## November 26, 2014

### 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.

Posted at November 26, 2014 1:49 AM UTC

TrackBack URL for this Entry:   https://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2785

### 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.

Posted by: Tim Porter on November 26, 2014 10:05 AM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

Ah, no wonder I had trouble translating the title — it’s poetry! Good thing someone cultured came along.

How would you render the penultimate sentence of the article?

Calme bloc, ici-bas chu d’un désastre obscur !

Posted by: Tom Leinster on November 26, 2014 12:42 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

Calme bloc, ici-bas chu d’un désastre obscur !

I would not attempt to translate it as its meanings are bound up with those of the imagery that is being used both in the article and in the poem.

This line is the first line of the last verse of the poem. The poem is entitled Le Tombeau d’Edgar Poe’. Mallarmé and several other French poets of the time had a high regard for the writings of Poe.

The ‘calme bloc’is the unsculpted block that was the memorial in Baltimore, which is imagined as having fallen from the heavens ‘like the poet’, a fall that is due to some unknown reason.

There is a neat explication’ of the poem (in French) at http://www.etudes-litteraires.com/mallarme-tombeau-edgar-poe.php and of course, that is where I got what I wrote above.😉

(The whole poem is also shown at that link in case anyone is interested.)

Posted by: Tim Porter on November 26, 2014 5:10 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

Thanks: that clarifies it a lot (if not entirely; I just don’t think my French is up to reading Mallarmé’s poems).

Posted by: Tom Leinster on November 26, 2014 6:05 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

It contrasts nicely with some of the obituaries in the UK press.

God, yes — I just accidentally saw the obit in the Times, and I see what you mean. It even manages to strike a sneery tone about his mathematics, astonishingly.

Posted by: Tom Leinster on November 27, 2014 2:58 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

Tom wrote:

It even manages to strike a sneery tone about his mathematics, astonishingly.

I’d like to see that, just so I can tut-tut about it.

Posted by: John Baez on November 28, 2014 4:25 AM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

Ha! The Times is paywalled, but there was a physical copy of the obituary lying around our common room. I’ll see if I can remember to look at it and pull out some choice quotes today, for your tutting pleasure.

(I think of tutting as very British. But openly admitting to your desire for a good tut probably isn’t.)

Posted by: Tom Leinster on November 28, 2014 8:19 AM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

Here it is. Have a good tut!

Now endowed with a Wittgensteinian sense of his own uniqueness, Grothendieck was entering his most intense phase. His lectures and seminars at the Institute [sic] des Hautes Études [sic] in Paris were widely attended but, one suspects, little understood.

(I suppose “[sic]” is a kind of learned form of “tut”.)

Posted by: Tom Leinster on November 28, 2014 11:07 AM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

I wonder if [sic] is not Times-speak for `foreign’! The article in the Times seems to be unsigned. Does anyone know who is the author? (I am asking just out of interest not with any intent on harrassment!)

Posted by: Tim Porter on November 28, 2014 12:24 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

The “[sic]”s are mine, to mark the Times’s mistakes (tut!). It looks like they wrote “Lebesque” too.

I don’t know who the author is. I don’t think many mathematicians view Wittgenstein as a particularly significant figure to mathematics, as the opening sentence implies, which suggests “non-mathematician” to me.

Posted by: Tom Leinster on November 28, 2014 1:04 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

Thanks for pointing out my error. I had not checked in the original.

Posted by: Tim Porter on November 28, 2014 1:44 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

The line that really struck me was the one in the first paragraph about the accomplishments for which “Grothendieck is credited in his adopted country” (emphasis mine). You can almost hear someone adding “But you know the French.”

The New York Times obituary is a lot less sneery.

Posted by: Mark Meckes on November 28, 2014 2:41 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

Thanks, Tom! I found the article a lot less tut-worthy than you’d led me to hope. But still fun to read.

I don’t think calling Grothendieck ‘Wittgensteinian’ means the author thinks Wittgenstein was any good as a mathematician. Both were intense, charismatic and troubled figures who gathered a circle of people around themselves but also fled this circle. I think the comparison is a helpful one… at least for people who know Wittgenstein.

They’re also very different. For example: for a while, Grothendieck interacted profitably with a circle of top-notch colleagues to create a huge body of work. Wittgenstein’s productions were always more individual. But some of this could be the difference between mathematics and philosophy: mathematics is more of a ‘coral reef’ built into a solid whole by the cooperation of many organisms.

Posted by: John Baez on November 28, 2014 10:01 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

I don’t think calling Grothendieck ‘Wittgensteinian’ means the author thinks Wittgenstein was any good as a mathematician.

I agree with your reading of that line, but the opening sentence that Tom referred to implies that Wittgenstein “seized the attention of the world of mathematics”, which sounds off to me.

Posted by: Mark Meckes on November 28, 2014 10:23 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

Yes, Mark’s right: I meant the opening sentence of the whole obituary, not of the bit I quoted. Sorry for the ambiguity.

