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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

One urban legend I remember was of a student who just wanted to schedule a language exam, but the professor opened a text to the introduction and asked him to translate it. The student asked to switch to the mathematics, saying, "I don't know any verbs!"

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That is not an urban legend, well, at least not the first half. My (French) language examiner at Princeton was disappointed that I brought a mathematics textbook (in French) for the exam. After looking around and couldn't find a French-language roman handy in his office, he begrudgingly passed me after I translated the Preface and Acknowledgements (in addition to several mathematics-laden passages from the middle of the book). –  Willie Wong Jan 24 '11 at 22:05
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I once took a math course for which the textbook was in French although the course was otherwise taught in English. You don't need to know much French to understand that sort of thing. –  Michael Hardy Jan 25 '11 at 2:54
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I heard from an older student in college that Nick Katz taught a course on local class field theory using Serre's Corps Locaux and that student didn't realize the book had been translated into English until after the course was over. –  KConrad Jan 25 '11 at 6:13
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@Someone: I actually dragged a Serbian friend of mine to seminar just for that. Otherwise they'd look at me and give the discussion in Chinese, and while it is my native language, it is by far not my native mathematical language. –  Willie Wong Jan 25 '11 at 12:49

I have heard the following story from a few sources (among them, I think, an MO thread, possibly Terence Tao's blog, and Richard Lipton's blog), so it might even be true.

The story goes that once upon a time a student wrote his thesis on Hölder-continuous maps with $\alpha > 1$, since he had only seen the case $\alpha \le 1$ addressed in his books. The student proved many wonderful theorems about these maps and was very excited for his defense.

At his thesis defense, one of the examiners (is that the right word?) asked him to provide a nontrivial example of such a map. The student was flustered. As it turns out, all such maps are constant - no wonder the theorems were so nice.

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That is a scary story: it paints a picture of mathematical education of extreme sadness! –  Mariano Suárez-Alvarez Jan 24 '11 at 21:20
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As I commented above, I heard the story (with Lipschitz instead of Holder) back in the 1950s, so it is a really old legend. –  Dick Palais Jan 24 '11 at 22:46
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I've heard this many times, and the question of which spaces these functions are defined on has always been omitted; presumably it is a manifold. I actually spend quite a lot of time working with non-trivial functions defined on compact totally disconnected spaces which are Hoelder with an exponent higher than $1$. –  Ian Morris Jan 25 '11 at 10:26
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By the way, in my version, the student was specifically studying the Banach space of such functions, and was eventually told that he was studying $\mathbb{R}$. –  Nate Eldredge Jan 27 '11 at 0:58
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I hear a similar story a few years ago, where a student proved exciting theorems about holomorphic functions with compact support. –  Orbicular May 23 '11 at 22:12

I've heard the following story (don't know if it was true, or who was supposedly involved):

As is well-known, at a certain big-name university the advisor defends the student's thesis. A student worked with a certain big-shot for five years and produced what many looked at as a fine dissertation. The day of the defence came. The advisor got up to the board, gave a quick introduction, and embarked on stating the main theorem in the dissertation. Half way through writing it, he put down the chalk, and paced around a bit. He then turned, apologized, and said, "I'm sorry, but I think I've found a counterexample."

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If we're thinking of the same big-name university, then I heard that the impetus for the whole "advisor defends the student's thesis" system arose from an advisor making a quip along the lines of "this is the best thesis I ever wrote" in a defense prior to this system. It's not clear why this would have been an effective solution to this sort of problem, so this is probably pure apocrypha. Amusing nonetheless! –  Ramsey Jan 24 '11 at 22:39
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I have heard the same story as Ramsey, about the same university -- but the quip is supposed to be "OK, so it's not the best thesis I ever wrote!" –  JSE Jan 24 '11 at 22:57
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When I was in grad school, a senior mathematician told me: "I never minded writing a student's dissertation, but I draw the line at having to explain it to him or her". –  Thierry Zell Jan 25 '11 at 0:08
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There's an old joke-definition of a dissertation, something like, "a research paper written by a senior academic under the most trying circumstances." –  Gerry Myerson Jan 25 '11 at 2:27
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This all somehow reminds me of a quote (supposedly from Haydn) "Don't make a sour face when listening to opening notes of a sonata written by some grand duke: you never know who actually composed it". –  fedja Jan 25 '11 at 4:01

Here is another scary example (known to be true, by way of two of the participants): a (then) young postdoc approached R. Langlands and A. Borel (this was in the late seventies), in the IAS tea room, and the following conversation ensued:

Postdoc: Do you guys know anything about automorphic forms?

