~
[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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