Grothendieck's comments on creativity have been very important in my life, especially the following quote (in translation from the French):
"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.
> Later in life, Grothendieck asked for people to cease re-publishing his work, even brief excerpts.
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.
Yes, he is is in some ways a very tragic figure. As a kid I was always inspired by his absolute dedication to truth, no matter what he saw it as. He really has the most incredible life story, from the child of a one armed Russian-Jewish Anarchist and a German activist, to hiding in France during WWII from the Holocaust, to finding his way after the war in a very odd path to the heights of Mathematics. He really was an exceptional human being.
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.
I actually became aware of Grothendieck's existence because of his isolation and will to be forgotten from this world (including his plead to have his work removed). I will never know the true reason behind his behavior but I'm a scientist myself (life sciences) and at some point of my life I started to hate the field and actually wanting to become isolated and not sharing the tiniest bit of my work with my peers.
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.
I was just reminded of something I read in the exchange between Einstein and Born; I tried to figure out how to quote it all without loosing context or making a mess, but failed. It's at http://archive.org/stream/TheBornEinsteinLetters/Born-TheBor... , search for "I enclose the text of my letter to the Reporter". Which in turn, now reminds me of Bob Dylan's "Masters of War":
You’ve thrown the worst fear
That can ever be hurled
Fear to bring children
Into the world
Which maybe isn't even that much of a stretch. It stinks that things that should be purely a celebration, namely to bring new life or new knowledge into the world, are not as clear cut, but I'd never blame the people who are having such second thoughts. If we can't create and sustain an environment where thought can flow and grow freely, then we shouldn't be surprised when we reap mostly commercial mediocrity.
"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.