B&L: Maybe

Postdoc: Well, can I ask a stupid question?

B&L: Well, you have already asked one.

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The version in Milne's apocrypha (jmilne.org/math/apocrypha.html) is slightly different: $$ $$ A newly arrived member of the Institute for Advanced Study went up to two senior looking people and asked if either of them knew anything about representation theory. Being Borel and Langlands, they answered "yes". "Well," said the member, "do you mind if I ask you a stupid question?" "You already have" responded Langlands. –  José Figueroa-O'Farrill Jan 24 '11 at 22:37
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The beauty of this story is that when you tell it to people, they all laugh but if you go one step further, they disagree on which of the two questions was stupid... –  fedja Jan 25 '11 at 2:21
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This story clearly comes in many variants. In my favorite, the Langlands retort to "do you mind if I ask you a stupid question" is "That's two already." –  Peter Woit Jan 25 '11 at 3:35
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In my first year I asked my professor in linear algebra, Schoenhage, whether he knew how to compute with large numbers (I was trying to write a program for testing the primality of Fibonacci numbers). –  Franz Lemmermeyer Jan 25 '11 at 6:58
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I once gave a seminar, and in response to a question from an unknown audience member, launched into an exposition of Baas-Sullivan theory. The organiser gently interrupted me: "I don't think you've met Nils Baas ..." –  Neil Strickland Jan 25 '11 at 8:33

I've heard the following story (I don't know if it is true). A math professor gave his PhD student this journal paper, and asked him what consequences he could derive from it. The student started proving more and more interesting results based on this paper, until finally he proved a result that the professor knew was false. This led them to look more closely at the original journal paper, and upon close inspection, they discovered that it was wrong, rendering all the research the student had done so far worthless.

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I've actually seen something like this happen. –  H A Helfgott Jan 29 '11 at 22:17
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That is a decisive argument for the motto "Give examples!". Examples are mental crutches, guides and railings too (as in this case) . - –  Jérôme JEAN-CHARLES Feb 3 '11 at 0:38

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

This one happened - I was there (as an observer, not a principal). Only the names have been changed.

X was Professor A's first doctoral student, and their relations weren't good. Rumor had it that the first time A saw most of X's thesis was when X handed in the final draft.

By the rules, there had to be a non-mathematician on the thesis defense committee - let's call him Professor H. Professor H made a valiant effort to read the thesis, understandably didn't get very far, but decided he was going to ask a question at the defense, to justify his being there in the first place. So he says to X, I notice you didn't provide a proof of your Lemma 2.3.1 - how does it go? X says, well, 2.3.1 isn't my work, it's a well-known result of van der Corput.

This satisfies H, but A says, OK, it's a result of van der Corput - but, how do you prove it? Well, X was prepared to answer questions on his own work, but hadn't brushed up on all the previous work that his thesis rested on. He hummed and hawed, started to give a proof, got stuck - at which point A gave him a hint. Using the hint, X got a little farther, but got stuck again - so A gave him another hint. This went on for an excruciating fifteen minutes (which, I'm sure, felt like 15 years to X), until finally Professor N broke the tension by saying, say, just whose thesis defense is this anyway, X's or van der Corput's?

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As an undergraduate at Yale in the '70s I heard a variation on the basic legend, which I'll spell out a little since it has a slightly different moral from any others above.

Student goes to advisor saying I'd like to do a thesis generalizing the results in article X. Advisor (and I think I heard it with Milnor as the advisor) says, "I don't recommend that because I don't think that's a very good article." Student persists, writes thesis, states theorem at the defense and at that point the advisor rises to say "consider the following counterexample..."


I also heard a variation on "functions which turn out to be constant" legend. But the version I heard has the thesis getting accepted, the vacuity of it contents going unnoticed for several years until an undergraduate supplies a one-line proof.


John Myhill told me about junior faculty at the University of Chicago about to grade qualifying exams in their legendarily ruthless way. André Weil pops his head in the door and says "Pass them all, they're no worse than you are."

