Alexander Grothendieck’s 80th birthday was this past March, and the September Notices of the AMS has several articles about his later years. There’s a long piece entitled Who is Grothendieck?, by Winfried Scharlau, who is writing a three-volume biography. The first volume (in German) is available here and mainly deals with the stories of his parents. The article contains the only pictures I’ve ever seen of the post 1970s Grothendieck and a wealth of information about his activities after leaving the mathematical research world.
The same issue contains a short piece Memories of Shourik, by Valentin Poenaru reminiscing about his friendship with Grothendieck during the 1960s. The most shocking thing in it to me was actually the part about Barry Mazur’s wife, who Poenaru describes as being only 17 when he met her living with Mazur at Bures-sur-Yvette.
Note added: Mazur’s biography here mentions just one wife, Grace Dane, a Harvard biology postdoc he married in 1960. If she was, as Poenaru claims, 17 in 62-63, that would have made her a 15 year-old postdoc when they married….
Finally, there’s a piece by Allyn Jackson about Grothendieck and the IHES, which is having its 50th birthday this year. Evidently Grothendieck has recently been in communication with the IHES:
Six months to the day before the start of the IHES anniversary celebration, Grothendieck wrote to the institute with a request for books. The IHES sent him the books as quickly as it could. But the exchange of letters between Grothendieck and the IHES administration culminated in his writing a furious “open letter” recounting his view of the exchange, which he took as deeply insulting towards him. He requested that copies of the open letter be sent to all members of the IHES Scientific Council and explicitly states that this letter is public (though he also says he will make no efforts on his own to publicize it). Having seen the open letter, I can say that it conveys an extreme outrage that indicates how difficult it would be to conduct reasonable communication with him.
At the same time, the open letter reveals the vivid personal tie that Grothendieck clearly still feels to the IHES. The letter also reveals an isolated individual who is reaching out in the only way he is able. In one place he speaks of his open letter as being a letter of farewell (“adieu”) to a world with which he no longer has anything in common. He ends on a note of apocalyptic foreboding, saying “that the time is near when…this letter, this cry will be known by all. In a world of the living.” This cry does not seem to concern misunderstanding over his original request for books. Rather, it speaks of anguish in the heart of one of the great mathematicians of modern times.
The IHES is having Recoltes et Semailles, Grothendieck’s long meditation on mathematics and his withdrawal from it, published this summer. Articles about this are beginning to appear in the French press, see here and here.