Monday, March 31, 2014

On Brilliance and Boredom

Our substantial essay on mathematical depth and difficulty, and the very different intellectual rungs on the ladders of those who attempt to reach it, has been repeatedly updated;  time perhaps to give a taste of these.  For the full essay, click here:


[Fifth appendix]   From a lecture by Professor Messing in Princeton, March 2002, in allusion to Robert Langlands of the Princeton Institute for Advanced Studies:

Langlands, with characteristic humility, wrote:  The virtue of Dieudonné theory  is that, for mathematicians of middling ability, it lets you translate difficult problems in abelian varieties  into straightforward problems in linear algebra.

I can well believe this.  I personally attended Professor Langlands IAS lecture series (autumn 1999);  in the first of these he stated that he'd wanted to be a physicist, but physics was "too difficult", so he had to settle for being a humble mathematics professor at the Institute for Advanced Studies.   Nor was this a pose;  his whole manner is that of straightforward humility, very … Canadian. 

John Conway, one of the most brilliantly elflike of mathematicians, confessed to a similar trajectory, during his time at Cambridge.  In a lecture at Princeton University (17 XI 1999) he confessed:

I studied Quantum Mechanics with Dirac.  Quantum Mechanics is hard to understand, even when you can answer the questions on the exams.  And I couldn't answer the questions on the exams anymore.

After his lecture, I went up with him to his office, and the sense of his almost Franciscan combination of humility and playfulness  was confirmed.   His small and crowded office (Princeton has an enormous endowment;  this is the way they treat their stars?)  was a four-dimensional playpen (of which, with my limited vision, I could perceive only three) of mathematical mind-toys, stacked up here and there, hanging from the ceiling, projecting from the walls …

[Sixth appendix]

Alex Masters, The Genius in my Basement  (2011)  [a book that treats of the  downfall of Simon Norton, once a key collaborator of John Conway]:

At Trinity College in Cambridge, there was a man who scored a double first in his undergraduate degree, took his PhD in the flash of an eye, and still gave up in despair  and became a tuba player.

How much more poignant, with the humble, doleful tuba, rather than piano or violin!

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[Seventh appendix]   On a related note:
In the moving coda to her splendid examination of the meteoric careers (or perhaps, fireworks-like, including the eventual fizzle) of a pair of brilliant (counter-)Freudians, In the Freud Archives,  Janet Malcolm, all passion spent, has a last interview with the man she has so closely followed, and not-unsympathetically depicted (and who would later sue her), Jeffrey Masson.   He says this, he says that;  and then she says:

“You know, as you’ve been talking, I’ve had the feeling that you’re bored with what you’re saying.”

The prodigy, his own passion likewise depleted, concedes that this is so.   He has seen farther than others, and has already said, and re-said, all that he has to say.  And then adds, fatefully:

“For people who are truly smart, like Bob Goldman, there really isn’t much they want to do, or can do.  The truly smart people seem to do less and less.  It’s terrible.  The dull have taken over.”

This chilling observation put me in mind of my best friend in high school, Ted Franklin, whose gifts in math and physics  lay far beyond my own.   I had an excursus in Europe before following him to Harvard, shortly after which time he had dropped out.   I did get to room (informally) with his erstwhile roommate, the brilliant math major David Collins -- who, however, himself promptly parachuted out of the university -- leaving the undergraduate mathematics to the tortoise, myself.  Both of them went on to quixotic social projects, and then I lost track.   Somehow neither one managed to stay sufficiently interested  to wind up doing anything intellectually really interesting.   They thought of themselves as rebels, but in that way they were more like Edwardians.   Leaving the field to us dullards.

How valid Masson’s plaint may be, in psychology or philology (two fields in which he greatly distinguished himself), I do not know.   But enormously smart people are doing deeper things than ever before, in mathematics.   They are not bored.

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