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For those who aren't familiar, Lebron was so talented and sought-after in high school that he was able to skip playing NCAA basketball and went right on to the NBA at the age of 19. Have there ever been any academic researchers who showed so much promise at one stage (in undergrad or grad school maybe) that they were offered funding to set up their own research institution, or a high-ranking position they'd typically be unqualified for?

This is just a curiosity of mine and not a reflection on my career plans.

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    Yale only realized that Lars Onsager didn't have a PhD after hiring him as a postdoctoral fellow. – Anyon Dec 14 '18 at 20:46
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    Louis de Broglie in "his 1924 thesis Recherches sur la théorie des quanta (Research on the Theory of the Quanta) introduced his theory of electron waves. This included the wave–particle duality theory of matter. (...) The wave-like behaviour of matter was first experimentally demonstrated in 1927." The Nobel Prize in Physics 1929 was awarded to Prince Louis-Victor Pierre Raymond de Broglie "for his discovery of the wave nature of electrons." A Nobel prize for a PhD thesis :) – user68958 Dec 14 '18 at 21:05
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    Anecdotal, but I know someone who was offered (and accepted) a postdoc at Cambridge while still in the 2nd year of his PhD. – astronat Dec 14 '18 at 22:55
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    Realistically LeBron skipped one or two years ahead. You seem to be talking about skipping a decade (or two) ahead. – StrongBad Dec 15 '18 at 3:13
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    TL;DR: Yes, there are some very gifted persons who made an academic career very early. (I don't think we need more individual examples.) – henning -- reinstate Monica Dec 20 '18 at 9:41
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I am not sure what aspect of LeBron James you are referring to. He was drafted straight out of high school. This is impressive, but there have been 45 others who did that. Something like 15% of NBA first round picks are one and done picks, so realistically he was a year or two ahead. He won his first MVP award at 24, but there have been 14 players under 25 to do that. Again, maybe he is a year or two ahead of his competition.

In academia, it the US a typical progression is 4 years undergrad, 5 years PhD, 2 years postdoc, 6 years pre-tenure. At any one of those stages a gifted and motivated person could skip a year (sometimes two). Being a year or two ahead is relatively easy.

What you seem to be asking about is skipping 5-10 years. This is much harder, but sometimes happens.

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Harvey Friedman doesn't have a high school, undergraduate, or master's degree. Just a Ph.D. in Math.

https://en.m.wikipedia.org/wiki/Harvey_Friedman

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Stephen Wolfram self-published a physics book at age 12 and then 3 more by the age of 14 (a lot of people do this, but you can look at the PDFs by clicking on the links here and I think you'll find that these could compete in quality to the works of many adults at the time).

That same link will tell you that he did not finish high school, or undergrad, but received a PhD at age 20 from Caltech. On the recommendation of Richard Feynman and Gerald Freund, he joined Caltech's faculty at age 21.

Have there ever been any academic researchers who showed so much promise at one stage (in undergrad or grad school maybe) that they were offered funding to set up their own research institution, or a high-ranking position they'd typically be unqualified for?

To qualify into the PhD program at Caltech, one typically needs at least an undergrad degree, and Stephen Wolfram did not have one. As user StrongBad points out, entering a PhD program at Caltech is far more exceptional than entering the NBA straight from high school, when you look at the percentage of people that have done either. Entering the faculty at a university like Caltech at age 21 and only 1 year after finishing the PhD, was also probably less common percentage-wise, than entering the NBA straight from high school.

You ask about "setting up their own research institution", at first I was going to tell you that including this in your question was a bit extreme, but after reading more about Wolfram I found out that he set up the Center for Complex Systems Research (CCSR).

However LeBron James stayed in the NBA for a fairly long career and has continued to be (arguably) the best player in the NBA. Wolfram "academic career" was short relative to most other academics, because he shifted to doing other things such as:
(1) making software for academics
(2) making educational resources and doing outreach
(3) managing businesses that help academics
He did continue to do academic work and published a book with academically original content, but it wasn't received as well as the mid- to late-career achievements of LeBron James. His success in (1), (2), and (3) though can definitely be compared to the mid- to late career achievements of LeBron James.

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The analogy is a bit weak for a few reasons. I realize Lebron also followed through on early promise, but at least in something like math (my field), it doesn't have to be a case of "promise", because it can be clear that someone is brilliant: they have results to back it up. Also there is no special big league that offers tons of money or that you need to get into while you are still young; being in grad school is comfortable place to do research and learn things.

