I’d never encountered this exquisitely characterizing passage from Grothendieck’s memoir before. I think even non-mathematicians will find it of interest.
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 or 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.
I’ll add just one remark: “The capacity to be alone” is a phrase made famous by the psychoanalyst D.W. Winnicott, who understood the development of this capacity to be a crucial phase in the maturation of the child. Winnicott’s sense of the term is quite specific: “the basis of the capacity to be alone is a paradox; it is the experience of being alone while someone else is present.” I don’t know whether Grothendieck was quoting Winnicott here (is it known whether he was analyzed, or familiar with the psychoanalytic literature at all?) but his sense of the phrase is much the same. The challenge is not to do mathematics in isolation, but to preserve a necessary circle of isolation and autonomy around oneself even while part of a mathematical community.
I should say that this is totally foreign to my own mode of mathematical work, which involves near-constant communication with collaborators and other colleagues and a close attention to the “notions of the consensus,” which I find are usually quite useful.
Also, Grothendieck’s distinction between himself and the less profound mathematicians who were quick studies and winners of competitions should give John Tierney something to think about.
I also find this quite interesting. Do you know where the French (presumably) original text can be found?
Emmanuel: Somewhere in “Recoltes et Semailles”, I think, although I don’t remember exactly
Yes, it’s R&S, Section 2.2.
Is “the capacity to be alone” a literal translation from the original? This might shed some light about whether AG was actually quoting Winnicott.
I identify pretty strongly with what Grothendieck says about his approach to mathematics (but I don’t agree with his criticism of his peers). In fact, I think some of what he says is more appropriate to me than him (in what universe is Grothendieck “clumsy” and “oafish”?). I’ve always assumed that every halfway decent mathematician reacts the same way as I do when I try to learn mathematics from papers, books, or lectures. If I ever understand the stuff at all (and mostly I never do), I lose patience with other person’s exposition and just start working things out for myself from scratch. I’m always muttering “there’s a better way than that” to myself. I have always looked for validation for my approach. That’s why I like repeating what Kazhdan would always do to one of his students. He would point to a book and say, “You see this? You should know everything in it, but don’t read it!”
Thanks for the pointer!
In answer to the next question of Jordan: Grothendieck writes (it’s the title of the section) “L’importance d’être seul”, and then uses “la capacité d’être seul” in the text. I’ll read this section and the translation for better comparison.
Thanks for the Grothendieck passage — I have never seen this before. I was reminded of the recent interview with Hironaka by Allyn Jackson:
“Also, I like basic things. Very clever people tend to jump to the new techniques: something is developing very fast, and you want to be on top of it; and if you are smart, you can be a top runner. But I am not so smart, so it is better that I start something where there are no techniques for the problem, and then I can just build step by step. But actually, it was not so hard. It turned out to be easier than I thought.”
Click to access fea-hironaka.pdf
For the interested, here is a link to 1958 Winnicott paper “The capacity to be alone” in the International Journal of Psyco-Analysis
This is probably hard to guess, but what ideas in which areas of mathematics could Grothendieck be referring to when he talks about other people picking them quickly “as if at play”, while he, apparently, wasn’t as quick?! Can’t be algebraic geometry now, can it ?:)
“The capacity to be alone” is an ability and sentiment felt frequently by strongly independent introverts around the world and throughout history. It is not an idea originated by Winnicott; there is no need to wonder whether Grothendieck quoted him or not.
[…] of meeting Adam Phillips was that I got to ask him about Grothendieck’s use of the phrase “the capacity to be alone,” generally associated with the psychoanalyst D.W. Winnicott. Winnicott was Phillips’s […]
[…] 2010 blog post about Grothendieck by Jordan […]
[…] and communicating with those around us. Grothendieck, in a deeply moving piece, describes his capacity to be alone, which I read as fully embracing the sense of […]
Thanks for posting this. I’ve gone back to this post many times to re-read it. I feel like in many things in life there is a struggle between “being alone” and following the consensus. I’ve never seen this so clearly stated as it was here by Grothendiek.
Reblogged this on tensorprodukt and commented:
An interesting reflection from Récoltes et Semailles by Grothendieck.
Recoltes Et Semailles was the most enriching text I have ever read, all categories confounded.The passage quoted here is nice, but the whole thing, which is 1000 pages long, is just a none-stop series of profound insights one after the other.Grothendieck’s genius perspective is apparent through and through.This isn’t a text for mathematicians, this is a text for anyone who dares to give his text a chance.It takes quite a bit of stamina to go on as he asks a lot from his readers.You need to be comfortable with none-stop analogies and introspective exploration.
[…] see the others every day. They surround me and talk around me and I am forced to listen. I am, as you were too, surprised by them sometimes, surprised by the facility with which they pick up, as if at play, new […]
Some very fine writing in these blog posts. Not a mathematician myself (a physician) but I have very fond memories of studying and getting lost in those texts for hours on end. It is becoming increasingly difficult to do so now given the multitude of distractions and interruptions in our daily lives.