and limit shapes of Abelian networks Advisor: Lionel Levine

David Mehrle Thesis: Commutative and Homological Algebra of Incomplete Tambara Functors Advisor: Inna Zakharevich First Position: Postdoctoral Scholar, University of Kentucky

Itamar Sales de Oliveira Thesis: A new approach to the Fourier extension problem for the paraboloid Advisor: Camil Muscalu First Position: Postdoctoral Researcher, Nantes Université

Brandon Shapiro Thesis: Shape Independent Category Theory Advisor: Inna Zakharevich First Position: Postdoctoral Fellow, Topos Institute

Ayah Almousa Thesis: Combinatorial characterizations of polarizations of powers of the graded maximal ideal Advisor: Irena Peeva First position: RTG Postdoctoral Fellow, University of Minnesota

Jose Bastidas Thesis: Species and hyperplane arrangements Advisor: Marcelo Aguiar First position: Postdoctoral Fellow, Université du Québec à Montréal

Zaoli Chen Thesis: Clustered Behaviors of Extreme Values Advisor: Gennady Samorodnitsky First Position: Postdoctoral Researcher, Department of and Statistics, University of Ottawa

Ivan Geffner Thesis: Implementing Mediators with Cheap Talk Advisor: Joe Halpern First Position: Postdoctoral Researcher, Technion – Israel Institute of Technology

Ryan McDermott Thesis: Phase Transitions and Near-Critical Phenomena in the Abelian Sandpile Model Advisor: Lionel Levine

Aleksandra Niepla Thesis:  Iterated Fractional Integrals and Applications to Fourier Integrals with Rational Symbol Advisor: Camil Muscalu First Position: Visiting Assistant Professor, College of the Holy Cross

Dylan Peifer Thesis: Reinforcement Learning in Buchberger's Algorithm Advisor: Michael Stillman First Position: Quantitative Researcher, Susquehanna International Group

Rakvi Thesis: A Classification of Genus 0 Modular Curves with Rational Points Advisor: David Zywina First Position: Hans Rademacher Instructor, University of Pennsylvania

Ana Smaranda Sandu Thesis: Knowledge of counterfactuals Advisor: Anil Nerode First Position: Instructor in Science Laboratory, Computer Science Department, Wellesley College

Maru Sarazola Thesis: Constructing K-theory spectra from algebraic structures with a class of acyclic objects Advisor: Inna Zakharevich First Position: J.J. Sylvester Assistant Professor, Johns Hopkins University

Abigail Turner Thesis: L2 Minimal Algorithms Advisor: Steven Strogatz

Yuwen Wang Thesis: Long-jump random walks on finite groups Advisor: Laurent Saloff-Coste First Position: Postdoc, University of Innsbruck, Austria

Beihui Yuan Thesis:  Applications of commutative algebra to spline theory and string theory Advisor: Michael Stillman First Position: Research Fellow, Swansea University

Elliot Cartee Thesis: Topics in Optimal Control and Game Theory Advisor: Alexander Vladimirsky First Position: L.E. Dickson Instructor, Department of , University of Chicago

Frederik de Keersmaeker Thesis: Displaceability in Symplectic Geometry Advisor: Tara Holm First Position: Consultant, Addestino Innovation Management

Lila Greco Thesis: Locally Markov Walks and Branching Processes Advisor: Lionel Levine First Position: Actuarial Assistant, Berkshire Hathaway Specialty Insurance

Benjamin Hoffman Thesis: Polytopes And Hamiltonian Geometry: Stacks, Toric Degenerations, And Partial Advisor: Reyer Sjamaar First Position: Teaching Associate, Department of , Cornell University

Daoji Huang Thesis: A Bruhat Atlas on the Wonderful Compactification of PS O(2 n )/ SO (2 n -1) and A Kazhdan-Lusztig Atlas on G/P Advisor: Allen Knutson First Position: Postdoctoral Associate, University of Minnesota