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@Yemon Graduate student that I was, the Myhill's story painted Weil for me as a hero. Myhill, a very seasoned faculty member by then thought Weil came off as a monster. A question of perspective I suppose. Myhill did say that that year all the students passed. –  David Feldman Jan 25 '11 at 2:28
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"Experience confirms that severity towards others and self-indulgence are one and the same vice" - La Bruyere (trans. Choi, probably badly) –  Yemon Choi Jan 25 '11 at 5:29
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@Yemon Choi : translation is ok : for completeness the original is : "L'expérience confirme que la mollesse ou l'indulgence pour soi, Et la dureté pour les autres n'est qu'un seul et même vice." Citation de Jean de La Bruyère ; Les Caractères, Du cœur - 1688. –  Jérôme JEAN-CHARLES Feb 3 '11 at 0:22
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@Feldman: The story would certainly paint Weil for me as a hero if he had said, "Pass them all, they're no worse than I am." –  Timothy Chow Apr 15 '11 at 1:37

Since the OP gave a physics example, here is another one, also at Princeton. Why are they always at Princeton? Student finishes his presentation on very mathematical aspects of string theory. An experimentalist on the committee asks him what he knows about the Higgs boson. He hems and haws and finally says "well, it was discovered a few years ago at Fermilab", Experimentalist: "Can you tell me the mass?" Student: "I think around 40 GeV."

This was more than 20 years ago and actually happened. I was there. The student passed, but the next year all Ph.D students working on string theory were required to take a course on the phenomenology of particle physics.

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+1 for being there! On a related note I had a physics honours thesis defense panel which consisted mainly of experimentalists (optics, atmospheric physics etc) and my thesis was on a mathematical aspect of string theory. –  David Roberts Jan 24 '11 at 23:49
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I was at another final oral where an experimentalist brought a thin box filled with small rods, a partition that looked like / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ dividing it into two sides but with gaps big enough for the rods to pass through, and a plexiglass top so you could see what was going on. Initially the rods were equally distributed, but after vigorous and random shaking by the student they all ended up on one side. The experimentalist then asked "Why doesn't this system violate the 2nd law of thermodynamics?" Those guys are tricky! –  Jeff Harvey Jan 25 '11 at 1:01
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Jeff -- that's interesting. So why doesn't it? –  algori Jan 25 '11 at 6:36

I have no idea whether this one is true - I heard it at Harvard, around 1970. The story goes that a PhD student was so sure no one would ever read his dissertation that he stuck in the middle of it an offer to send fifty dollars to the first five people who asked. Every few years he'd get a letter from someone who stumbled across the offer, and he'd pay out.

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Something like this has certainly happened at least once, though the legend probably predates it: snopes.com/college/homework/foundcar.asp –  Harry Altman Jan 25 '11 at 0:21
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Coincidentally, I recently found forty dollars in the middle of a book on moduli spaces I had checked out from the library. –  zeb Jan 25 '11 at 4:54
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Visiting a friend's place in graduate school, I saw many brand new GTMs on his shelf. Or at least their condition was as good as new. Suspecting some of these books would remain unread for a while, I stuck a small note in one GTM which said "Today is [date here]. Let me know when you find this note. [Signature]" I heard from him a couple of years after he finishes grad school. –  KConrad Jan 25 '11 at 6:04
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Another story: suspecting students were not reading solutions I was writing to homework in an abstract algebra course, in the middle of one solution I inserted the sentence "I will give a free chocolate bar to the first person who reads this." Nobody claimed the chocolate bar. Or maybe I offered an orange? –  KConrad Jan 25 '11 at 6:06
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In the Caltech library there is a very big tome on combinatorics which I once idly opened at random. In it, I found a letter from an undergrad in the 1970s, who wrote this letter to posteriority saying that although he enjoyed working on his project, he was disheartened by the fact that nobody would probably ever care about it. –  jvkersch Apr 15 '11 at 4:10

I have a story of this kind. My thesis advisor J.-M. Souriau used to talk this story about one of his close friend (I'll keep quiet the name) : "Avant de devenir directeur de l'école normale supérieure (Ulm) il a passé la moitié de sa vie mathématique à définir le nombre de [[put his name here]] et l'autre moité à démontrer qu'il était égal à 1." I don't know if it is true, I doubt but not that much :-)

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Is this poor soul's number a candidate for mathoverflow.net/questions/32967/… ? –  Willie Wong Jan 25 '11 at 0:39

Not a horror story. On the much nicer end of the spectrum, there is a well-known urban legend about a student unwittingly solving an open problem, thinking it was homework. Though details of the tale may vary, there is at least one instance where the urban legend is true, George Dantzig in 1939. The funniest part of the story is when Don Knuth apparently came to learn of this story through a sermon by an Indiana pastor!

