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When I was a young and impressionable graduate student at Princeton, we scared each other with the story of a Final Public Oral, where Jack Milnor was dragged in against his will to sit on a committee, and noted that the class of topological spaces discussed by the speaker consisted of finite spaces. I had assumed this was an "urban legend", but then at a cocktail party, I mentioned this to a faculty member, who turned crimson and said that this was one of his students, who never talked to him, and then had to write another thesis (in numerical analysis, which was not very highly regarded at Princeton at the time). But now, I have talked to a couple of topologists who should have been there at the time of the event, and they told me that this was an urban legend at their time as well, so maybe the faculty member was pulling my leg.

So, the questions are: (a) any direct evidence for or against this particular disaster? (b) what stories kept you awake at night as a graduate student, and is there any evidence for or against their truth?

EDIT (this is unrelated, but I don't want to answer my own question too many times): At Princeton, there was supposedly an FPO in Physics, on some sort of statistical mechanics, and the constant $k$ appeared many times. The student was asked:

Examiner: What is $k?$

Student: Boltzmann's constant.

Examiner: Yes, but what is the value?

Student: Gee, I don't know...

Examiner: OK, order of magnitude?

Student: Umm, don't know, I just know $k\dots$

The student was failed, since he was obviously not a physicist.

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Since every finite CW complex is weakly homotopically equivalent to a finite topological space, that does not sound so bad... :) –  Mariano Suárez-Alvarez Jan 24 '11 at 20:54
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Perhaps not an urban legend per se, but when I was learning algebra, my professor, in an attempt to impress upon us the necessity of checking that certain maps are well-defined, told us the story of a classmate of his who got several years into his Ph.D. thesis before realizing that the maps he was investigating weren't well defined. Horrified, we asked him if this was true. "No" he said, "but that's one lie you'll never forget!" –  Nick Salter Jan 24 '11 at 21:04
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Mathematical urban legends have been collected by Steven Krantz in the book, Mathematical Apochrypha (and I think there's a second volume). A few refer to the thesis defense. –  Gerry Myerson Jan 24 '11 at 23:18
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Though this question and its answers are very entertaining, I think it is a little unfair to close other questions as "offtopic" which are even closer to mathematical research as this one ... –  Martin Brandenburg Jan 25 '11 at 8:54
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I have to agree with Martin. This is a very entertaining thread but it seems quite outside the mandate of MO. –  Ryan Budney Jan 26 '11 at 16:30

69 Answers 69

Prof. M eventually says to his student: "There's nothing more I can teach you on this subject, I'll have to send you to Prof. B". So the student goes to study with Prof. B. A few months later he returns to Prof. M, a whimpering wreck. Prof. M calls up Prof. B. "What did you do to my student?" "You told me to stretch him." "Yes, but not on the rack.".

OTOH Another Prof. B told me that this was exactly the kind of story that the original Prof. B used to calculatedly spread about himself to give himself a certain reputation.

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I've heard stories about von Neumann chatting up recent Ph.D.'s and solving their thesis problems in his head. An incident along those lines is recounted in Sylvia Nasar's biography of John Nash. Perhaps someone here can shed some light on which von Neumann stories are purely mythological?

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This actually happened in one of the initial lectures in an introductory course in linear algebra. This was an altogether new experience for us to get acquainted with abstract way of thinking. So the teacher said -"Let a, b and c be three linearly independent vectors in the vector space R^n." A guy interjected -" Sir, can you be more concrete?" "Ok"-said the professor and continued - ""Let alpha, beta and gamma be three linearly independent vectors in R^n".

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I don't really get it...The joke is that some professor thinks that "$\alpha$" is more concrete than "a"? To me that's just weird. –  Pete L. Clark Apr 17 '11 at 8:50

Allegedly, when Peter Lax was receiving his National Medal of Science, everyone had to describe their more notable accomplishments, and being somewhat cowed by the tales of curing cancer, turning water into wine, etc, etc, when the turn came to him, his description of his accomplishments was:

I integrated by parts...

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Denis Serre has unfortunately already posted this... –  Qiaochu Yuan May 23 '11 at 19:35
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Not so unfortunate, but I should pay more attention:) –  Igor Rivin May 23 '11 at 20:08

(A rather sad story)

For obvious reasons, I won't give the place and/or names.

On a thesis defence (we have here a procedure very different from Europe or US; for instance, the committee is more or less fixed) one member of the committee rose and asked to vote against the thesis because of plagiarism: the thesis contained (almost verbatim!) definitions from a book X.