Pak-Hin Li Thesis: A Hopf Algebra from Preprojective Modules Advisor: Allen Knutson First position: Associate, Goldman Sachs

Anwesh Ray Thesis: Lifting Reducible Galois Representations Advisor: Ravi Ramakrishna First Position: Postdoctoral Fellowship, University of British Columbia

Avery St. Dizier Thesis: Combinatorics of Schubert Polynomials Advisor: Karola Meszaros First Position: Postdoctoral Fellowship, Department of , University of Illinois at Urbana-Champaign

Shihao Xiong Thesis: Forcing Axioms For Sigma-Closed Posets And Their Consequences Advisor: Justin Moore First Position: Algorithm Developer, Hudson River Trading

Swee Hong Chan Thesis: Nonhalting abelian networks Advisor: Lionel Levine First Position: Hedrick Adjunct Assistant Professor, UCLA

Joseph Gallagher Thesis: On conjectures related to character varieties of knots and Jones polynomials Advisor: Yuri Berest First Position: Data Scientist, Capital One

Jun Le Goh Thesis: Measuring the Relative Complexity of Mathematical Constructions and Theorems Advisor: Richard Shore First Position: Van Vleck Assistant Professor, University of Wisconsin-Madison

Qi Hou Thesis: Rough Hypoellipticity for Local Weak Solutions to the Heat Equation in Dirichlet Spaces Advisor: Laurent Saloff-Coste First Position: Visiting Assistant Professor, Department of , Cornell University

Jingbo Liu Thesis: Heat kernel estimate of the Schrodinger operator in uniform domains Advisor: Laurent Saloff-Coste First Position: Data Scientist, Jet.com

Ian Pendleton Thesis:  The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds Advisor: Tara Holm

Amin Saied Thesis: Stable representation theory of categories and applications to families of (bi)modules over symmetric groups Advisor: Martin Kassabov First Position: Data Scientist, Microsoft

Yujia Zhai Thesis:  Study of bi-parameter flag paraproducts and bi-parameter stopping-time algorithms Advisor: Camil Muscalu First Position: Postdoctoral Associate, Université de Nantes 

Tair Akhmejanov Thesis: Growth Diagrams from Polygons in the Affine Grassmannian Advisor: Allen Knutson First position: Arthur J. Krener Assistant Professor, University of California, Davis

James Barnes Thesis:  The Theory of the Hyperarithmetic Degrees Advisor: Richard Shore First position: Visiting Lecturer, Wellesley College

Jeffrey Bergfalk Thesis:  Dimensions of ordinals: set theory, homology theory, and the first omega alephs Advisor: Justin Moore Postdoctoral Associate, UNAM - National Autonomous University of Mexico

TaoRan Chen Thesis: The Inverse Deformation Problem Advisor: Ravi Ramakrishna

Sergio Da Silva Thesis: On the Gorensteinization of Schubert varieties via boundary divisors Advisor: Allen Knutson First position: Pacific Institute for the Mathematical Sciences (PIMS) postdoctoral fellowship, University of Manitoba

Eduard Einstein Thesis:  Hierarchies for relatively hyperbolic compact special cube complexes Advisor: Jason Manning First position: Research Assistant Professor (Postdoc), University of Illinois, Chicago (UIC)

Balázs Elek Thesis:  Toric surfaces with Kazhdan-Lusztig atlases Advisor: Allen Knutson First position: Postdoctoral Fellow, University of Toronto

Kelsey Houston-Edwards Thesis:  Discrete Heat Kernel Estimates in Inner Uniform Domains Advisor: Laurent Saloff-Coste First position: Professor of Math and Science Communication, Olin College

My Huynh Thesis:  The Gromov Width of Symplectic Cuts of Symplectic Manifolds. Advisor: Tara Holm First position: Applied Mathematician, Applied Research Associates Inc., Raleigh NC.