Posted by: Tom Leinster on November 29, 2014 6:07 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

I don’t have access to the Times (presumable the London, not the New York), but the short article at 9news.com.au, the only one I could find in the Australian general media coverage, is terrible.

Posted by: David Roberts on November 28, 2014 4:21 AM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

[Comment deleted; see my comment below — TL]

Posted by: Roy on November 27, 2014 10:14 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

May I suggest that political discussions on this site be limited to those directly connected to the political and ethical responsibilities faced by mathematicians as mathematicians?

[Rest of comment deleted; see my comment below — TL]

Posted by: Michael Harris on November 27, 2014 11:23 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

Thanks for your suggestion, Michael, which I’m going to follow (including that of deleting your comment — or most of it, anyway).

There’s an important interplay between mathematics and world affairs, and as I’ve said before, I think discussion of it very much belongs on a blog about math, physics and philosophy, just as it belongs on the pages of the Notices of the AMS and the newsletter of the LMS.

However, doing these posts comes with the risk that the conversation drifts too far into politics and away from anything related to mathematics. I don’t think most readers of this blog want that, and I don’t either. So ever since I started writing about the crossover between mathematics and politics, I’ve kept a close eye on the conversations and tried to keep them from straying too far away from mathematics and mathematicians. It’s sometimes a difficult judgement, and there’s no way to do it objectively, but that’s been my aim.

Of course, people who want to have unmoderated conversations about politics are free to have them on thousands of other websites. It’s just not going to happen here.

Posted by: Tom Leinster on November 28, 2014 12:16 AM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

Incidentally, the nLab page Tohoku was linked to from the obit at the Guardian, which mentioned the paper as G.’s breakthrough on the international stage.

Posted by: David Roberts on November 28, 2014 4:32 AM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

Note that the Guardian obituary was written by Harvey Shoolman who is involved with the Grothendieck Circle.

Posted by: Tim Porter on November 28, 2014 11:53 AM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

I deleted another comment.

Comments expressing views on Grothendieck’s work or statements are welcome, whether positive or negative or neither. But if they’re unnecessarily inflammatory, or don’t have much to do with mathematics or mathematicians, I’ll delete them.

Posted by: Tom Leinster on November 28, 2014 3:29 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

I don’t think that my previous comment you deleted had nothing to do with Grothendieck or maths. Grothendieck stopped doing maths once we asked to himself “why should I do maths ?”, and he found the answer we all know. My previous comment was here to show that the answer he believed firmly in is not at all universal or to be seen as “provable”, that’s all.

Posted by: sure on November 28, 2014 7:19 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

If anyone here hasn’t read this yet, I recommend it:

It goes much deeper into Grothendieck’s mathematics and life than any newspaper obituary could. Let me just quote the start:

Introduction

It is superfluous to introduce Alexander Grothendieck to mathematicians: he is recognized as one of the greatest scientists of the 20th century. For other audiences, however, it is important to explain that Grothendieck is much more than his rather sulphurous reputation, that of a man in a state of rupture, committing what one could call the suicide of his work, or at any rate consciously destroying the scientific school that he had created. What I want to discuss here are the interactions between his scientific work and his extraordinary personality. Grothendieck’s story is not absolutely unique in the history of science; one may think of Ludwig Boltzmann for example. But there are essential differences: Boltzmann’s work was rejected by the scientific community of his time and remained unrecognized until after his death, whereas Grothendieck’s scientific work was immediately and enthusiastically accepted in spite of its innovative nature, and developed and continued by top-notch collaborators. The path traveled by Grothendieck appears different to me: a childhood devastated by the effect of Nazi crimes, an absent father who soon perished in the torments of the time, a mother who held her son in thrall and permanently affected his relationship with other women; all of this compensated for by an unlimited investment in mathematical abstraction, until psychosis could no longer be held off and came to drown him in the anguish of death — his own and the world’s.

The case of Georg Cantor is an intermediate one, which has been beautifully analysed by Nathalie Charraud. After encountering violent opposition to his ideas, the support of great mathematicians such as Dedekind and Hilbert allowed him to reach an apotheosis at the International Congress of Mathematicians1 in 1900 in Paris. The French school of analysis, from Poincaré to Borel, Baire and Lebesgue, was converted with enthusiasm to Cantor’s ideas. Cantor’s ultimate mental shipwreck may perhaps be attributed to the “Nobel syndrome”, by which term I mean a type of depression which has been observed to occur in certain Nobel prize winners. Incapable of confronting their own individuality and the life that remains before them — especially when the prize has been attributed at a young age — with the world-renowned public figure they have now become, they fear that they have already given the best of themselves and will never again be able to reach the same height. There is an echo of self mockery in this feeling.

