Alexander Grothendieck and the Question of Intellectual Property

Today I’m going to talk about a subject that, I believe, will rarely be broached on our blog: math.

Or at least a mathematician. A couple of months ago, when I was brainstorming ideas for my week of blogging, my boyfriend suggested that I write about a famous mathematician. I laughed.

“No,” he said. “Hear me out.” And then he told me the story of Alexander Grothendieck.

Grothendieck was born in 1928, the son of radical parents who went to Spain for the Civil War and fled Germany in the advent of the Nazis. He himself stayed in Germany with a foster family until the situation grew too dangerous for the Jewish Grothendieck. So in 1939 he joined his parents in France. With such a restless childhood, it’s no surprise that Grothendieck’s formal education was scattershot, but he eventually earned a Ph.D. working on topological vector spaces.

It was in 1954 that Grothendieck turned to the field in which he would make his name: algebraic geometry. Over the next decade, he reshaped the field and published two fundamental works: the Séminaire de Géométrie Algébrique du Bois Marie (based on Grothendieck’s seminar notes) and Éléments de géométrie algébrique. Algebraic geometry today relies on these texts, and, according to this article, this “systematic rebuilding permitted the solution of deep number-theoretic problems, among them the final step in the proof of the Weil Conjectures by Deligne, the proof of the Mordell Conjecture by Faltings, and the solution of Fermat’s Last Problem by Wiles.” In 1968, he received the Fields Medal.

But by 1970, Grothendieck “had done mathematics twelve hours a day, seven days a week, and twelve months a year for twenty years.” This focus on math at the exclusion of all else led to a sudden reversal: he quit his job, embraced political activism, and began, gradually, to extract himself from the mathematical community. He lived in a commune. He left Paris for the small towns of France. He adopted Buddhism, but eventually discarded that for Christian mysticism. He officially retired in 1988, and has been living as hermit for some time.

Earlier this year, Grothendieck wrote a letter withdrawing his permission to print or otherwise disseminate his work, and condemning those that had done so since his retirement. He asked that publishers remove those books from circulation, and librarians to remove them from their shelves. The result, as you can see in the comments on this page, was a flurry of discussion among mathematicians. Some questioned his motives, his intent, and the underlying principles of the issue:

“Awesome, Grothendieck still has contact to other people. It’s funny that he really cares about illegal publications and stuff. Anyways, what is he going to do if people still publish and copy his work. Really suit [sic] somebody? That would be awesome (only if he appears in court of course! I would be so happy to see him.)”

“i don’t recognize the existence of ‘intellectual property’ at all, especially not in science and mathematics . . . G stands to gain nothing from this. He doesn’t want money, etc., he merely wants to suppress his own work. We wouldn’t accept results being suppressed by another mathematician. Indeed, G in the past and the current G are completely different people.”

“While I find this news as disturbing as most of you seem to, bear in mind that copyright protects words, not ideas. If someone were to write a fresh exposition of the insights in SGA, they would still be able to publish it. Indeed, most of us learn this material primarily from more modern paraphrases already. And, of course, there are enough copies already in libraries that there is no reason to worry about losing the text for decades to come.”

Others hastily made plans to salvage what they could:

“In any case, I will grab everything from the grothendieck circle and so on before it’s too late…”

“Don’t worry . . . It will eventually appear in one of the pirate book sites anyway, even Groth. circle is taken down and you miss it now. The only difference will be that instead of pdf you will get djvu format.”

So why bring all this up? As the third comment above suggests, Grothendieck’s ideas are integral to the field of algebraic geometry—present in those “modern paraphrases” as well as in the original texts. So integral, in fact, that many of the mathematicians on this board absolutely refuse to respect Grothendieck’s request, arguing instead for the invalidity of intellectual property in science and math, for the disjunct between the Grothendieck of 40 years ago (dedicated to math, happy to contribute to the mathematical community, and with the greater claim to the work done) and the Grothendieck of today, and consoling themselves with the inevitable piracy of the two books.

What do you think? Is there a difference between intellectual property among the disciplines, or between fiction and nonfiction? When do ideas become public domain—in spirit if not in law, when the public fights an author for access? Is it ever right to dismiss an author’s wishes for their work? Is it ever right to pirate?