Hossein Lamei Ramandi Thesis: On the minimality of non-σ-scattered orders Advisor: Justin Moore First position:  Postdoctoral Associate at UFT (University Toronto)

Christine McMeekin Thesis: A density of ramified primes Advisor: Ravi Ramakrishna First position: Researcher at Max Planck Institute

Aliaksandr Patotski Thesis:  Derived characters of Lie representations and Chern-Simons forms Advisor: Yuri Berest First position: Data Scientist, Microsoft

Ahmad Rafiqi Thesis:  On dilatations of surface automorphisms Advisor: John Hubbard First position: Postdoctoral Associate, Sao Palo, Brazil

Ying-Ying Tran Thesis:  Computably enumerable boolean algebras Advisor: Anil Nerode First position: Quantitative Researcher

Drew Zemke Thesis:  Surfaces in Three- and Four-Dimensional Topology Advisor: Jason Manning First position: Preceptor in , Harvard University

Heung Shan Theodore Hui Thesis: A Radical Characterization of Abelian Varieties  Advisor: David Zywina First position: Quantitative Researcher, Eastmore Group

Daniel Miller Thesis: Counterexamples related to the Sato–Tate conjecture Advisor: Ravi Ramakrishna First position: Data Scientist, Microsoft

Lihai Qian Thesis: Rigidity on Einstein manifolds and shrinking Ricci solitons in high dimensions Advisor: Xiaodong Cao First position: Quantitative Associate, Wells Fargo

Valente Ramirez Garcia Luna Thesis: Quadratic vector fields on the complex plane: rigidity and analytic invariants Advisor: Yulij Ilyashenko First position: Lebesgue Post-doc Fellow, Institut de Recherche Mathématique de Rennes

Iian Smythe Thesis: Set theory in infinite-dimensional vector spaces Advisor: Justin Moore First position: Hill Assistant Professor at Rutgers, the State University of New Jersey

Zhexiu Tu Thesis: Topological representations of matroids and the cd-index Advisor: Edward Swartz First position: Visiting Professor - Centre College, Kentucky

Wai-kit Yeung Thesis: Representation homology and knot contact homology Advisor: Yuri Berest First position: Zorn postdoctoral fellow, Indiana University

Lucien Clavier Thesis: Non-affine horocycle orbit closures on strata of translation surfaces: new examples Advisor: John Smillie First position: Consultant in Capital Markets, Financial Risk at Deloitte Luxembourg

Voula Collins Thesis: Crystal branching for non-Levi subgroups and a puzzle formula for the equivariant cohomology of the cotangent bundle on projective space Advisor: Allen Knutson FIrst position: Postdoctoral Associate, University of Connecticut

Pok Wai Fong Thesis: Smoothness Properties of symbols, Calderón Commutators and Generalizations Advisor: Camil Muscalu First position: Quantitative researcher, Two Sigma

Tom Kern Thesis: Nonstandard models of the weak second order theory of one successor Advisor: Anil Nerode First position: Visiting Assistant Professor, Cornell University

Robert Kesler Thesis: Unbounded multilinear multipliers adapted to large subspaces and estimates for degenerate simplex operators Advisor: Camil Muscalu First position: Postdoctoral Associate, Georgia Institute of Technology

Yao Liu Thesis: Riesz Distributions Assiciated to Dunkl Operators Advisor: Yuri Berest First position: Visiting Assistant Professor, Cornell University

Scott Messick Thesis: Continuous atomata, compactness, and Young measures Advisor: Anil Nerode First position: Start-up

Aaron Palmer Thesis: Incompressibility and Global Injectivity in Second-Gradient Non-Linear Elasticity Advisor: Timothy J. Healey First position: Postdoctoral fellow, University of British Columbia 

Kristen Pueschel Thesis: On Residual Properties of Groups and Dehn Functions for Mapping Tori of Right Angled Artin Groups Advisor: Timothy Riley First position: Postdoctoral Associate, University of Arkansas

Chenxi Wu Thesis: Translation surfaces: saddle connections, triangles, and covering constructions. Advisor: John Smillie First position: Postdoctoral Associate, Max Planck Institute of