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In the Hebrew University, it is told about Avinoam Mann. –  Daniel Moskovich Jan 25 '11 at 2:43
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At Princeton, it is told about (who else) Jack Milnor. The result is the "Fary-Milnor" theorem, on the total curvature of a knotted curve (there is an Annals paper to back up the story...) –  Igor Rivin Jan 25 '11 at 2:45
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The version I heard was that Milnor was late to class, and copied down several (open) problems written on the board that he thought were homework. At a later class he says, "That homework was hard! I only got 2 of them." –  Jonas Meyer Jan 25 '11 at 3:25
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The Huffman code story I heard is that in an information theory class, Huffman had a choice of writing a term paper or taking a final. His term paper was the discovery of an algorithm for finding optimal binary codes (i.e., Huffman codes). –  Peter Shor Jan 25 '11 at 5:49

I heard this story a couple of years back (not sure though if it is true): A young Japanese mathematician was giving a talk based on his results at Courant Institute. His work was built on the work of S.R.S Varadhan. But apparently during the talk Varadhan had his eyes closed and the speaker mistook it for him sleeping. He made a joke by saying somthing like "hopefully not everybody is sleeping". A few minutes later Varadhan open his eyes and said "consider this counterexample". But Varadhan liked the speaker's idea and invited him to spent some time at Courant institute. The correct result is now known as 'Speaker'-Varadhan theorem.

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I suppose you mean S.R.S.Varadhan? –  fherzig Jan 25 '11 at 19:38
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Haha. Last August at the ICM, when he was chairing a session, even I thought he was sleeping. :) –  Koundinya Vajjha Mar 8 '11 at 16:29

The following story is a bit strange to be true, but we all believed it as students, and I think I still do believe that a somewhat weaker version of events must have indeed occurred.
Michael Maschler (most famous in Israel as author of the standard math textbooks for middle-schools and high-schools) was in the middle of teaching an undergraduate course- I think it was Linear Algebra- when one afternoon he walks into the lecture hall and announces the discovery of a new class of incredible Riemannian symmetric spaces with incredible properties, missed by Elie Cartan. The undergrads have no idea what he is on about; but the faculty all get very excited, and start sitting in on his Linear Algebra course. Ignoring the syllabus, Prof. Maschler begins to give lecture upon lecture about the new incredible symmetric spaces which he discovered. The excitement builds. Will he win a prize? Will he win the Fields Medal?...
And then, 3 lectures in, a student (some say it was Avinoam Mann, about whom many stories are told) gets up and asks, "Excuse me, sir. How can you distinguish your space from a sphere?"
Maschler turns to answer the "stupid question", but he freezes in mid-motion... Gradually, his face turns white. The lecture hall is so silent you can hear a pin drop. Finally, after what seems like an eternity, Prof. Maschler unfreezes. "By golly, a sphere it is," he murmurs in an undertone. And he picked the Linear Algebra textbook up from his desk, and resumed teaching where he had left off. The subject was never broached again.
And so, some Hebrew University students of my generation call spheres "Maschler spaces".

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I have no details to provide, but it is said that Ofer Gabber has derailed more than one talk at IHES after the speaker presents a definition by asking, "But what about the empty set?"

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He has actually derailed many Sem. Bourbaki by asking a stream of questions in English (the official language was, and presumably still is, French), until the speaker would start speaking in English. –  Igor Rivin Jan 25 '11 at 3:57
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I don't think the Séminaire Bourbaki has an official language. Like any lecture in France (or, I guess, in a French-speaking country), it's just convenient to do it in French unless the speaker isn't francophone. –  Maxime Bourrigan Jan 25 '11 at 22:26
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I recall a seminaire bourbaki in which Gabber persistently questioned Deligne in English, who answered just as persistently in French. –  roy smith Apr 13 '11 at 17:35

George Mackey is reported to have been overheard saying "I'll write his thesis for him, but I'll be damned if I'm going to explain it to him."

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A wholly different set of "named urban legends" (in order of time):

Allegedly, Jacobi came to show Gauss his cool results on elliptic functions. Gauss' response was to open a drawer, point at a sheaf of papers, and say: that's great you are doing this! I have actually discovered these results a while ago, but did not think they were good enough to publish... To which Jacobi responded: Funny, you have published a lot worse results.

When the logician Carnap was immigrating to the US, he had the usual consular interview, where one of the questions was (and still is, I think): "Would you favor the overthrow of the US government by violence, or force of arms?". He thought for a while, and responded: "I would have to say force of arms..."

Finally, on the graduate experience front, it was rumored at Princeton that Bill Thurston's qualifying exams at Berkeley were held as his wife was in labor with his first child -- the department refused to change the date for such a minor reason! I have just asked him about this, and it's true...

