Recoltes et Semailles (Gleanings and Sowings)

Alexandre Grothendieck (1928- ) is a German-born mathematician whose contributions to many modern mathematical fields, such as algebraic geometry, made him one of the most influential mathematicians of the period between 1950 and 1988. Grothendieck’s family was Jewish. His father died in a concentration camp during World War II. After the war, Grothendieck became a stateless person, never attaining citizenship in any of the countries in which he later lived, due to his passionate and increasingly radical political views. He did his most important mathematical work in France, at several eminent universities and at the Institut des Hautes Études Scientifiques. He later began to withdraw from the world in many respects. His mathematical output dwindled after 1960, and he began personally criticizing his colleagues, alienating himself in the academic world. This alienation culminated in his disappearance in 1991, when he abandoned his home without notice. Currently, he is thought to be living in the Alps, perhaps in France. Towards the end of his active career, Grothendieck wrote an extensive autobiography, which he titled Recoltes et Semailles (Gleanings and Sowings). This work contains an overview of some of his favorite mathematical works, as well as his striking personal musings on life and mathematics. Unfortunately, his unflattering views of his fellow mathematicians are present in this work as well. His style ranges from beautiful, moving, descriptive prose to jerky, rambling, disjointed first draft. Due to a combination of these factors, the book has never found a publisher. I think this is a shame. This excerpt, which I’ve translated from the original French, hints at the beauty contained in this overlooked work:
Chapter 4—the Five-Leafed Clover 4.1.1—Dream and Accomplishment
About three years ago, in July, I had an extraordinary dream. I say “extraordinary” only because this was the impression I had after the fact, in recollection. The dream itself seemed to me like the most natural, the most obvious thing in the world, without pomp or herald. Even after awakening, I very nearly paid no attention, secreting it away in the oubliette of my mind in order to get on with the business at hand.
Since the previous day I had been musing on my relationship with mathematics. It was the first time in my life that I had taken pains to do this—and even then, if I took a moment to reflect, it was practically as though I had been forced into it! There were strange things, even violent things which occurred in the months and years preceding—explosions of mathematical passion which created an eruption in my life and showed no signs of approaching a stop, such that it truly was no longer possible to continue without noting what was going on.
The dream I speak of did not include a scenario or action of any sort. It consisted of a single image, immobile, but at the same time full of life. It was the head of a person, in profile. It was an adult man, clean-shaven, with his wild hair about his head like a halo. The overall impression that radiated from this head was one of youthful strength and joy, which seemed to flow forth from its supple and vigorous lines (this was more felt than seen). The expression of the face was more that of a mischievous youth, delighted with some feat that he had pulled off or was premeditating, than that of a mature adult of stable situation. It exuded everywhere an intense joie de vivre, bursting with playfulness...
There was no other person present, not even an “I” to regard or contemplate this image. Nonetheless, I had an intense perception of this head. It did not have anyone to witness it or feel its effects, to comment, or to attach to it a personal name, that is to say a “such-and-such”. There was only this intensely vibrant thing, this head of a man, and an equally vibrant, intense perception.
When I awoke, the dream of the man’s head did not present itself with any particular intensity among the various dreams of the night, until I had contemplated it. There was no peculiar power about it that cried, “You should be looking at me!” But when the dream appeared in my casual review of the night’s dreams, in the quiet warmth of my bed, I was strongly moved to identify the vision I had just seen. I did not have to search long, for it very soon became clear to me that the head from my dream was none other than my own.
It was no small thing, I thought then to myself, to imagine one’s own head in a dream as though it were the head of another! The dream showed itself as though through the greatest of accidents. As though I had fallen upon a four-leafed clover, or even a five-leafed, so I was dumbfounded for a few moments as may be expected, and then pursued my own path as though nothing had happened.
It was in this way that it happened. But happily, as I am accustomed to do in this kind of situation, I had nonetheless made a note of this little incident, and thus began a contemplation that was to continue on the subject of that of the previous day. Then, along this thread, this contemplation plunged me into the sense of the dream, its unique image, and its message to me.
The dream showed me myself, “just as I am.” But it was equally clear to me that in my waking life I was clearly not what the dream had shown me—burdens and restrictions have long made (and still make) an obstacle that always keeps me from being simply myself. During these past three years, although the thought of this dream did not occur to me very often, the dream moved me in a certain way. It was nothing like a sort of model or ideal upon which I attempted to reconstruct myself, but simply a discrete reminder of a joyous simplicity that “was me,” a “me” that manifests itself in many hidden ways, and which cries to be liberated from the continuation of all that weighs it down, and to blossom. This dream was a link, both delicate and vigorous, to a time between a present still weighted down with the burdens of the past and, quite close to the present, a “tomorrow” which is contained in a seed, a tomorrow that exists in my present, and which surely has always been within me...

That last paragraph moves me deeply. I think it's such a privilege to see into the mind of someone who is about to retreat from the entire world he has known, and see his reasons for that departure from his perspective instead of from the perspective of all those around him who called him insane and lazy for leaving academia.

I intend to go on translating this work for the next several years, doing a bit here, a bit there, making it one of my hobbies. My plan is to edit and abridge shamelessly, smoothing out the rough run-on sentences and cutting out most vitriolic personal attacks, until I’m left with a lyrical, readable memoir of mathematics. Perhaps someone will publish it. Perhaps I’ll just put it all here on E2. Eventually I’ll get it all done. I think it’s worth it.

(Note: Alexandre Grothendieck died in Saint-Girons, France, on November 13, 2014.)

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