"To state it in slightly different terms: in those critical years [roughly from age 17 to 20] I learned how to be alone."

"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 3 years of work in isolation, 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 lyé 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", "unproblematic", etc. I'd gone over their heads, almost as a matter of course, even as Lesbesgue himself had, several decades before, gone over their heads. It is in this gesture of "going beyond", to be something 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."

Very late in his life, Grothendieck asked for people to cease re-publishing his work, even brief excerpts. (See: http://sbseminar.wordpress.com/2010/02/09/grothendiecks-lett... ) So I have mixed feelings about quoting the above. But I do so in the hope that it can help others as it has helped me.

I think Grothendeick used Mathematics as a way to rebel against/escape from the world he grew up in. It was a formal discipline that could provide concrete results, unlike the mundance political arguing and nonsense that he commonly saw elsewhere controlling the world. But, I bet as he grew older he noticed that even his very own mathematical work could be used in mundane academic political nonsense. Thus, a disenchantment with everything ensued leading to a total isolationist viewpoint.

It's unfortunate his disillusionment led him to leave math completely, and slowly retreat out of society, and probably to develop the mental illness that dominated his later life. A while ago I found some of his writings from the post-math era online, I wonder if they're still around. Strange stuff, all about hermaphroditic angels and his personal beliefs?

We have lost a truly unique and incredible human being, but I'm not sure he would appreciate me saying that "we" lost anything.

People will quickly judge you as a bad person if you don't want to give your work for the greater good of humanity and science, however, for a person that's outside the field it's easy to overlook the many things (not neccesarily related to science itself) that a scientist has to deal with.

Science, like all profession, has its own demons and bad times, and how do you cope with those is a fundamental skill that you have to develop in order to be able to, well, do science.

Anyway, a little off-topic but I wanted to say that I sympathize with the guy and I think that he has all the right to ask the community to stop sharing their ideas, just as anyone has all the right to come up with their own ideas and decide to share them or not.

    You’ve thrown the worst fear
    That can ever be hurled
    Fear to bring children
    Into the world

I think he devoted himself to nuclear disarmament and became disillusioned by the fact that his peers did not take the issue seriously.

From the notices of the AMS: http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf

By Pierre Cartier: http://xahlee.info/math/i/Alexander_Grothendieck_cartier.pdf

By Pierre Deligne (in French): http://www.emis.de/journals/SC/1998/3/pdf/smf_sem-cong_3_11-...

[1]: He spelled his own name different from the French spelling, apparently.

I was briefly a math major at the university, I studied at a technical school in France, I read a lot on technical forums such as HN where some people seem to know his work, like many I am fascinated by geniuses and their eccentricities, I browse Wikipedia for fun, and yet I was totally unaware of his life and work. Maybe I'd heard his name in passing, but no mention of his talent or writings, or his eccentric life because then I would've remembered his name.

I find it sad that he is so obscure, though I see that it was his wish. On the one hand, you want to respect someone who obviously had his own reasons for withdrawal, on the other it seems like a madman's wish to be erased from the history books and even from the annals of science. That's not how science works, and that he thought he could be the exception shows a disjunction. I don't want to imply it was a mental illness, but I'd like to read more to try to understand his state of mind. Now that he lived and died in (relative) obscurity, it won't hurt to learn about him and learn from him.

His personal story is also interesting and unique.

Pierre Cartier recently published an appreciation of his life and work -- Alexander Grothendieck: A Country Known Only By Name -- which is well worth the read even if you aren't a mathematician. http://inference-review.com/article/a-country-known-only-by-...

I am obviously leaving the maths apart: we hope to stand on his shoulders, we and many future generations.

https://ztfnews.files.wordpress.com/2014/11/grothendiecks-de...

I've read the 1st volume of the biography and fully recommend it, so if you find AG's life interesting, you can consider donating a few bucks.

May we never forget the Grothendieck prime, 57.