A recent example that comes to mind is John Pardon. While still an undergraduate he published multiple papers including one in the Annals of Mathematics. This is one of the top few journals in math and is basically unheard of these days for an undergrad to publish there. But he still took a normal amount of time as a grad student at Stanford, it's just he became a full professor at Princeton the year after graduating...

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In computational chemistry/physics:

Peter Wolynes became a professor at Harvard at age 23.

Henry Schaefer III became a professor at Berkeley at age 25.

These appointments were at that time more rare (percentage-wise) than entering the NBA out of high school. Both of them went on to be world-leaders in their fields, but I think Klaus Schulten's h-index of 152 is far above anyone else's in the field of Peter Wolynes (computational biochemical physics) and the 165 h-index of Donald Truhlar (also a professor from age 25) is far above anyone else's in the field of Henry Schaefer III (quantum chemistry). Don Truhlar's i-10 index of 1167 is maybe the highest in the world if divided by the number of co-authors (since in fields like medicine and particle physics, papers can have far more authors, meaning each one of them has usually put in far less work).

I therefore claim that Don Truhlar is the LeBron James of computational chemistry/physics.
All these metrics need to be taken with a grain of salt, but knowing the field quite well, I'm comfortable with making this claim.

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There are certainly many people who have entered academia who were child prodigies, who have taken an unusually rapid route into senior academic positions. A quintessential example is the Hungarian physicist, mathematician and computer scientist John von Neumann. Von Neumann was a child prodigy who learned differential and integral calculus when he was eight-years-old. By the age of nineteen he had published two important mathematical papers.

Von Neumann's father insisted that he go through the regular schooling grades for his age, but he also had private tutoring to supplement this. After his schooling, he enrolled directly in a PhD candidature in mathematics concurrently with programs in chemical engineering, the latter due to pressure from his father to pursue a profession with good financial prospects. He did them both concurrently, and after receiving his PhD in mathematics he became the youngest person ever elected privatdozent at the University of Berlin. Even before this he had published several mathematics papers at a level of original contribution that would exceed the contributions of most modern tenured professors.

If you haven't had a chance to read about the extraordinary genius of this guy then you are in for a real treat. He makes the basketball skill of Lebron James look pretty ordinary by comparison. Other brilliant physicists and mathematicians who knew him, including Nobel laureates, regarded Von Neumann to be someone of super-human genius who could basically run rings around them. He had a photographic memory, and could recite verbatim books he had read years ago, including translating them to English in the process, reportedly without any diminution in speed. To entertain his friends he memorised pages of phone directories and then recited the contents of randomly chosen pages. There is a famous story about him doing a mathematical problem called the "fly puzzle" where he is reputed to have performed a difficult mathematical operation almost instantaneously in his head. The physicist Hans Bette referred to him as being of a superior "species", an "evolution beyond man". Some consider him to have been the smartest person of the twentieth century, if not one of the smartest people ever to exist.

  • For those interested about these von Neumann stories, see The legend of John von Neumann by Paul R. Halmos (1973). Regarding the "fly puzzle", this gives a description of it, and a lot of references to it (up to 2006) are given here. – Dave L Renfro Dec 20 '18 at 8:28
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A couple more:

M. King Hubbert was hired to teach advanced classes and actually founded a program (!) in geophysics at Columbia. He worked there for several years, not having finished his Ph.D. from Chicago, yet. See the biography by Mason Inman.

Also Jaime Escalante (the teacher in Stand and Deliver) was hired to teach at three schools in Columbia while he was still a student in teachers college. The Jay Matthews biography has the details.

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Freeman Dyson never got his Ph.D.

https://en.wikipedia.org/wiki/Freeman_Dyson

Really though, I think skipping the undergrad and moving directly into Ph.D. or direct research work would be more impressive and more direct to Lebron. (Don't have a good example.) But the reason I say this is Ph.D. students are often already productive working researchers. (So not completing or even skipping entirely the graduate degree is not as impressive.)

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Gerald Bull, famous for his work on long-range artillery, obtained his PhD age 23. The rumour (which I cannot source) is that, at the time, he was the youngest PhD from the University of Toronto. A recognized genius of ballistics he would be (in)famous for his work on various super-guns.

John Moffat eventually got a position at the University of Toronto. He was awarded a PhD from Cambridge without ever obtaining an undergraduate degree; prior to his work in relativity he was a painter in Paris. His personal correspondence with Einstein may have worked in his favour.