David Belanger Thesis: Sets, Models, And Proofs: Topics In The Theory Of Recursive Functions Advisor: Richard A. Shore First position: Research Fellow, National University of Singapore

Cristina Benea Thesis: Vector-Valued Extensions for Singular Bilinear Operators and Applications Advisor: Camil Muscalu First position: University of Nantes, France

Kai Fong Ernest Chong Thesis: Face Vectors and Hilbert Functions Advisor: Edward Swartz First position: Research Scientist, Agency for Science, Technology and Research, Singapore

Laura Escobar Vega Thesis: Brick Varieties and Toric Matrix Schubert Varieties Advisor: Allen Knutson First position: J. L. Doob Research Assistant Professor at UIUC

Joeun Jung Thesis: Iterated trilinear fourier integrals with arbitrary symbols Advisor: Camil Muscalu First position: Researcher, PARC (PDE and Functional Analysis Research Center) of Seoul National University

Yasemin Kara Thesis: The laplacian on hyperbolic Riemann surfaces and Maass forms Advisor: John H. Hubbard Part Time Instructor, Faculty of Engineering and Natural Sciences, Bahcesehir University

Chor Hang Lam Thesis: Homological Stability Of Diffeomorphism Groups Of 3-Manifolds Advisor: Allen Hatcher

Yash Lodha Thesis: Finiteness Properties And Piecewise Projective Homeomorphisms Advisor: Justin Moore and Timothy Riley First position: Postdoctoral fellow at Ecole Polytechnique Federale de Lausanne in Switzerland

Radoslav Zlatev Thesis: Examples of Implicitization of Hypersurfaces through Syzygies Advisor: Michael E. Stillman First position: Associate, Credit Strats, Goldman Sachs

Margarita Amchislavska Thesis: The geometry of generalized Lamplighter groups Advisor: Timothy Riley First position: Department of Defense

Hyungryul Baik Thesis: Laminations on the circle and hyperbolic geometry Advisor: John H. Hubbard First position: Postdoctoral Associate, Bonn University

Adam Bjorndahl Thesis: Language-based games Advisor: Anil Nerode and Joseph Halpern First position: Tenure Track Professor, Carnegie Mellon University Department of Philosophy

Youssef El Fassy Fihry Thesis: Graded Cherednik Algebra And Quasi-Invariant Differential Forms Advisor: Yuri Berest First position: Software Developer, Microsoft

Chikwong Fok Thesis: The Real K-theory of compact Lie groups Advisor: Reyer Sjamaar First position: Postdoctoral fellow in the National Center for Theoretical Sciences, Taiwan

Kathryn Lindsey Thesis: Families Of Dynamical Systems Associated To Translation Surfaces Advisor: John Smillie First position: Postdoctoral Associate, University of Chicago

Andrew Marshall Thesis: On configuration spaces of graphs Advisor: Allan Hatcher First position: Visiting Assistant Professor, Cornell University

Robyn Miller Thesis: Symbolic Dynamics Of Billiard Flow In Isosceles Triangles Advisor: John Smillie First position: Postdoctoral Researcher at Mind Research Network

Diana Ojeda Aristizabal Thesis: Ramsey theory and the geometry of Banach spaces Advisor: Justin Moore First position: Postdoctoral Fellow, University of Toronto

Hung Tran Thesis: Aspects of the Ricci flow Advisor: Xiaodong Cao First position: Visiting Assistant Professor, University of California at Irvine

Baris Ugurcan Thesis: LPLP-Estimates And Polyharmonic Boundary Value Problems On The Sierpinski Gasket And Gaussian Free Fields On High Dimensional Sierpinski Carpet Graphs Advisor: Robert S. Strichartz First position: Postdoctoral Fellowship, University of Western Ontario

Anna Bertiger Thesis: The Combinatorics and Geometry of the Orbits of the Symplectic Group on Flags in Complex Affine Space Advisor: Allen Knutson First position: University of Waterloo, Postdoctoral Fellow

