misce stultitiam consiliis brevem

Mathematical non-games

The world of Algebraic Geometry (to which I have personal but absolutely no professional ties) is kind of tempest-tossed at the moment. I wouldn’t be suprised but what a number of you would enjoy thinking about and commenting on what’s going on.

In brief, lay terms, as I have heard it, there was this brilliant young French mathematician in the 1950s by the name of Alexandre Grothendieck who all but single-handedly revolutionized/created certain fields of Algebraic Geometry. Some 10-15 years later, he gave up academic life, moved to the Pyrrenées, and became a sheep farmer.

Since Grothendieck’s disengagement, his body of work has remained wildly useful and has formed a bedrock for later mathematical generations. The respect accorded to his own writings has gone so far as to inspire its own personal Distributed Proofreaders analogue for creating a TeX version of a long systematic work, “Séminaire de Géométrie Algébrique” (or SGA). The free electronic SGA project has been ongoing for the better part of a decade or more; volumes SGA 1 and SGA 2 are up on the arXiv already.

It seems just possible that might not be true much longer.

Behold the text of the until-recently-current webpage for the SGA 4 project:

Alexandre Grothendieck a malheureusement souhaité que cessent les travaux de réédition de SGA. Les pages qui étaient consacrées sont donc closes.
Dernière actualisation : 2 février 2010.

There is slightly more information, and much discussion, at Scott Morrison’s post on the Secret Blogging Seminar, a group math weblog. Again in brief (and English), Grothendieck apparently resurfaced enough to put out a letter stating that he doesn’t want his work republished or translated.

And he wags his finger at anyone who has done so or wants to.

Which is the really weird part. Assuming the letter is genuine, what legal ramifications does it actually have? Why use a phrase like “unlawful in my eyes,” which sounds to me deliberately obfuscatory? (Legality is not a matter of an individual’s vision.) The comments on the SBSeminar post seem weighted towards arguments as to the moral dimensions of Grothendieck’s stated wishes and a given mathematician’s obligation to respect them (or not). To me, the legal questions are more pressing and pertinent. Whether one has a moral obligation to respect an author’s wishes is a decision one makes for oneself. Whether the mathematical community as a whole has a legal obligation to take Grothendieck at his word has greater ramifications–and probably a single, findable answer (unlike a question of personal morality).

Edixhoven, one of the prior leaders of the TeX SGA project, did research the distribution question through the publishers and was told copyright had in fact reverted to the original authors (as he states on the linked page). This seems to indicate Grothendieck is not out of line to say he withholds his permission. But the questions only start there. …

Some on the SBSeminar comment thread made the “glass half full” suggestion that maybe it’s time SGA got a revamp anyhow. Yet the original is still a precious resource. I’ll be interested to try to follow what decisions are made.