EDIT A certain (now well-known) mathematician was a postdoc at IHES in the late 1980s. Call him R. R comes to lunch, and finds himself across the table from Misha Gromov. Gromov, very charmingly, asks him what he was working on. R tells him, Gromov has some comments, they have a good conversation, lunch is over. The next day R finds himself across from Gromov again. Misha's first question is: so, what are you working on now?

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I'd never heard the Carnap story. It's reminiscent of Godel's US citizenship test. en.wikipedia.org/wiki/… –  Ed Dean Jan 25 '11 at 4:35
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Gauss was some 20 years older than Jacobi and was, well, Gauss. It would have take great nerve... –  Mariano Suárez-Alvarez Jan 25 '11 at 4:45
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The Thurston story is recounted in his interview in More Mathematical People. –  Todd Trimble Jan 25 '11 at 9:05
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Around the Jacobi/Gauß anecdote: the correspondence between Jacobi and Legendre is fascinating and worth reading. It's quite moving to see this old mathematician welcoming with enthusiasm the work of two younger ones (Jacobi and Abel) following the study of his favorite mathematical field. It's almost melodramatic, with episodes of anger against Gauß (Legendre has had his share of paternity disputes with him, for example regarding the quadratic reciprocity law or the law of least squares) or mourning after Abel died... –  Maxime Bourrigan Jan 25 '11 at 16:22
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... And as usual with mathematical texts of this time, the elegance of the language is baffling. Particularly so if one remembers that Jacobi doesn't write in his mother tongue. –  Maxime Bourrigan Jan 25 '11 at 16:24

Professor A at Harvard told the following story, supposedly a first hand account of his student days at Chicago, though it never struck me as remotely plausible. (I think he just told it so that he would seem like a teddy bear in comparison.) But I wonder if anyone else has heard variants of this.

At the beginning of a course, Professor X would start asking some reasonable questions, the answers to which students taking the course could be expected to already know. Finally, he would ask one unfortunate student a question which no one taking the course would be able to answer. Upon the student's failure to answer correctly, Professor X wouldn't explain that the student's ignorance was justified, instead letting this event undermine the student's confidence about taking the course. Professor X would continue to single out this poor target for humiliation until he or she finally dropped the course. Professor A claimed to believe that Professor X's motivation was to have lit a fire under the remaining students and make them band together.

Again, it's a rather unlikely tale of abuse. Though perhaps with a plant "student" playing along as the victim it could be an effective ploy ...

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A version of this happened at my undergraduate institution, but with a plant student. At the very first lecture, the professor sent the plant student to the blackboard and assigned a difficult exercise. The plant student does a nice job (one much better than any other students could do presumably), but the professor gives him a really hard time, harping on any flaw and concluding that this was "barely the level required to survive this lecture". The next day, six students had given up the course, so that the professor had to make sure words reached them that it was all a joke. –  Olivier Jan 25 '11 at 10:00

I heard the following story told about R. L. Moore.

It seems he was teaching a class in which several of the students were obnoxious and unruly. So one day he walked into the lecture hall, opened his briefcase, took out a pistol, set it on the table in front of him, and then began to lecture as usual. He had no further trouble with the rowdy students.

I have no particular reason to believe this is true, but it makes a good story. I think I have seen other references to firearms in the math department at the University of Texas, though.

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But I thought Moore didn't lecture! –  JSE Jan 25 '11 at 6:13
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As in all the best urban legends, it does not really matter if it's true or not: it does sound like something Moore would do. –  Thierry Zell Jan 25 '11 at 16:23
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I think Moore gave lectures in some of his classes at some points of his career. –  Pete L. Clark Jan 26 '11 at 8:35
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A friend of the family claims that in first grade, his teacher had a glass eye. The students didn't know until he had to leave the room to go to the bathroom. As he got up to go, he took out his eye and placed it on the table saying "Be good while I am gone - I'm watching you". These are 6 year olds... –  Steven Gubkin Jan 29 '11 at 1:47
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What Pete said is correct. Mary Ellen Rudin recounts in her interview for More Mathematical People that Moore gave lectures for calculus classes, and Halmos in his automathography recalls being permitted to sit in on one of Moore's calculus lectures. I think nevertheless that he would send students to the board in such classes. –  Todd Trimble May 23 '11 at 20:53

I have heard (from two sources) that at the University of Chicago a senior faculty member was temporarily banned from teaching undergraduate courses. The reason is that during a first semester undergraduate linear algebra course he did everything over the Quaternions.

