Grothendieck’s Activism And What It Says About The World
Posted by Tom Leinster
Mathematician Ivar Ekeland has an excellent, thoughtful, article at Mediapart, reflecting on the second phase of Grothendieck’s adult life.
The article is perhaps more about mathematics and its place in the world than about Grothendieck specifically. Among the questions Ekeland asks: What exactly are you, as a researcher, looking for? What are your intellectual boundaries? How do you justify spending your life on mathematics? Why was Grothendieck a less successful activist than mathematician? And what does that say about the world?
Below the fold is my translation of selected passages from Ekeland’s article, which is in French. Feel free to suggest improvements to the translation.
The rest of this post is a translation of parts of Ivar Ekeland’s article at Mediapart.
While for many of us, research is a career (although an honourable one, and preferable to many others), for Grothendieck it was everything: the search for the truth is an end in itself, for which any sacrifice is merited. […] And there we have the first of the questions that Grothendieck’s life poses to me: what exactly are you searching for? Does the quest for truth stop at the boundaries of mathematics?
As far as he was concerned, obviously not. He sought the truth wherever it could be found, and he examined our society with the same gaze he brought to mathematics. But he did not have the same success. As his student Pierre Deligne said, “he had the impression that the fact of having proved the reality of the problems would make things change, as it does in mathematics”. This is the immense disappointment that must be faced every day by campaigners in all causes, whether it is against global warming, tax havens, social injustice, or the occupation of the Palestinian territories: much as one might demonstrate the reality of the problems, that does not make things change!
Why is that? For one thing, because most people do not reflect, and the higher one climbs up the social hierarchy, the less time one has to reflect, submerged as one is by urgent and important matters. This is what Pascal called “distraction”: positions of responsibility are sought out exactly because in taking up your time, they remove from you the opportunity to think. Every day brings us proof that neither the [French] president nor his ministers take the time to reflect.
The other reason why it is so difficult to make these problems understood is that, when people think, they do it within ready-made frameworks: there is an “off-the-peg” style of thought [un prêt-à-porter de la pensée]. This is true everywhere, even in mathematics, and Grothendieck analysed it well in his book Récoltes et Semailles, which you will excuse me for quoting at length. “Most mathematicians… tend to confine themselves to a conceptual framework, in a ‘Universe’ fixed once and for all — that which, essentially, they found ‘ready-made’ at the time when they were students. […]”
The unhappy fact, in this business, is that words no longer carry weight. In mathematics, words have weight, because it is impossible to lie: everyone can check for themselves whether a theorem is true or false; the most junior participant at Grothendieck’s seminar could verify what the master was saying. The mathematical word must be true. In politics, this constraint disappears: one cannot verify a historical fact or somebody’s good faith in the same way that one verifies a proof. The word becomes an instrument of power, and the search for truth is transformed into the art of communication: the spin doctor replaces the researcher, and the “elements of language” transmitted by newspapers and television replace facts. […]
And here is the last question that Grothendieck’s life poses to me: how to act in a world where words no longer carry weight? What is the use of doing mathematics when the survival of the human species is in question, when the planet is threatened by global warming and the end of biodiversity, and humanity is threatened by the proliferation of arms of all kinds and the perfection of surveillance techniques? Must we be like Nero, fiddling while Rome burned? […] Must we follow the the advice of Voltaire, and tend our gardens, that is to say, take no interest in the big questions and dedicate ourselves to matters where we are capable of making some difference? […]
I have no answer to these questions. Grothendieck had his. He was a perfectly free man, in the sense of Spinoza: what he did, he did after mature reflection, and it was determined purely by what he believed to be the truth, not by external circumstances or social pressures.
Re: Grothendieck’s Activism And What It Says About The World
Thanks for that link, Tom. It contrasts nicely with some of the obituaries in the UK press.
The title of Ivar’s blog piece is from a poem by Mallarmé and is its first line. In the second stanza of the poem is another line that might perhaps be applied to Grothendieck:
”Donner un sens plus pur aux mots de la tribu,”
which T. S. Elliot in `Little Gidding’translates as
`to purify the dialect of the tribe’,
and perhaps that is what Grothendieck did.