Mathematical ‘Urban Legends’

One particular topic at mathoverflow.net has accumulated a large series of incredible stories. While many of them might not be true, they are fantastic. So I thought I would share some of them.

Blowing up points on a plane

This happened just last year, but it certainly deserves to be included in the annals of mathematical legends:

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.

They don’t notice other travelers slowly backing away from them.

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?

The student finally realizes the problem, pulls out a pre-print of his paper, and proceeds to explain to the interrogators exactly what “blowing up points on a plane” means in Algebraic Geometry.

Draw the right diagram

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.

I did that?

In the late 1930’s, Enrico Fermi attended a seminar of Oppenheimer. Walking out at the end of the lecture, he found Emilio Serge and said, “Emilio, I must be getting senile. I went to a learned theoretical seminar and could not understand anything except the last words, which were ‘And this is Fermi’s theory of beta decay.’ ”

It seems this story is taken from Emilio Serge’s autobiography.

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 in 1929 von Neumann was giving a lecture on some theorem on Hilbert spaces when Hilbert said, “Dr. von Neumann, ich mÃ¶chte gern wissen, was ist dann eigentlich ein Hilbertscher Raum?” (The translation given: “Dr. von Neumann, I would very much like to know, what after all is a Hilbert space?”).

Jacobi and Gauss

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.

There are plenty more at mathoverflow.

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