This one isn't so much academically scary, but my advisor told me that it was always interesting riding to conferences with the above professor because he would refuse to defrost the windshield so that he could draw diagrams on it and do math while he was driving.

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Actually, that is not that bad of an idea! I have seen the face of my students when I tell them «you should go through your linear algebra notes to see how much of it carries over to the case of skew-fields» right before proceeding to pick a basis for an $\mathbb H$-module, say... –  Mariano Suárez-Alvarez Jan 25 '11 at 5:57
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As an undergraduate I heard a secondhand story about a knot theorist teaching an introductory calculus class. The first question on the final was basic calculus; the rest involved knot theory. –  Steve Huntsman Jan 25 '11 at 7:01
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In Germany many professors would be happy to get banned from teaching undergraduate courses (and behave accordingly). There used to be payment by number of students some years ago, but now it has been levelled, and teaching undergraduate courses has become nothing more than a chore people want to get rid of. –  darij grinberg Jan 25 '11 at 8:24
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This story sounds strange to me because (at least the past few years, when I was there) the University of Chicago, SFAIK, doesn't have a straight-up linear algebra class for math majors. The easier stuff you're basically expected to just up, the harder stuff gets stuffed into the general "algebra" sequence. –  Harry Altman Jan 25 '11 at 10:09
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Concerning quaternions, there is also a story, which has happend in Cambridge as my brother told me: A professor asks in a lecture: "Is here somebody who does not know everything about quaternions?" A single student raises slowly her hand. "What?? Then learn it until tomorrow!" - it goes without saying that there were students in the class who did not raise their hand and did not even know what quaternions are... –  Lennart Meier Feb 4 '11 at 20:48

Since this has become a free-for-all, allow me to share an anecdote that I wouldn't quite believe if I hadn't seen it myself.

I attended graduate school in Connecticut, where seminars proceeded with New England gentility, very few questions coming from the audience even at the end. But my advisor Fred Linton would take me down to New York each week to attend Eilenberg's category theory seminars at Columbia. These affairs would go on for hours with many interruptions, particularly from Sammy who would object to anything said in less than what he regarded as the optimal way. Now Fred had a tendency to doze off during talks. One particular week a well-known category theorist (but I'll omit his name) was presenting some of his new results, and Sammy was giving him a very hard time. He kept saying "draw the right diagram, draw the right diagram." Sammy didn't know what diagram he wanted and he rejected half a dozen attempts by the speaker, and then at least an equal number from the audience. Finally, when it all seemed a total impasse, Sammy, after a weighty pause said "Someone, wake up Fred." So someone tapped Fred on the shoulder, he blinked his eyes and Sammy said, in more measured tones than before, "Fred, draw the right diagram." Fred looked up at the board, walked up, drew the right diagram, returned to his chair, and promptly went back to sleep. And so the talk continued.

Thank you all for your indulgence - I've always wanted to see that story preserved for posterity and now I have.

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Another urban legend, which I've heard told about various mathematicians, and which Misha Polyak self-effacingly tells about himself (and therefore might even be true), is the following:

As a young postdoc, Misha was giving a talk at a prestigious US university about his new diagrammatic formula for a certain finite type invariant, which had 158 terms. A famous (but unnamed) mathematician was sitting, sleeping, in the front row. "Oh dear, he doesn't like my talk," thought Misha.
But then, just as Misha's talk was coming to a close, the famous professor wakes with a start. Like a man possessed, the famous professor leaps up out of his chair, and cries, "By golly! That looks exactly like the Grothendieck-Riemann-Roch Theorem!!!"
Misha didn't know what to say. Perhaps, in his sleep, this great professor had simplified Misha's 158 term diagrammatic formula for a topological invariant, and had discovered a deep mathematical connection with algebraic geometry? It was, after all, not impossible. Misha paced in front of the board silently, not knowing quite how to respond. Should he feign understanding, or admit his own ignorance? Finally, because the tension had become too great to bear, Misha asked in an undertone, "How so, sir?"
"Well," explained the famous professor grandly. "There's a left hand side to your formula on the left."
"Yes," agreed Misha meekly.
"And a right hand side to your formula on the right."
"Indeed," agreed Misha.
"And you claim that they are equal!" concluded the great professor. "Just like the Grothendieck-Riemann-Roch Theorem!"