Mariya Bessonov Thesis: Probabilistic Models for Population Dynamics Advisor: Richard Durrett First position: CUNY City Tech, Assistant Professor, Tenure Track

Igors Gorbovickis Thesis: Some Problems from Complex Dynamical Systems and Combinatorial Geometry Advisor: Yulij Ilyashenko First position: Postdoctoral Fellow, University of Toronto

Marisa Hughes Thesis: Quotients of Spheres by Linear Actions of Abelian Groups Advisor: Edward Swartz First position: Visiting Professor, Hamilton College

Kristine Jones Thesis: Generic Initial Ideals of Locally Cohen-Macaulay Space Curves Advisor: Michael E. Stillman First position: Software Developer, Microsoft

Shisen Luo Thesis: Hard Lefschetz Property of Hamiltonian GKM Manifolds Advisor: Tara Holm First position: Associate, Goldman Sachs

Peter Luthy Thesis: Bi-parameter Maximal Multilinear Operators Advisor: Camil Muscalu First position: Chauvenet Postdoctoral Lecturer at Washington University in St. Louis 

Remus Radu Thesis: Topological models for hyperbolic and semi-parabolic complex Hénon maps Advisor: John H. Hubbard First position: Milnor Lecturer, Institute for Mathematical Sciences, Stony Brook University

Jenna Rajchgot Thesis: Compatibly Split Subvarieties of the Hilbert Scheme of Points in the Plane Advisor: Allen Knutson First position: Research member at the Mathematical Sciences Research Institute (fall 2012); postdoc at the University of Michigan

Raluca Tanase Thesis: Hénon maps, discrete groups and continuity of Julia sets Advisor: John H. Hubbard First position: Milnor Lecturer, Institute for Mathematical Sciences, Stony Brook University

Ka Yue Wong Thesis: Dixmier Algebras on Complex Classical Nilpotent Orbits and their Representation Theories Advisor: Dan M. Barbasch First position: Postdoctoral fellow at Hong Kong University of Science and Technology

Tianyi Zheng Thesis: Random walks on some classes of solvable groups Advisor: Laurent Saloff-Coste First position: Postdoctoral Associate, Stanford University

Juan Alonso Thesis: Graphs of Free Groups and their Measure Equivalence Advisor: Karen Vogtmann First position: Postdoc at Uruguay University

Jason Anema Thesis: Counting Spanning Trees on Fractal Graphs Advisor: Robert S. Strichartz First position: Visiting assistant professor of mathematics at Cornell University

Saúl Blanco Rodríguez Thesis: Shortest Path Poset of Bruhat Intervals and the Completecd-Index Advisor: Louis Billera First position: Visiting assistant professor of mathematics at DePaul University

Fatima Mahmood Thesis: Jacobi Structures and Differential Forms on Contact Quotients Advisor: Reyer Sjamaar First position: Visiting assistant professor at University of Rochester

Philipp Meerkamp Thesis: Singular Hopf Bifurcation Advisor: John M. Guckenheimer First position: Financial software engineer at Bloomberg LP

Milena Pabiniak Thesis: Hamiltonian Torus Actions in Equivariant Cohomology and Symplectic Topology Advisor: Tara Holm First position: Postdoctoral associate at the University of Toronto

Peter Samuelson Thesis: Kauffman Bracket Skein Modules and the Quantum Torus Advisor: Yuri Berest First position: Postdoctoral associate at the University of Toronto

Mihai Bailesteanu  Thesis: The Heat Equation under the Ricci Flow Advisor: Xiaodong Cao First position: Visiting assistant professor at the University of Rochester

Owen Baker  Thesis:  The Jacobian Map on Outer Space Advisor: Karen Vogtmann First position: Postdoctoral fellow at McMaster University

Jennifer Biermann  Thesis: Free Resolutions of Monomial Ideals Advisor: Irena Peeva First position: Postdoctoral fellow at Lakehead University

