I want to know examples of very flattering comments from famous scientists or mathematicians concerning younger colleagues. Here's an example of what I have in mind (I shall provide more as an answer): after reading de Broglie’s master’s thesis, Einstein wrote: “He raised a corner of the big veil”.
1$\begingroup$ G.H. Hardy championed Ramanujan. $\endgroup$– DJohnsonMay 11 at 12:17
A few about John von Neumann:
”You know, Herb, Johnny can do calculations in his head ten times as fast as I can. And I can do them ten times as fast as you can, so you can see how impressive Johnny is” — Enrico Fermi (Nobel Prize in Physics, 1938)
“One had the impression of a perfect instrument whose gears were machined to mesh accurately to a thousandth of an inch.” — Eugene Wigner (Nobel Prize in Physics, 1963)
“I have sometimes wondered whether a brain like von Neumann’s does not indicate a species superior to that of man” — Hans Bethe (Nobel Prize in Physics, 1967)
“Evidently, a Ph.D. thesis and examinations did not constitute an appreciable effort” — Eugene Wigner
This anecdote also may be of interest:
“There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann” — George Pólya
In 1946, Carl Siegel asked Harald Bohr what had happened in Europe in mathematics during the war. Bohr answered in one word: "Selberg". This was after Atle Selberg had defended his thesis in 1943, showing that a positive proportion of the zeros of the Riemann zeta function lie on the critical line.
Isaac Newton wrote about Roger Cotes: “If he had lived we would have known something.”
Albert Einstein once said that the reason why he kept going to the Institute of Advanced Studies after having retired was “to have the privilege of walking with Gödel to go home”.
Ananyo Bhattacharya provides a number of examples in his recent biography of John von Neumann.
For example, Abraham Fraenkel channeled Bernoulli:
[...] a long manuscript of an author unknown to me, Johannes von Neumann, with the title Die Axiomatisierung der Mengenlehre [...] I don't maintain that I understood everything, but enough to see that this was an outstanding work and to recognize ex ungue leonem. (to know the lion by his claw)
One which made me laugh out-loud was Hilbert's comments on von Neumann. Von Neumann quickly became a favourite of Hilbert at Göttingen, much to the annoyance of the "old guard". The pair would go for walks in Hilbert's garden and lock themselves up together to discuss mathematics and the new quantum theory. Hilbert, being one of the examiners at von Neumann's oral exam is alledged to have asked just one question:
In all my years I have never seen such elegant evening clothes: pray, who is the candidates tailor?
(This is reminiscent in spirit to Russell's comment to Moore when entering the examination room for Wittgenstein's oral exam.)
I found this claim rather confusing since von Neumann did his doctorate at Berlin rather than Göttingen.
Gauss had some very flattering things to say of Riemann, describing his doctoral thesis as being of "gloriously fertile originality."
$\begingroup$ I could not change just the two letters in the typo for "Riemann"... $\endgroup$ May 10 at 21:31
$\begingroup$ @paulgarrett Thanks. $\endgroup$– nwrMay 10 at 21:50
There is a lecture (available online) by Leonard Susskind at Cornell University, where Susskind makes a break when discussing the holographic principle to talk about Juan Maldacena:
It was in 1994 or so this conjecture was put forward. Most people at the time thought it was a screwball in motion. But it took a couple of years, basically until 1998 a young Argentinian physicist, whose name you should know. I ask people, do you know who Juan Maldacena is? I'm talking about physicists or physic groupies and so forth, often they don't. Juan Maldacena is perhaps the greatest physicist of his generation. I won't tell you how old he is. He's younger than me, so he's not necessarily greater than me... [audience laughs] but he is certainly the greatest physicist, the greatest theoretical physicist of his generation.
(from transcript, source: Lecture 2: Black Holes and the Holographic Principle May 30th, 2014).
There is also Enrico Fermi c.a. 1939, who speaking to Giuseppe Cocconi about Ettore Majorana's mysterious disappearance, praised:
You see, in the world there are various categories of scientists: there are people of a secondary or tertiary standing, who do their best but do not go very far. There are also those of high standing, who come to discoveries of great importance, fundamental for the development of science. But then there are geniuses like Galileo and Newton. Well, Ettore was one of them. Majorana had what no-one else in the world had.
source: Esposito, S. (2006). Fleeting genius. Physics world, 19(8), 34.
Gauss, in the last 10 years of his life, thought very highly of Eisenstein (then 22), describing the latter’s talent as that which nature bestows only a few times per century. See here.