from Grothendieck's Récoltes et Semailles:
In those critical years I learned how to be alone. [But even] this
formulation doesn’t really capture my meaning. I didn’t, in any
literal sense, learn to be alone, for the simple reason that this
knowledge had never been unlearned during my childhood. It is a basic
capacity in all of us from the day of our birth. However these three
years of work in isolation [1945-1948], when I was thrown onto my own
resources, following guidelines which I myself had spontaneously
invented, instilled in me a strong degree of confidence, unassuming
yet enduring in my ability to do mathematics, which owes nothing to
any consensus or to the fashions which pass as law. By this I mean
to say: to reach out in my own way to the things I wished to learn,
rather than relying on the notions of the consensus, overt or tacit,
coming from a more or less extended clan of which I found myself a
member, or which for any other reason laid claim to be taken as an
authority. This silent consensus had informed me both at the lycee
and at the university, that one shouldn’t bother worrying about
what was really meant when using a term like “volume” which
was “obviously self-evident”, “generally known,” “in
problematic” etc... it is in this gesture of ”going beyond to be
in oneself rather than the pawn of a consensus, the refusal to stay
within a rigid circle that others have drawn around one -- it is in
this solitary act that one finds true creativity. All others things
follow as a matter of course.
Since then I’ve had the chance in the world of mathematics that
bid me welcome, to meet quite a number of people, both among my
“elders” and among young people in my general age group who were
more brilliant, much more ‘gifted’ than I was. I admired the
facility with which they picked up, as if at play, new ideas, juggling
them as if familiar with them from the cradle -- while for myself I
felt clumsy, even oafish, wandering painfully up an arduous track,
like a dumb ox faced with an amorphous mountain of things I had to
learn (so I was assured) things I felt incapable of understanding
the essentials or following through to the end. Indeed, there was
little about me that identified the kind of bright student who wins
at prestigious competitions or assimilates almost by sleight of hand,
the most forbidding subjects.
In fact, most of these comrades who I gauged to be more brilliant
than I have gone on to become distinguished mathematicians. Still
from the perspective of thirty or thirty five years, I can state
that their imprint upon the mathematics of our time has not been
very profound. They’ve done all things, often beautiful things in
a context that was already set out before them, which they had no
inclination to disturb. Without being aware of it, they’ve remained
prisoners of those invisible and despotic circles which delimit the
universe of a certain milieu in a given era. To have broken these
bounds they would have to rediscover in themselves that capability
which was their birthright, as it was mine: The capacity to be alone.
From the comments of HackerNews.
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