Mingzhong Cai  Thesis: Elements of Classical Recursion Theory: Degree-Theoretic Properties and Combinatorial Properties Advisor: Richard A. Shore First position: Van Vleck visiting assistant professor at the University of Wisconsin at Madison

Ri-Xiang Chen  Thesis: Hilbert Functions and Free Resolutions Advisor: Irena Peeva First position: Instructor at Shantou University in Guangdong, China

Denise Dawson  Thesis: Complete Reducibility in Euclidean Twin Buildings Advisor: Kenneth S. Brown First position: Assistant professor of mathematics at Charleston Southern University

George Khachatryan Thesis: Derived Representation Schemes and Non-commutative Geometry Advisor: Yuri Berest First position: Reasoning Mind

Samuel Kolins  Thesis: Face Vectors of Subdivision of Balls Advisor: Edward Swartz First position: Assistant professor at Lebanon Valley College

Victor Kostyuk Thesis: Outer Space for Two-Dimensional RAAGs and Fixed Point Sets of Finite Subgroups Advisor: Karen Vogtmann First position: Knowledge engineering at Reasoning Mind

Ho Hon Leung  Thesis: K-Theory of Weight Varieties and Divided Difference Operators in Equivariant KK-Theory Advisor: Reyer Sjamaar First position: Assistant professor at the Canadian University of Dubai

Benjamin Lundell  Thesis: Selmer Groups and Ranks of Hecke Rings Advisor: Ravi Ramakrishna First position: Acting assistant professor at the University of Washington

Eyvindur Ari Palsson  Thesis: Lp Estimates for a Singular Integral Operator Motivated by Calderón’s Second Commutator Advisor: Camil Muscalu First position: Visiting assistant professor at the University of Rochester

Paul Shafer  Thesis: On the Complexity of Mathematical Problems: Medvedev Degrees and Reverse Advisor: Richard A. Shore First position: Lecturer at Appalachian State University

Michelle Snider  Thesis: Affine Patches on Positroid Varieties and Affine Pipe Dreams Advisor: Allen Knutson First position: Government consulting job in Maryland

Santi Tasena Thesis: Heat Kernel Analysis on Weighted Dirichlet Spaces Advisor: Laurent Saloff-Coste First position: Lecturer professor at Chiang Mai University, Thailand

Russ Thompson  Thesis: Random Walks and Subgroup Geometry Advisor: Laurent Saloff-Coste First position: Postdoctoral fellow at the Mathematical Sciences Research Institute

Gwyneth Whieldon Thesis: Betti Numbers of Stanley-Reisner Ideals Advisor: Michael E. Stillman First position: Assistant professor of mathematics at Hood College

Andrew Cameron Thesis: Estimates for Solutions of Elliptic Partial Differential Equations with Explicit Constants and Aspects of the Finite Element Method for Second-Order Equations Advisor: Alfred H. Schatz First position: Adjunct instructor of mathematics at Tompkins Cortland Community College

Timothy Goldberg Thesis: Hamiltonian Actions in Integral Kähler and Generalized Complex Geometry Advisor: Reyer Sjamaar First position: Visiting assistant professor of mathematics at Lenoir-Rhyne University

Gregory Muller Thesis: The Projective Geometry of Differential Operators Advisor: Yuri Berest First position: Assistant professor at Louisiana State University 

Matthew Noonan Thesis: Geometric Backlund transofrmation in homogeneous spaces Advisor: John H. Hubbard

Sergio Pulido Niño Thesis: Financial Markets with Short Sales Prohibition Advisor: Philip E. Protter First position: Postdoctoral associate in applied probability and finance at Carnegie Mellon University

How long is a PhD dissertation? [Data by field]

The final piece of the PhD journey is the PhD dissertation. It takes many years to accumulate enough original and new data to fill out a dissertation to the satisfaction of experts in your field. Interestingly, the PhD dissertation length and content vary significantly based on the field you are studying and the publishing conventions.

