An unusual PhD thesis

by Guest Wed Jan 09, 2013 2:05 am

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), which is 3 pages plus bibliography. (Dan Kan, his advisor, likes short papers.)

http://mathoverflow.net/questions/54775/what-is-the-shortest-ph-d-thesis

by Guest Wed Jan 09, 2013 2:07 am

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(iΩ(f(z))) is a bounded integral function. (Ω is inverse to the elliptic modular function.)

http://mathoverflow.net/questions/54775/what-is-the-shortest-ph-d-thesis

by Guest Wed Jan 09, 2013 2:08 am

Note: Littlewood was a collaborator of G.H Hardy, the mentor of Ramanujan.

by Seva Lamberdar Wed Jan 09, 2013 11:47 am

Rashmun wrote: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), which is 3 pages plus bibliography. (Dan Kan, his advisor, likes short papers.)

http://mathoverflow.net/questions/54775/what-is-the-shortest-ph-d-thesis

The question really is whether a university should give a Ph.D. for a 9 page thesis or should make him write a 150 page thesis before granting the degree?

by Guest Wed Jan 09, 2013 8:04 pm

Seva Lamberdar wrote:
Rashmun wrote: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), which is 3 pages plus bibliography. (Dan Kan, his advisor, likes short papers.)

http://mathoverflow.net/questions/54775/what-is-the-shortest-ph-d-thesis

The question really is whether a university should give a Ph.D. for a 9 page thesis or should make him write a 150 page thesis before granting the degree?

in my opinion quality is more important than quantity. this applies to number of publications also. "few but ripe" as Gauss used to say about his publications. Unfortunately in the mad rush to get funding quality is often compromised by many scientists in favor of high number of publications of mediocre quality.

by MaxEntropy_Man Wed Jan 09, 2013 8:08 pm

van der waals's phd thesis was 17 pages long.

by Guest Wed Jan 09, 2013 8:11 pm

There is a famous example of one-page (actually "one-blackboard") proof which would easily have won a Ph.D. if Frank Cole did not have one already:

In 1903, Frank Nelson Cole was scheduled to give a lecture to the American Mathematical Society, whose title was "On the Factorization of Large Numbers". Cole went to the blackboard, and without saying a word wrote down a calculation to obtain 2^67 - 1 by repeated multiplication with two. He finally had the number 147573952589676412927 on the blackboard. Then, still without saying anything, he multiplied 761838257287 x 193707721 -- and got the same number. He went back to his seat, still in silence.

The audience erupted in applause. Cole had proved that 2^67 - 1 is not a prime number, contrary to what mathematicians had believed for centuries.

http://forums.randi.org/archive/index.php/t-234673.html

by Guest Wed Jan 09, 2013 8:14 pm

MaxEntropy_Man wrote:van der waals's phd thesis was 17 pages long.

Max have you ever taken a look at the professional work of Ramanujan, Hardy or Littlewood?

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