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This sounds like a whole generation of French-educated algebraists has never seen an equation in their whole life :D –  darij grinberg Jan 25 '11 at 15:29
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I guess nowadays one has the analogous "But that is a special case of the (coarse) Baum-Connes conjecture for (quantum) group(oid)s" ... –  Yemon Choi Jan 25 '11 at 21:15
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If my memory serves me correctly, Victor Ginzburg once said something like: "that's a Langlands correspondence, because it's a correspondence between two sets" in a seminar. –  Amritanshu Prasad Oct 7 '13 at 7:53

Here's another great one: a certain well known mathematican, we'll call him Professor P.T. (these are not his initials...), upon his arrival at Harvard University, was scheduled to teach Math 1a (the first semester of freshman calculus.) He asked his fellow faculty members what he was supposed to teach in this course, and they told him: limits, continuity, differentiability, and a little bit of indefinite integration.

The next day he came back and asked, "What am I supposed to cover in the second lecture?"

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A little more context from (the version I heard) of this one: the mathematician’s previous experience had been in the USSR — I think in Moscow. (This hopefully adds something useful without getting too specific…) –  Peter LeFanu Lumsdaine Jan 25 '11 at 16:57
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This is really not specific, because in the USSR one was taught these concepts in school. –  darij grinberg Jan 25 '11 at 17:05
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well, and in large parts of the rest of europe, too. –  Delio Mugnolo Apr 12 '13 at 21:08

A legend that I heard from my father, who heard it from ... ... ...: Levi-Civita was teaching a course in a room on (what Americans call) the second floor of a building. One day, as a prank, his students "borrowed" a donkey from one of the fruit vendors on the street in front of the building. Somehow, they brought this donkey up the stairs into the lecture hall and had it standing there as Levi-Civita entered to begin his lecture. Levi-Civita set his notes down on the lectern, looked up at the class, commented "I see we have one more today," and proceeded with his lecture.

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This story was told to me by my advisor.

A Ph.D. student in logic was having an extremely difficult time finishing his thesis and was starting to succumb to hopelessness. Every evening he would trudge home, open a beer, and sit down in front of the television. This was the 1960's. Evidently there was a running show called Whiz Kids that showcased the achievments of child prodigies; I'm imagining something of a Johnny Carson style setting involving banter with an unctuous host before a studio audience. One week, the young Harvey Friedman was on the show. The host asked Harvey what he had been up to recently, to which the latter responded that he had proved that "every end extension of a model of standard arithmetic has an elementary submodel such that..." and on to the technical details, much to the amusement of the studio audience. The student watching home at that moment realized: that closes precisely the gap I need to finish my thesis!

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The version I heard of this story the show was the Guinness Book of World's Rescords show hosted by Flip Wilson. While I don't know if the story is true, I have seen a photo of Harvey with Flip Wilson. Also this show aired in 1970 which fits the time frame. –  Dave Marker Jan 25 '11 at 17:24

Here's something that keeps me up at night:

During the Russian revolution, there is a story of a mathematician (I've heard Igor Tamm may be the one) who was mistaken by rebels to be a communist spy. He was promptly captured by a local gang and interrogated. When he said that he is a mathematician, the gang leader asked him to back up his claim by deriving the formula for the Taylor Remainder Theorem. He was warned that if he failed, he would be shot on the spot. After some sweating the mathematician finally derived the result. The gang leader was satisfied with the proof and let him go.

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So that's why when I was a first year graduate student at Harvard, the question "state and prove Taylor's theorem" appeared on the written qualifying exam! I think the professor who put this on the exam (we all thought it was Andy Gleason) was skeptical about whether the graduate students knew freshman calculus properly. As it happens, I knew how to do this only because I had been teaching freshman calculus that semester. Otherwise, I would have had to do some sweating, too. –  Deane Yang Jan 25 '11 at 17:45
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According to Gamow, it was Tamm (references: books.google.com/… and springerlink.com/content/w0934gm403641227 ) –  Harun Šiljak Jan 25 '11 at 18:47
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For some reason I feel slightly wistful for a world (or a time) where gang leaders even knew there was such a thing as the Taylor Remainder Theorem ... –  Yemon Choi Jan 25 '11 at 21:13
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@Yemon: what makes you so sure that gang leaders today don’t know it? –  Peter LeFanu Lumsdaine Jan 31 '11 at 18:06
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Russian math education is solid! even Gang leader know Taylor remainders... –  36min Apr 15 '11 at 1:21

Bob Stong told me that a Ph.D. candidate once presented his thesis in topology without any examples. One of the committee asked for any space for which the work was true. The student said that he had yet to think of one. He was failed in short order. I seem to remember that the story was from University of Chicago, but I could be wrong. Whether Professor Stong was pulling my leg or not is not known.