A PhD can be anywhere from 50 pages to over 450 pages long. This equates to between about 20,000 words to 100,000 words. Most PhD theses are between 60,000 and 80,000 words long excluding contents, citations and references.

A PhD thesis contains different sections including an introduction, methods, results and discussion, conclusions, further work, and references. Each one of these different sections will vary in length depending on the field of study and your particular topic.

Ultimately, a PhD dissertation should contain as many pages and words as it takes to communicate the results of your multi-year investigation.

It is very rewarding to see your thesis come together as you are writing day after day. When I was writing my PhD dissertation I wrote the sections separately and my heart filled with joy when I finally put them all together and compile them into a single PDF document.

Counting the pages should not be the way to determine a PhD dissertation’s value but it certainly helps when your thesis is starting to look substantial in thickness.

How many pages should a PhD dissertation be?

A PhD dissertation should contain as many pages and words as it takes to outline the current state of your field and provide adequate background information, present your results, and provide confidence in your conclusions. A PhD dissertation will also contain figures, graphs, schematics, and other large pictorial items that can easily inflate the page count.

Here is a boxplot summary of many different fields of study and the number of pages of a typical PhD dissertation in the field. It has been created by Marcus Beck from all of the dissertations at the University of Minnesota.

Typically, the mathematical sciences, economics, and biostatistics theses and dissertations tend to be shorter because they rely on mathematical formulas to provide proof of their results rather than diagrams and long explanations.

On the other end of the scale, English, communication studies, political science, history and anthropology are often the largest theses in terms of pages and word count because of the number of words it takes to provide proof and depth of their results.

At the end of the day, it is important that your thesis gets signed off by your review committee and other experts in the field. Your supervisor will be the main judge of whether or not your dissertation is capable of satisfying the requirements of a PhD in your field.

If you want to know more about how long a Masters’s thesis and PhD dissertation is you can check out my other articles:

• How Long is a Masters Thesis? [Your writing guide]
• How long is a Thesis or dissertation? [the data]

Can a PhD dissertation be too long?

A PhD thesis should contain enough evidence and discussion to report on the most significant findings of your PhD research.

A PhD dissertation should not contain everything that you have done during your PhD. It should only include the data and information required to convince your PhD examining body that wraps up and tells the full story of particular lines of investigation.

Including random results, thoughts, or superfluous explanation can result in a dissertation that is unfocused. I have heard of music PhD is being described as too verbose and physical sciences PhD dissertations as being unfocused.

Therefore, a PhD thesis can be too long if the information it contains does not form a full and cohesive story.

One of my colleagues during their PhD removed an entire chapter from the thesis after writing it as the supervisor said that it needed more experiments to be a full story. They did not want to spend the next six months gathering the data and simply removed the chapter altogether.

How short can PhD dissertation be?

The shortest PhD dissertations are typically found in mathematics.

George Bernard Danzig was an American mathematical scientist who made contributions to industrial engineering and many other mathematical-related fields. An interesting miscommunication led to 1 of the shortest PhD theses ever.

In 1939 his professor wrote two problems on the blackboard and Danzig thought they were homeless assignments. He stated that they were harder than usual but handed in solutions to the surprise of the professor.

They were, in fact, open mathematical problems in statistics.

His professor said to bind the solution to the two problems together and submit them as his thesis – the total thesis length = 14 pages.

Obviously, most PhD theses and dissertations will be so much longer than that!

My PhD dissertation was 256 pages long. It was full of schematics, diagrams, and tables to demonstrate and communicate my findings.

I would say that most people’s PhD thesis experience will be closer to mine than Prof George Bernard Danzig’s.

Why PhD dissertations are typically so long

PhD dissertations are often over 200 pages long.

One of the primary reasons they are so long is that it is a single document that summarises many years of hard work. Also, summarising the research field to date and making sure that all of your references and citations are included so you avoid plagiarism will bolster the word count of the thesis dramatically.

Here are all of the reasons PhD dissertations tend to be so long.

Many years of work

PhD theses or dissertations contain many years of research and analysis.

