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Grothendieck quote

edited May 31 in Chat

In Récoltes et Semailles, Alexander Grothendieck wrote:

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 whom I gauged to be more brilliant than me 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 all done 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.

Comments

  • 1.
    edited June 1

    Grothendieck was rather modest fellow it would seem---hard to believe since I consider him a true genius. What I found particularly striking is the influence of J.-P. Serre on his development. Grothendieck was an eagle soaring far above the frogs.

    Comment Source:Grothendieck was rather modest fellow it would seem---hard to believe since I consider him a true genius. What I found particularly striking is the influence of J.-P. Serre on his development. Grothendieck was an eagle soaring far above the frogs.
  • 2.

    @John..thanks.. very interesting and, somehow, it makes me remember of this one attributed to A.Einstein:

    "I think 99 times and find nothing. I stop thinking, swim in silence, and the truth come to me"

    Best

    Comment Source:@John..thanks.. very interesting and, somehow, it makes me remember of this one attributed to A.Einstein: "I think 99 times and find nothing. I stop thinking, swim in silence, and the truth come to me" Best
  • 3.
    edited June 1

    Walter wrote:

    Grothendieck was rather modest fellow it would seem.

    I don't think so; just honest. Later in the same book he writes:

    In terms of its quantity, my work during these productive years found its concrete expression in more than 12,000 published pages in the form of articles, monographs or seminars, and by hundreds, if not thousands of original concepts which have become part of the common patrimony of mathematics, even to the very names which I gave them when they were propounded.

    In the history of mathematics I believe myself to be the person who has introduced the greatest number of new ideas into our science, and at the same time, the one who has therefore been led to invent the greatest number of terms to express these ideas accurately, and in as suggestive a manner as possible.

    And all this is true, just like the "modest" remarks I quoted earlier!

    Comment Source:Walter wrote: > Grothendieck was rather modest fellow it would seem. I don't think so; just honest. Later in the same book he writes: > In terms of its quantity, my work during these productive years found its concrete expression in more than 12,000 published pages in the form of articles, monographs or seminars, and by hundreds, if not thousands of original concepts which have become part of the common patrimony of mathematics, even to the very names which I gave them when they were propounded. > In the history of mathematics I believe myself to be the person who has introduced the greatest number of new ideas into our science, and at the same time, the one who has therefore been led to invent the greatest number of terms to express these ideas accurately, and in as suggestive a manner as possible. And all this is true, just like the "modest" remarks I quoted earlier!
  • 4.
    edited June 3

    A paper of Colin McLarty starts with other thought of Grothendiek (also in recoltes i think) that helps to start explaining what's to love in the theme this course derives from:

    At a time when mathematical fashion despises generality (seen as gratuitous “generalities”, i.e. vacuities) I affirm the principle force in all my work has been the quest for the “general.” In truth I prefer to accent “unity” rather than “generality.” But for me these are two aspects of one quest. Unity represents the profound aspect, and generality the superficial aspect.

    Comment Source:A paper of Colin McLarty starts with other thought of Grothendiek (also in _recoltes_ i think) that helps to start explaining what's to love in the theme this course derives from: > At a time when mathematical fashion despises generality (seen as gratuitous “generalities”, i.e. vacuities) I affirm the principle force in all my work has been the quest for the “general.” In truth I prefer to accent “unity” rather than “generality.” But for me these are two aspects of one quest. Unity represents the profound aspect, and generality the superficial aspect.
  • 5.

    Nice quote, Jesus! Grothendieck's thoughts are fun to read. They set a good example to try to follow. Not so easy in practice!

    Comment Source:Nice quote, Jesus! Grothendieck's thoughts are fun to read. They set a good example to _try_ to follow. Not so easy in practice!
  • 6.

    This reminds me of several things Jaynes writes about in Probability Theory such as:

    ... to make progress in a new area it is necessary to develop a healthy disrespect for tradition and authority, which have retarded progress throughout the 20th century.

    Comment Source:This reminds me of several things Jaynes writes about in _[Probability Theory](https://bayes.wustl.edu/)_ such as: > ... to make progress in a new area it is necessary to develop a healthy disrespect for tradition and authority, which have retarded progress throughout the 20th century.
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