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I was actually present for something like this. This was in Oregon, maybe 15 years ago. The speaker lectured for 75 minutes on the cohomoolyg of a certain class of spaces. I was a beginning graduate student at the time, so I didn't really understand the talk, but, apparently, the class of spaces had very unusual properties. Someone asked - as in your story - at the end of the talk if the speaker could give an accessible example of this class. The speaker said, unabashed, that he couldn't. In fact, he strongly suspected that there were \textit{no} examples at all! –  John Iskra Jan 28 '11 at 17:31
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I don't think this is so unreasonable. I am sure many people try to characterize, eg, $\{x | \zeta(x)=0, \Re(x) \neq \frac12\}.$ –  Igor Rivin Jan 28 '11 at 23:04
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I heard once that Cauchy wrote a paper about "Bounded Entire Functions". From what I know, he later proved the Liouville Theorem. –  Nick S Feb 6 '11 at 17:45
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The paper at annals.math.princeton.edu/2010/171-1/p10 which is based on a PhD thesis, makes Igor's point even better than his example does. –  Dan Fox Apr 13 '11 at 16:50
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[Igor probably meant to include a hypothesis such as $x \notin \bf Z$ :-)] –  Noam D. Elkies Jun 5 '11 at 23:35

(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

Lacking sufficient reputation on this site to comment on posts, I'm going to make this an answer, and you know it's a true urban legend if you read the posts above. Once, at a Princeton physics exam, a group of the senior Princeton physics faculty were trying to figure out why, when you shake a bunch of rods in a container with certain asymmetries in the geometry of the container, the rods assume a "more ordered" state (they tended to concentrate on one side), and they couldn't figure out why this did not contradict the second law of thermodynamics! In an amazing twist, they speculated that the result had to do with finite size effects.....

(for those who aren't in on why this is just too crazy to believe: the shaken container is not a closed system, so the second law doesn't apply. Further, the forces on the rods, a combination of shaking and frictional forces, do not correspond to thermal noise and dissipation, so there is no reason for the system to go to thermal equilibrium. It's like asking why, when there is a baited mousetrap and a live mouse in the room at time t=0, is it the case that after a certain amount of time the entropy decreases in that the mouse is more likely to be in the mousetrap than not. I think the most clever answer for the student is: "I notice that this exam has gone on for 30 minutes already and you are still walking and talking. Why are you not relaxing to thermal equilibrium? Perhaps the food you ate this morning is helping keep you out of equilibrium?")

:-)

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I was one of those confused professors (although not senior) and you may well be right that finite size effects have nothing to do with it, but I don't find your analogy terribly convincing either. Do you think the behavior would not have been observed if the system was just coupled to a heat bath rather than shaken? I'd really enjoy hearing a more detailed analysis of what is going on. –  Jeff Harvey Jan 25 '11 at 20:33
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it is a condensed matter analogue of the "anything not forbidden is compulsory" in particle physics. Consider a particle at point x in a potential U(x) with some non-thermal noise and a damping (so force=U'-eta v+noise, where eta is friction and noise has non-thermal spectrum). Suppose the potential has a sawtooth shape. This shape destroys reflection symmetry. The non-thermal noise then means detailed balance is broken, and so nothing forbids a current. If you pick a generic potential and non-thermal noise an dissipation and run it on a computer, odds are you will see the current. –  user12494 Jan 25 '11 at 21:17
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Thanks for the explanation. I talked to my local condensed matter guru and he also emphasized the role of dissipation, although in this system it is not clear without more analysis whether dissipation in collisions between the rods or in the rod-boundary collisions is more important in driving the system. Amusingly you can replace the rods by spheres and make the barrier symmetric and you will still get an accumulation on one side, but which side it is will be random. Dissipation from collisions increases at higher density and cool the system, so a fluctuation towards higher density grows. –  Jeff Harvey Jan 25 '11 at 21:35
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Yes, Chicago has some real experts on this kind of thing! My favorite absolutely bizarre thing I learned about in Chicago has to do with the "brazil nut" effect, that if you shake a jar of mixed nuts, the brazil nuts (the bigger ones) tend to wind up on top. Well, I'd heard about that effect before visiting Chicago, and you can try to puzzle out what happens, why exactly the Brazil nuts wind up on top. So, the crazy thing I learned is that if you repeat the experiment in a vacuum (or maybe it was just in a different liquid, I forget the exact details), the effect is reversed! –  user12494 Jan 25 '11 at 21:42

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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