Urban Game Questions

[Concordia Zentner]

WhenI 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?

A graduate student (let's call him Saeed) is in the airport standing in a security line. He is coming back from a conference, where he presented some exciting results of his Ph.D. thesis in Algebraic Geometry. One of the people whom he met at his presentation (let's call him Vikram) is also in the line, and they start talking excitedly about the results, and in particular the clever solution to problem X via blowing up eight points on a plane.

Less than a minute later, the TSA officers descend on the two mathematicians, and take them away. They are thoroughly and intimately searched, and separated for interrogation. For an hour, the interrogation gets nowhere: the mathematicians simply don't know what the interrogators are talking about. What bombs? What plot? What terrorism?

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.

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.

Although David Hilbert was one of the first to deal seriously with infinite-dimensional complete inner product spaces, the practice of calling them after him was begun by others, supposedly without his knowledge. The story goes that one day a visitor came to Gttingen and gave a seminar about some theorem on "Hilbert spaces". At the end of the lecture, Hilbert raised his hand and asked, "What is a Hilbert space?"

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.

Apparently, there was Asst Professor X at a provincial department Y, and he was up for tenure. Professor X's advisor was a famous Japanese mathematician Z at an Ivy League school. Naturally, he was asked for a letter, which he duly sent. The letter said:

X has a very nice body of work, he proved the following interesting theorems, extended such and such results, used such and such techniques... and so on for two pages.The last sentence was: all in all, X is a very good second-rate mathematician.

The committee was mortified, but figured that the rest of the letter was so good, they should call Z, since maybe since English was not his native language... So, call they did, and the phone conversation went about the same as the letter: did this, improved that, ..., all in all a very good second-rate mathematician.

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".

I've heard that in the earliest days of communist Hungary, Pal Turan was stopped on the street by a patrol. These patrols were charged with collecting a quota of people to be shipped off to Siberia (Stalin was still in charge, and arbitrary punishment is a big part of inducing the Stockholm Syndrome). While being searched and interrogated for his "crimes", the policeman was surprised and impressed (and perhaps a bit intimidated himself) to find a reprint of a paper of Turan's published pre-war in a Soviet journal. Turan was allowed to go free. That day, he wrote a letter to Erdos beginning, "I have discovered a most wonderful new application of number theory..."

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?

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!"

3a8082e126