Earlier this year I bought a copy of the recently published version of Grothendieck’s Récoltes et Semailles, and spent quite a lot of time reading it. I wrote a bit about it here, intended to write something much longer when I finished reading, but I’ve given up on that idea. At some point this past fall I stopped reading, having made it through all but 100 pages or so of the roughly 1900 total. I planned to pick it up again and finish, but haven’t managed to bring myself to do that, largely because getting to the end would mean I should write something, and the task of doing justice to this text looks far too difficult.
Récoltes et Semailles is a unique and amazing document, some of the things in it are fantastic and wonderful. Quoting myself from earlier this year
there are many beautifully written sections, capturing Grothendieck’s feeling for the beauty of the deepest ideas in mathematics. One gets to see what it looked like from the inside to a genius as he worked, often together with others, on a project that revolutionized how we think about mathematics.
A huge problem with the book is the way it was written, providing a convincing advertisement for word processors. Grothendieck seems to have not significantly edited the manuscript. When he thought of something relevant to what he had written previously, instead of editing that, he would just type away and add more material. Unclear how this could ever happen, but it would be a great service to humanity to have a competent editor put to work doing a huge rewrite of the text.
The other problem though is even more serious. The text provides deep personal insight into Grothendieck’s thinking, which is simultaneously fascinating and discouraging. His isolation and decision to concentrate on “meditation” about himself left him semi-paranoid and without anyone to engage with and help channel his remarkable intellect. It’s frustrating to read hundreds of pages about motives which consist of some tantalizing explanations of these deep mathematical ideas, embedded in endless complaints that Deligne and others didn’t properly understand and develop these ideas (or properly credit him). One keeps thinking: instead of going on like this, why didn’t he just do what he said he had planned earlier, write out an explanation of these ideas?
As an excuse for giving up on writing more myself about this, I can instead recommend Pierre Schapira’s new article at Inference, entitled A Truncated Manuscript. Schapira provides an excellent review of the book, and also explains a major problem with it. Grothendieck devotes endless pages to complaints that Zoghman Mebkhout did not get sufficient recognition for his work on the so-called Riemann-Hilbert correspondence for perverse sheaves. Mebkhout was Schapira’s student, and he explains that a correct version of the story has the ideas involved originating with Kashiwara, who was the one who should have gotten more recognition, not Mebhkout. According to Schapira, he explained what had really happened to Grothendieck, who wrote an extra twenty pages or so correcting mistaken claims in Récoltes et Semailles, but these didn’t make it into the recently published version. If someone ever gets to the project of editing Récoltes et Semailles, a good starting point would be to simply delete all of the material that Grothendieck included on this topic.
The extra pages described are available now here, as part of an extensive website called the Grothendieck Circle, now being updated by Leila Schneps. For a wealth of material concerning Grothendieck’s writings, see this site run by Mateo Carmona. It includes a transcription of Récoltes et Semailles that provides an alternative to the recently published version.
The Schapira article is a good example of some of the excellent pieces that the people at Inference have published since they started nearly ten years ago (another example relevant to Grothendieck would be Pierre Cartier’s A Country Known Only by Name from their first issue). I’ve heard news that they have lost a major part of their funding, which was reportedly from Peter Thiel and was one source of controversy about the magazine. I wrote about this here in early 2019 (also note discussion in the comments). My position then and now is that the concerns people had about the editors and funding of Inference needed to be evaluated in the context of the result, which was an unusual publication putting out some high quality articles about math and physics that would likely not have otherwise gotten written and published. I hope they manage to find alternate sources of funding that allow them to keep putting out the publication.
Rereading the Cartier article I am struck by his language; C. is quite the stylist, even in translation.
Schapira’s article does not offer the same linguistic pleasure, but does at least correct the record – though little is needed. Kashiwara’s genius, so evident in his extraordinary papers (not only those on D-modules, microlocal analysis, RH) speaks for itself, as does Mebkhout’s subsequent output. But the historical notes in some Kashiwara-Schapira books are cringe inducingly hagiographical about K, I’ve often wondered what K. thinks about them.
Hi Peter, happy New Year! Glad to begin the year myself reading some of your excellent musing about Grothendieck. As you know, I’m greatly interested in his personality and his mathematics and I’ve written about him on my blog (which you kindly linked some time ago in another post you’ve dedicated to him).
I’ve read Récoltes et Semailles (in French) in its entirety, and boy, it’s a rough ride indeed. I agree with the fact it clearly wasn’t edited. But I deeply feel the “unedited” version is the one we should read. Not that this version is the one Grothendieck himself would have liked us to read because I think in the end he didn’t intend Récoltes to be published. But it’s important we read it because in my opinion it has been assumed for too long that R&S is just the monumental rant of a terminally paranoid recluse. It’s not. As you say, it has moments of absolute brilliance, mathematical or not.
I’ve been in touch for some time with people who are/were familiar with Grothendieck’s past, and I’ve somehow changed my attitude toward some of his most controversial decisions, including him leaving the IHES. I’ve long thought he had been overcome at a certain point by his personal problems which he somehow had rationalized in the refusal to work for the “institutions”. It turns out he had a point of being wary of IHES connections to the military, and other people shared his views. But while Grothendieck was principled AND not well off, others were either principled and with enough means to get away with IHES money, or had not enough financial security to break ties with that institution. Long story, and not exactly a new one…
Off topic, but, alas,
has passed away.
Is there any ongoing effort to translate Grothendieck’s works into English language? I know some people independently translated some pieces of his work, but I have not seen any organized program to translate all his work, including Recoltes.
Pierre Schapira’s article “A Truncated Manuscript” is available on ArXiv
Hi, Peter. You might be interested in this mildly unpleasant experience I had with Inference magazine a couple years ago. The short story is they contacted me, asked me for an article, it went through a couple rounds of revision where at each step I had to bug them for comments, then suddenly they dropped it for no reason.
My guess is that they were never so excited about the article in the first place. But the main thing I remember was the obsequious tone of the email from the assistant who solicited the article, followed later by a complete lack of explanation for why they dropped it.
As I wrote in the above-linked post, I can’t really be angry at them–they have every right to ask for an article and then change their mind. The whole experience was kinda weird, not like any other interaction I’d had with any other publication. A bizarre mix of hot and cold.
This may be the place to note some sad news: Mikio Sato, the creator of algebraic analysis, who is mentioned in Schapira’s article, passed away this Jan. 9th:
Here’s an old (1990) AMS interview of Sato:
Like Grothendieck, he was one of the really visionary mathematicians of the 20th century.