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When I read up the bibliography of the mathematicians and scientists in the early 19th to 20th century, I am always shocked at how they were able to graduate university with PhD(s) at such a young age.

For example, John Von Neumann graduated from two universities simultaneously at the age of 22 with two PhD degrees and critical papers published.

John Forbes Nash graduated with a PhD at 22 on game theory. Enrico Fermi finished school at 21 with thesis on X-ray diffraction. Kurt Gödel finished school at 23 with dissertation on predicate calculus. Abel finished at 20 with thesis on quintic equations. Galois never graduated but created a field of his own before dying at the young age of 20 and the list goes on and on...

I am not knowledgeable of the trend in the social sciences but I suspects much of the same.

  • Can someone tell me if there has been a major shift in how university education is conducted such that university across the world takes longer to get through than it used to be
  • or is it truly because these people are unusually talented and are able to get through university purely based on their almost unnatural abilities?

Most importantly (and relevant), why is there such a decline in these young PhDs (I've never heard of a professor at my university who graduated at 21) and is it still possible for people to graduate at such a young age nowadays?

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    Modern example: Terence Tao got his PhD at 21 and became a full professor at 24. en.wikipedia.org/wiki/Terence_Tao – Davidmh Nov 20 '14 at 8:35
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    I think your sample of scientists is severely biased and hence, the conclusion that there is a decline in the number of young PhDs is not supported. I suppose that the relative number of young PhDs is decreasing (just because the total number of PhDs is increasing fast) but I do not see any evidence for the absolute number to be decreasing. – Dirk Nov 20 '14 at 8:40
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    I submit that your sample set is seriously atypical, consisting as it does of 5 mathematical geniuses (every one a household name) and one of the leading theoretical/experimental physicists of the 20th century (Fermi). If you are making a collection of famous mathematical prodigies, you could add Norbert Weiner to the list. :-) Having said that, there might be a reasonable question in there, if you can refine it further. You'd need to actually try and get hold of some concrete statistics if you are trying to show that people graduated more quickly in earlier years. – Faheem Mitha Nov 20 '14 at 9:27
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    "or is it truly because these people are unusually talented and are able to get through university purely based on their almost unnatural abilities?" There are famous mathematicians that don't get through university super-fast too. – Faheem Mitha Nov 20 '14 at 9:29
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    In my country (Italy), it is forbidden to finish any study before the legal end. A BSc cannot take less than 3 years, a MSc cannot take less than 2 years, and a PhD cannot take less than 3 years. You cannot even take exams of the second year if you are enrolled in the first year of any program. So, if one starts the university at the age of 18-19, it is not legally possible to obtain a PhD before being 26-27 years old. Perhaps this holds true in other countries and it might provide a partial answer to your question. – dgraziotin Nov 20 '14 at 10:10
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One relevant aspect is the shift in the socially acceptable career schedule of people. The age of adulthood has been shifted from 13-15 y.o. to 18 in Europe and 21 in North America. This is not only true of scientists, but of all other professions. In the early 19th century, people started their professional career at 15 and peaked around 30, blacksmiths or scientists.

This shift likely happened during the 20th century. One example from the UK*:

the minimum school leaving age increased from 12 to 14 in 1918, to 15 in 1947 and 16 in 1972.

I've heard it's 17 now.

Nowadays, kids spend years filling coloring books and playing the recorder awkwardly before they first hear of mathematics, natural sciences or philosophy. And even after that, it's socially accepted to enjoy teen years riding a skateboard and playing beer-pong. So, we can certainly argue that we had a more laid back childhood than our 19th century counterparts, but it sure delays PhD graduation.

Some still go faster than others. For example this guy did his PhD in 2 years, got hired as a faculty at Columbia at 25 and got a tenure track position at EPFL at 29.

*Education: Historical statistics, Standard Note: SN/SG/4252, available: http://www.parliament.uk

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    FWIW re: your example, a Ritt Assistant Professor at Columbia is essentially a postdoc. Certainly postdocs are faculty members, but being a postdoc at Columbia at 25 (while impressive) is quite different from being a tenure-track/tenured faculty member at Columbia at 25. – Aru Ray Nov 20 '14 at 20:42
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    @Cape Code: A "named" assistant professor is usually a postdoc -- or, more precisely, a non-tenure track job. This is a top-drawer postdoc offered by very good departments. – Pete L. Clark Dec 27 '14 at 23:17
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There are several issues:

  1. Your examples are somewhat biased, since you've selected researchers who were not only brilliant but also prodigies. By contrast, Riemann finished his Ph.D. dissertation at the somewhat older age of 25, and Weierstrass didn't start his research career until he was 39 or so. Brilliant researchers are more likely to get an early start than average researchers are, but the correlation is far from perfect. Focusing on prodigies gives a misleading picture.

  2. There are plenty of prodigies today (Terry Tao, Noam Elkies, Akshay Venkatesh, Erik Demaine, etc.). If they occupy a smaller fraction of academia, it's probably because academia has grown enormously even relative to the population. The faculty in the top departments today are stronger on average than a hundred years ago, but there are many more departments nowadays, so the average professor is overall probably not as talented.

  3. The amount that's known is steadily increasing, so getting to the 19th century research frontier takes quite a bit less time than getting to the 21st century research frontier. This is not as relevant in very new fields, but finishing a Ph.D. in algebraic geometry in two years is a more impressive feat today than it was a hundred years ago. This increase in knowledge doesn't translate perfectly into an increase in time to degree: people also compensate by specializing more and then broadening later in their career. However, the obstacles to a quick Ph.D. are certainly increasing over time.

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