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A number of years ago, I read a (non-fiction) story about a young mathematician whose professor wrote an open problem on the board and the student went ahead and wrote down a solution after a moment of thought. The writer goes on to say something like

From that moment on, I was afraid of [this student].

I think the article mentioned that, when asked questions in class, many students would offer ideas without thought but that this particular student would think quietly before saying what was correct. Would someone know where this story can be found, probably in an article, and who the student was? I would like to say that the student was a young Grothendieck but my Google searches in that direction were fruitless.

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That's John von Neumann, about whom George Pólya wrote:

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.

Edit: I have confirmed that the passage above can be found at The Pólya picture album, edited by G. L. Alexanderson (Birkhäuser, 1987, p. 154). The sentences quoted above are part of the caption of a picture of von Neumann and Abraham Taub, which begins with:

This is my only picture of von Neumann. He is the only student of mine I was ever intimidated by. He was so quick.

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  • $\begingroup$ Yes, that's the one! Do you have a reference? The following link says it can be found on "2nd ed. (1957), p. xv" of "How to Solve it" but that page falls in the table of contents in my edition of the book: math.stackexchange.com/questions/659153/… $\endgroup$
    – Favst
    Commented Jan 22, 2021 at 19:46
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    $\begingroup$ All bibliographical references that I was able to locate say that, but you're right: it's not there. On the other hand, it seems that you will find it at The Pólya picture book, edited by G. L. Alexanderson (Birkhäuser, 1987, p. 154). At least, that's what it says at Rosemary Schmalz's Out of the Mouths of Mathematicians: A Quotation Book for Philomaths. $\endgroup$
    – José Carlos Santos
    Commented Jan 22, 2021 at 20:14
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    $\begingroup$ Reading this quote definitely rings a bell, and I'm fairly certain I've seen this before. Looking around a bit I found a less detailed version on p. 386 of The legend of John von Neumann by Paul Halmos (1973), which I've read all of at least twice so I would have seen it there, but it doesn't seem to be in my copy of Pólya's How To Solve It or in a few other books I looked at (e.g. Pólya's interview in Mathematical People. Profiles and Interviews by Albers/Alexanderson -- at least (continued) $\endgroup$
    – Dave L Renfro
    Commented Jan 23, 2021 at 14:42
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    $\begingroup$ not in the first edition), but a google-books search definitely shows several places it can be found. $\endgroup$
    – Dave L Renfro
    Commented Jan 23, 2021 at 14:44

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