  One striking characteristic of Grothendieck’s
  mode of thinking is that it seemed to rely so little
  on examples. This can be seen in the legend of the
  so-called “Grothendieck prime”. In a mathematical
  conversation, someone suggested to Grothendieck
  that they should consider a particular prime number.
  “You mean an actual number?” Grothendieck asked. 
  The other person replied, yes, an actual prime number. 
  Grothendieck suggested, “All right, take 57."

  But Grothendieck must have known that 57 is not
  prime, right? Absolutely not, said David Mumford
  of Brown University. “He doesn’t think concretely.”

Grothendieck certainly knew what it means for p to be prime. I don't know, but maybe his thoughts went along the line of "primes are some substructure of the natural numbers and such and such changes happen in the functions that we can build on them".

So he was obviously able to speak about some collection of primes, yet whether an actual number is prime he probably doesn't think much about.

That vision is only achievable for those able to live alone, to wander with their thoughts, to lose themselves in the island of their inner world. Their inner world and ideas are more real and concrete than what we see with our eyes. They don't see a prime number, a prime ideal is only point in the spectrum of a ring, their math ideas are so colorful that nobody can reach that peak without forgetting where we come from and that the earth is our planet. They live in a different math heaven always climbing to reach the book (Erdos ideal).

"... the greatest of all modern mathematicians and arguably the greatest mathematician of all time ..."

"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 lycée 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," "unproblematic," etc....It is in this gesture of "going beyond," to be something 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 much 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 that 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 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 had to rediscover in themselves that capability which was their birthright, as it was mine: the capacity to be alone."

[1] Quote translation found in [2] from Alexander Grothendieck, Récoltes et Semailles, 1986, English translation by Roy Lisker, www.grothendieck-circle.org, chapter 2.

[2] Smolin, Lee - The Trouble with Physics

For anyone wondering, lycée is high school in French.

"2.2. L’importance d’être seul

Quand j’ai finalement pris contact avec le monde mathématique à Paris, un ou deux ans plus tard, j’ai fini par y apprendre, entre beaucoup d’autres choses, que le travail que j’avais fait dans mon coin avec les moyens du bord, était (à peu de choses près) ce qui était bien connu de "tout le monde", sous le nom de théorie de la mesure et de l’intégrale de Lebesgue". Aux yeux des deux ou trois aînés à qui j’ai parlé de ce travail (voire même, montré un manuscrit), c’était un peu comme si j’avais simplement perdu mon temps, à refaire du "déjà connu". Je ne me rappelle pas avoir été déçu, d’ailleurs. A ce moment-là, l’idée de recueillir un "crédit", ou ne serait-ce qu’une approbation ou simplement l’intérêt d’autrui, pour le travail que je faisais, devait être encore étrangère à mon esprit. Sans compter que mon énergie était bien assez accaparée à me familiariser avec un milieu complètement différent, et surtout, à apprendre ce qui était considéré à Paris comme le B.A.BA du mathématicien2.

Pourtant, en repensant maintenant à ces trois années, je me rends compte qu’elles n’étaient nullement gas- pillées. Sans même le savoir, j’ai appris alors dans la solitude ce qui fait l’essentiel du métier de mathématicien - ce qu’aucun maître ne peut véritablement enseigner. Sans avoir eu jamais à me le dire, sans avoir eu a ren- contrer quelqu’un avec qui partager ma soif de comprendre, je savais pourtant, "par mes tripes" je dirais, que j’étais un mathématicien : quelqu’un qui "fait" des maths, au plein sens du terme - comme on "fait" l’amour. La mathématique était devenue pour moi une maîtresse toujours accueillante à mon désir. Ces années de so- litude ont posé le fondement d’une confiance qui n’a jamais été ébranlée - ni par la découverte (débarquant à Paris à l’âge de vingt ans) de toute l’étendue de mon ignorance et de l’immensité de ce qu’il me fallait apprendre : ni (plus de vingt ans plus tard) par les épisodes mouvementés de mon départ sans retour du monde mathématique ; ni, en ces dernières années, par les épisodes souvent assez dingues d’un certain "Enterrement" (anticipé et sans bavures) de ma personne et de mon oeuvre, orchestré par mes plus proches compagnons d’antan. . .