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I don't understand, were the definitions supposed to be part of the original work of the author? –  Sean Tilson Jan 25 '11 at 18:22
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@Sean I had understood that as being the point of the story. –  Daniel Moskovich Jan 25 '11 at 19:47
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It's possible for a definition to be creative or unique; in such case it should have been cited. –  David Harris Jan 25 '11 at 21:15

When I was a grad student, I lived across the street from an electronics store. The owner of the store  had done some graduate work (in some sort of Engineering, I think). He ran a weekly ad in the local newspaper, and placed at the bottom of the ad a relatively hard math problem. And he gave anyone who could solve the problem the choice of a free radio or telephone (each of which would retail for less than ten dollars). After solving one of his problems, and speaking with him for a bit, I convinced him to place a problem from group theory (it was about equations over the group $Z_2$) in the next ad.

The next week the ad came out. My problem was there in print. My first publication. A few days later I went to talk to the owner of the store. He was furious. A whole bunch of people had come in with solutions and he gave away a lot of free radios and telephones.

The sad thing was that none of the solutions were correct.

EDIT- now for the mathematical urban legend...

A well-known topologist, let's call him X, told me that this had happened to him. He had been in a seminar for graduate students. The student speaker was proving one of X's theorems. X found this boring and fell asleep. And he started snoring.

They had to wake him up because no one could hear the speaker.

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There is also the story of the young mathematician which speaks in a conference, and at the end of his talk a (famous) mathematician provides a counterexample to his main theorem. This is just another variation to the story posted by WW.

I head this story from couple people (they claim they were there), but, if I recall right, I also read it in "The Puzzling adventures of Dr. Ecco".

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I know one case when that actually happened only it was not a conference but a colloquium, it was a famous (OK, not a celebrity, but still...) mathematician who was giving the talk, and it was a young fellow who gave a counterexample. I'll not disclose the names but if you really want to dig for the details, search east of lake Erie... –  fedja Jan 25 '11 at 1:22
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I witnessed something like that happening at a conference some 20 years ago. About 15 minutes into a talk a Fields medalist in the audience commented loudly (and laughing....!) that a "theorem" just written on the board couldn't possibly be true for this and that reason. The speaker blushed, stared silently at the board for a couple of minutes and then had to admit that he was wrong. We had a longer-than-usual coffee break....... –  Andrea Mori Jan 25 '11 at 14:16
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Concerning these stories I always ask myself: Does "wrong" mean that the theorem is absolutely wrong, or that we can repair it by, say, adding some assumptions or modifying the definitons? –  Martin Brandenburg Jan 26 '11 at 22:51
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@Andrea: I did not post this story because I only heard it second hand, but the way you describe the Field medalist (loud and laughing) makes me think it's the exact same incident that I heard about from somebody else who witnessed it. It sounded absolutely mortifying. –  Thierry Zell Jan 27 '11 at 16:24
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I witnessed an incident with perhaps a better moral. Immediately after or maybe during a conference talk (some 35 years ago) by a young analyst, it was noticed that the main claim could not be right. The speaker was dejected but one famous listener, possibly Joe Kohn, responded: "Look, even if that statement is wrong, you are proving Something, let's just see what it is." I believe they shortly arrived at a correct version, and the young man was relieved, but the kind helpfulness and the positive attitude was the main lesson I took away. –  roy smith Apr 13 '11 at 16:11

Was the Chicago professor M. H. Stone of Stone-Weierstrass fame? Prof. Abhyankar has several times recollected his lectures at tata institute, which he attended as an undergraduate student, starting with : let X be a Hilbert space, over reals or complex nos or quaternions.

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In a fabulous French comedy La moutarde me monte au nez Pierre Richard's character is a maths teacher at a local girls' college. One day he accidentally ends up in a mansion that belongs to an American movie star (Jane Birkin). Frighened of a potentially dangerous intruder, she sets her pet cheetah on him, and the academic promptly jumps on a huge chandelier.

To prove to her that he was indeed a maths lecturer, he had to answer a few questions. First - to expand $(ax+b)^2$ (which he did) and then - to integrate $\sin(ax+b)$ (again, success). All that - hanging from a chandelier, with a cheetah pacing below.

Only after that she allows him to climb down to the floor... and then they have a romantic dinner, needless to say.

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That doesn't seem to be an urban legend. –  Douglas Zare Jan 28 '11 at 13:36

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