Saturday, August 12, 2023

In mathematics it is possible to write a great PhD dissertation in a very short time. Here are some examples: George Dantzig was a doctoral student of the great statistician Jerzy Neyman at Berkeley. In one of his classes, Neyman wrote two problems on the board. Dantzig arrived late to the class that day, and thought they were the homework for the week. He solved and submitted them. Then he was told that they were two of the unsolved problems in mathematics. Later, when Dantzig met Neyman to discuss possible dissertation topics, Neyman told him he could submit the “homework” he had done as dissertation. Later, the two were published. Very brief. In dissertation work what counts in posterity is the quality of work and not the bulk. Some of the greatest dissertations i history are ridiculously short. Alan Turing (father of Computer Science) dissertation at Princeton was only 28 typed pages long. The dissertation of John Nash (one of the greatest Game Theorists, also at Princeton, was only 27 typed pages long. The shortest PhD dissertation is supposed to be one in mathematics at MIT that is only 9 pages long. 

 Tragically, the average length of dissertations is 133 pages. See: https://www.universityaffairs.ca/news/news-article/researcher-determines-average-length-theses-dissertations-quebec/#%3A~%3Atext%3D%E2%80%9CThe%20world%20record%20for%20the%2Chave%20become%20longer%20over%20time.

The length of dissertation titles seems to be getting longer. A grotesque example is the one in Psychology:

“Stress maternel prénatal et développement précoce : données de naissance, attention et sécrétion cortisolaire à trois mois. Association entre le stress maternel prénatal, l’âge gestationnel et le poids de naissance du bébé : une analyse d’études prospectives. Association entre le stress maternel prénatal, l’attention/éveil et la sécrétion cortisolaire de l’enfant à trois mois.”

That probably deserves an IgNobel prize.

For those interested, here are the two papers by Dantzig:

Dantzig, G.B., 1940. On the non-existence of tests of" Student's" hypothesis having power functions independent of σ. The Annals of Mathematical Statistics, 11(2), pp.186-192.

Dantzig, G.B. and Wald, A., 1951. On the fundamental lemma of Neyman and Pearson. The Annals of Mathematical Statistics, 22(1), pp.87-93.

Altogether they are only 12 pages long. Incredible. At first I thought it was a tall tale, but then found it had been vetted by snopes:

The Legend of the 'Unsolvable Math Problem' A student mistook examples of unsolved math problems for a homework assignment and solved them.

https://www.snopes.com/fact-check/the-unsolvable-math-problem/ The Dantzig story is supposed to be the inspiration for the popular movie “Goodwill hunting”.

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