Pour le dire autrement : j’ai appris, en ces années cruciales, à être seul3. J’entends par là : aborder par mes propres lumières les choses que je veux connaître, plutôt que de me fier aux idées et aux consensus, exprimés ou tacites, qui me viendraient d’un groupe plus ou moins étendu dont je me sentirais un membre, ou qui pour toute autre raison serait investi pour moi d’autorité. Des consensus muets m’avaient dit, au lycée comme à l’université, qu’il n’y avait pas lieu de se poser de question sur la notion même de "volume", présentée comme "bien connue", "évidente", "sans problème". J’avais passé outre, comme chose allant de soi - tout comme Lebesgue, quelques décennies plus tôt, avait dû passer outre. C’est dans cet acte de "passer outre", d’être soi-même en somme et non pas simplement l’expression des consensus qui font loi, de ne pas rester enfermé à l’intérieur du cercle impératif qu’ils nous fixent - c’est avant tout dans cet acte solitaire que se trouve "la création". Tout le reste vient par surcroît.

Par la suite, j’ai eu l’occasion, dans ce monde des mathématiciens qui m’accueillait, de rencontrer bien des gens, aussi bien des aînés que des jeunes gens plus ou moins de mon âge, qui visiblement étaient beaucoup plus brillants, beaucoup plus "doués" que moi. Je les admirais pour la facilité avec laquelle ils apprenaient, comme en se jouant, des notions nouvelles, et jonglaient avec comme s’ils les connaissaient depuis leur berceau - alors que je me sentais lourd et pataud, me frayant un chemin péniblement, comme une taupe, à travers une montagne informe de choses qu’il était important (m’assurait-on) que j’apprenne, et dont je me sentais incapable de saisir les tenants et les aboutissants. En fait, je n’avais rien de l’étudiant brillant, passant haut la main les concours prestigieux, assimilant en un tournemain des programmes prohibitifs.

La plupart de mes camarades plus brillants sont d’ailleurs devenus des mathématiciens compétents et ré- putés. Pourtant, avec le recul de trente ou trente-cinq ans, je vois qu’ils n’ont pas laissé sur la mathématique ⋄ de notre temps une empreinte vraiment profonde. Ils ont fait des choses, des belles choses parfois, dans un contexte déjà tout fait, auquel ils n’auraient pas songé à toucher. Ils sont restés prisonniers sans le savoir de ces cercles invisibles et impérieux, qui délimitent un Univers dans un milieu et à une époque donnée. Pour les franchir, il aurait fallu qu’ils retrouvent en eux cette capacité qui était leur à leur naissance, tout comme elle était mienne : la capacité d’être seul.

Le petit enfant, lui, n’a aucune difficulté à être seul. Il est solitaire par nature, même si la compagnie occasionnelle ne lui déplaît pas et qu’il sait réclamer la totosse de maman, quand c’est l’heure de boire. Et il sait bien, sans avoir eu à se le dire, que la totosse est pour lui, et qu’il sait boire. Mais souvent, nous avons perdu le contact avec cet enfant en nous. Et constamment nous passons à côté du meilleur, sans daigner le voir. . .

Si dans Récoltes et Semailles je m’adresse à quelqu’un d’autre encore qu’à moi-même, ce n’est pas à un "public". Je m’y adresse à toi qui me lis comme à une personne, et à une personne seule. C’est à celui en toi qui sait être seul, à l’enfant, que je voudrais parler, et à personne d’autre. Il est loin souvent l’enfant, je le sais bien. Il en a vu de toutes les couleurs et depuis belle lurette. Il s’est planqué Dieu sait où, et c’est pas facile, souvent, d’arriver jusqu’à lui. On jurerait qu’il est mort depuis toujours, qu’il n’a jamais existé plutôt - et pourtant, je suis sûr qu’il est là quelque part, et bien en vie.