In many of my YouTube videos I recommend that a PhD student work towards their PhD thesis by doing at least three hours of focused work every work day.

This amount of work quickly adds up.

Of course, not every bit of work makes it into the PhD dissertation but a lot of it does. It can be difficult to work out what to include or leave out of your thesis.

As a PhD student, I perfected the art of turning one experiment into many different types of grafts and schematics to fully explore the limits of my data. The graphs can take up a lot of space in your PhD thesis and, therefore, bolster the page count significantly.

In depth literature review

One of the most substantial parts of a PhD dissertation is the literature review.

The literature review can take up a huge portion of the early part of your PhD dissertation depending on the amount of data and publications in your field.

Writing an in-depth literature review requires just as much meticulous data analysis and searching as the central part of your dissertation.

Figures and schematics

Some fields end up producing a lot of figures and schematics.

My thesis had many full-page figures of atomic force microscopy experiments with much more explanation on subsequent pages.

As they say, a picture paints a thousand words and a dissertation can really benefit from having many schematics to highlight the important aspects of your findings.

References and citations

The recommended PhD dissertation word count from an institution or university does not include citations, references, or other thesis parts such as summary of abbreviations, table of figures, et cetera.

However, these components of your dissertation can take up many pages and add to the overall thickness of your PhD dissertation.

University formatting rules

University formatting rules will also dictate how you many pages your words take up.

I often get roasted on my YouTube channel for having doublespaced lines and wide margins. Unfortunately, this layout was dictated by my university before printing.

PhD dissertations often end up going into long-term storage and therefore, need to adhere to archival and standardised formatting rules.

Deep in the depths of the University of Newcastle, there is a copy of my thesis on a shelf. The formatting and binding rules mean that my thesis looks like everyone else’s.

Universities will often have their own requirements for PhD dissertation cover colour, quality, and type of paper. Even the quality of the paper can change the thickness of the PhD dissertation significantly.

PhD by publication

It is becoming increasingly common to submit a number of peer-reviewed papers bound together with supplementary information in between instead of a PhD dissertation.

The benefits of this to the researcher and university are:

• More early career peer-reviewed journals for career advancement
• an easier review process – they have already been peer-reviewed
• an early focus on publishing means better research outcomes for the researcher, supervisor, and Department.
• No mad rush at the end to finish a thesis
• continually writing peer-reviewed papers throughout your PhD helps with timely analysis and communication of results

Even though this option has been available to PhD students for a number of years, I have only known a handful of students actually submit their PhD via publication.

Nonetheless, having this option will suit some research fields better than others and lead to a more productive PhD.

Wrapping up

This article has been through everything you need to know about the length of a PhD dissertation and the common lengths of PhD dissertations for various fields.

Ultimately, there is no predefined length of a PhD .

A PhD thesis is as long as it needs to be to convince your examiners that you have contributed significantly enough to an academic field to be awarded the title of Dr of philosophy.

Mathematical and analytical theses tend to be shorter and can be as short as 50 pages (with one of the shortest being only 14 pages long). At the other end of the spectrum, PhD students in anthropology and history tend to produce the longest dissertations.

Dr Andrew Stapleton has a Masters and PhD in Chemistry from the UK and Australia. He has many years of research experience and has worked as a Postdoctoral Fellow and Associate at a number of Universities. Although having secured funding for his own research, he left academia to help others with his YouTube channel all about the inner workings of academia and how to make it work for you.

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PhD Dissertations

In 1909 the department awarded its first PhD to  Grace M. Bareis , whose dissertation was directed by Professor Harry W. Kuhn. The department began awarding PhD degrees on a regular basis around 1930, when a formal doctoral program was established as a result of the appointment of Tibor Radó as a professor at our department. To date, the department has awarded over 800 PhD degrees. An average of approximately 15 dissertations per year have been added in recent times. Find below a list of PhD theses completed in our program since 1952. (Additionally, search Ohio State at  Math Genealogy , which also includes some theses from other OSU departments.)