The typology of Grothendieck is incredibly complex. Like Gauss, Riemann, and so many other mathematicians, his major obsession was with the idea of space. But Grothendieck’s originality was to deepen the idea of a geometric point. As futile as such research might appear, it is nevertheless of considerable metaphysical importance, and the philosophical problems related to it are far from entirely solved. But what kind of intimate concerns, what secret fears are indicated by this obsession with the point? The ultimate form of this research, that of which Grothendieck was proudest, was that concerning the concept of a “motive”, considered as a beam of light illuminating all the incarnations of a given object in its various guises. But this is also the point at which his work became unfinished: a dream rather than an actual mathematical creation, contrarily to everything else I will describe below in his mathematical work.

Thus, his work eventually opened onto an abyss. But Grothendieck’s other originality is that of fully accepting this. Most scientists are careful to efface their footprints on the sand and to silence their fantasies and dreams, in order to construct their own inner statue, in the words of Francois Jacob. André Weil was typical in this: he left behind a perfectly finished product in the classical style, in two movements: his Scientific Works, recently graced by a compelling Commentary written by himself, and a fascinating but carefully filtered autobiography, Memories of an Apprenticeship, in which the effects of privacy and self-censorship are veiled by the appearance of a smooth and carefree tale.

Grothendieck played at a different game, nearer to Rousseau’s Confessions. From the depths of his self-imposed retreat, of now nearly ten years – which it would be indecent to attempt to force – he sent us a vast introspective work: Récoltes et Semailles. I will make use of this confession to try to clarify some of the main features of his work. But let us not fool ourselves: Grothendieck reveals himself in all his nakedness, exactly as he appears to himself, but there are clear signs of well-developed paranoia, and only a subtle analysis could reveal all the partly unconscious blockages and silences. The existence of Récoltes et Semailles aroused a somewhat unhealthy curiosity in the eyes of a certain public, akin to the sectarian devotion to a guru, an imaginary White Prince. For myself, I will stick to an analysis of the work and of the biography of the author, remaining as rational and honest as possible, before letting Récoltes et Semailles illuminate this exceptional body of work from within.

Posted by: John Baez on November 28, 2014 9:53 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

I’ll translate this related illustrated comment by Grothendieck from German http://en.wikipedia.org/wiki/File:Grothendieck-Riemann-Roch.jpg

“Hells kitchen 1971

Riemann-Roch-theorem: the latest craze: the diagram commutes! To sketch the result for f:X->Y, I would have to abuse the patience of the audience for almost two hours. Black on white (in Springers lecture notes) it’s about 400, 500 pages.

A striking example for how knowledge and curiosity creates a suffocating ideological delirium, while life itself goes to hell - and is threatened with its definite destuction. It’s about time to chance the course!”

What I don’t like about the article is all the presumptions of the writer. For example, I’m not interested in math because I want to find “truth”. It’s more like an exciting story with fascinating plot twist. I don’t quite see how the questions posed in that article do really relate to mathematics - if I was a web designer or a cook, I could just as well ask me why I don’t do something which has a bigger impact on the course of the world. The author makes the comparison of how a proof can be checked by everyone, but a real life situation cannot always be clearly seen and examined in order to be solved. But like Grothendieck, he has a clear picture of “good” and “bad” and forces it upon us. The text implies that after “thinking” and “reflecting” people would come to the realization that acting against global warming, social injustice, etc. is what one ought to do. It’s one thing to show that there a problems, but another to demand of others not to be selfish and change the world we live in. While I happen to agree with some of the political agenda, I think one should avoid a moral imperative in ones writing.

Posted by: NikolajK on December 1, 2014 1:45 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

The text implies that after “thinking” and “reflecting” people would come to the realization that acting against global warming, social injustice, etc. is what one ought to do.

I don’t see that anywhere in the text. He merely gives global warming, social injustice, etc. as examples of causes that some people campaign for (or rather against). It’s true that he describes them as “problems”, but on the one hand, that could reasonably be taken as a view attributed to those campaigners, and on the other, it’s an extremely mild assertion (who doesn’t view social injustice as a problem?).

he has a clear picture of “good” and “bad” and forces it upon us.

Again, I’m not seeing that in the text.

Posted by: Tom Leinster on December 1, 2014 1:55 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

First he’s comparing approaches to math translate to their use in the world. He analyzes why it didn’t work for Grothendieck and that’s the interesting part.

Then I’m asked to “justify spending your life on mathematics” and answer “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…”. I’m scared of surveillance techniques too, but what’s the deal with “the end of biodiversity” and how do geopolitics relate to the usefulness of mathematics? Since this is asked in the context of what Grothendieck did, I’m concluding that, since doing math takes time and energy, he makes an appeal to think about it - we ought to make a change - for certain causes the author identified.

Posted by: NikolajK on December 1, 2014 5:12 PM | Permalink

### Re: Grothendieck’s Activism And What It Says About The World

I just deleted an entirely off-topic comment. Not sure why this post is attracting so many inflammatory and irrelevant comments, but I can’t be bothered dealing with them, so I’m going to close this thread now.

Posted by: Tom Leinster on December 2, 2014 10:53 PM | Permalink