Et je sais aussi quel est le signe que je suis entendu. C’est quand, au delà de toutes les différences de culture et de destin, ce que je dis de ma personne et de ma vie trouve en toi écho et résonance ; quand tu y retrouves aussi ta propre vie, ta propre expérience de toi-même, sous un jour peut-être auquel tu n’avais pas accordé attention jusque là. Il ne s’agit pas d’une "identification", à quelque chose ou à quelqu’un d’éloigné de toi. Mais peut-être, un peu, que tu redécouvres ta propre vie, ce qui est le plus proche de toi, a travers la redécouverte que je fais de la mienne, au fil des pages dans Récoltes et Semailles et jusque dans ces pages que je suis en train d’écrire aujourd’hui même."

- - -

When I finally made contact with the mathematical world at Paris, one or two years later, I ended up learning, among a lot of other things, that the work that I had done in my area with the means at hand, was (pretty much) something well known to "everybody", under the names of measure theory and of Lebesgue integrals. To the eyes of the two or three seniors to whom I had spoken of this work (or even shown a manuscript), it was a little as if I had simply wasted my time, by re-doing that which was "already known". I do not recall having been disappointed, before. At that moment, the idea of collecting "credit", be it the praise or let alone the interest of others, for the work that I was doing, would have been foreign to my spirit, still. Besides, my energy was well enough spent in familiarizing myself with a completely different milieu, and, more, learning that which was considered at Paris the equivalent of a B.A. in mathematics.

However, in thinking back now on those three years, I realize they were in no way wasted. Without even knowing it, I had learned in solitude that which was essential to the mathematician's work - that which no teacher, truly, could teach. Without ever having it said to me, without having met anyone with whom to share my thirst for knowing things, I was, however, aware, "in my gut", I would say, that I was a mathematician : someone who "did" math, in the full sense of the term - like you "make" love. Mathematics was becoming for me a mistress always welcoming of my desire. Those years of solitude had formed the basis of a confidence which has never been shaken - neither by the discovery (disembarking in Paris at the age of 20 years) of the whole extent of my ignorance and of the immensity of that which it would be necessary to learn : neither (more than 20 years later) by the uproar of my leaving for good the mathematical world ; neither, in these last years, by the frequently pretty crazy events of a certain kind of "burial" (anticipated and painless) of my person and my work, orchestrated by my closest friends of old. . .

- - -

[other paragraphs; see above]

- - -

The infant, he has no difficulty being alone. He is alone by nature, even if occasional company doesn’t displease him and he knows to reach for his mother’s breast, when it’s time to drink. He knows well, without having had it said to him, that the breast is for him, and that he knows how to drink. But often, we have lost contact with that infant in us. And constantly we pass next to better things, without deigning to see. . .

If in these Récoltes et Semailles I address myself to someone other than myself, it’s not to the "public". I address myself to you, who reads me as one person, and to one person alone. It’s to them, and you, who know how to be alone, to the infant, that I would like to speak, and to other people. The infant is often far away, I know it well. There, he’s seen all the colors, for ages and ages. He’s hidden God knows where, and it is easy, often, to stumble upon him. You would swear he’s been dead since forever, that he had never existed at all - but I am sure that he’s there sometimes, and very much alive.

And I know also what the sign is, when I’ve been heard. It’s when, despite all the differences of culture and destiny, that which I’ve said about my person and life finds echo and resonance in you ; when you also find there your proper life, your proper experience of yourself, on a day on which you were not, perhaps, giving attention to it. It doesn’t mean anything along the lines of "identification", to something or someone distant from you. But maybe, a little, that you rediscover your proper life, that which is closest to you, in going over the rediscovery that I did of mine, through the pages in Récoltes et Semailles, and up to these pages that I am in the process of writing even today.

Did Roy Lisker translate the book in its entirety or just partially? I know you might argue it's a bad question but I have no clue whether it is hard to find a translation because of Grothendieck's wishes or because there is none yet.

he was a truly revolutionary mathematician and his contribution to the (hard) science of mathematics cannot be overstated. people who live on principle are rare, and those willing to go without salary as part of that protest are even rarer [1].

[1] - http://www.fermentmagazine.org/Quest88.html