Alexandre Grothendieck, born in 1928, was the greatest mathematician of the twentieth century and arguably the greatest of all time. Between 1958 and 1972 he reformulated the fundamental concepts of geometry —concepts like point, space and covering (as in, “the northern and southern hemispheres cover the entire earth”) so completely that it is no longer possible to imagine what geometry would be about if Grothendieck had never lived.
In this endeavor, he collaborated with several of the world’s finest mathematicians who put their own research agendas on hold for the privilege of attending Grothendieck’s daily seminars, fleshing out his ideas, and committing them to paper. The resulting documents, totalling over 10,000 pages, revolutionized geometry, arithmetic and algebra by viewing all of mathematics from a height of abstraction at which subjects blend together, every unnecessary detail is stripped away, and essential truths are almost automatically revealed.
Today he lives alone in a cabin in the Pyrenees, tending a garden and refusing visitors.
It’s been over 30 years since Grothendieck’s abrupt retreat from civilization, and for most of that time I’ve been waiting for someone to write his biography. This is, after all, a compelling story. Its hero is a brilliant eccentric described by everyone who’s known him as a man of indescribable charisma. (It was this legendary charisma, no less than the brilliance and clarity of the Grothendieck vision, that lured so many first-rate mathematicians away from their own research for the sake of the grand collaboration.) Besides his mathematical work, he’s given us several thousand pages of introspective autobiography, philosophy and theology, including a several-hundred page proof of the existence of God. (The thrust of the argument, as I understand it: We all have dreams, don’t we? And what could dreams be, if not messages from God? And how could God send us messages if he didn’t exist? Q.E.D.)
It’s a story touched by many of the defining events of the twentieth century: a father who died in Auschwitz, a leadership role in the antiwar and counterculture movements of the late sixties, and a career abandoned at its height partly to protest NATO’s role in the funding of mathematical research—and then, to add to the drama, decades of isolation punctuated by cryptic pronouncements and long rambling screeds that, in the opinion of many former friends and colleagues, indicate he’s gone stark raving mad.
The telling of this tale is long overdue but it looks like the waiting is over. Allyn Jackson’s superb two-part article has appeared here and here, and a full length book (by Winfried Scharlau) is apparently in the works. There is also a brilliant lecture by Colin McLarty on Grothendieck’s philosophy of mathematics. Both McLarty’s and Jackson’s pieces require some mathematical sensibility. It remains to be seen whether someone will distill the Grothendieck story down to the comfort level of, say, the average New Yorker subscriber while remaining true to the spirit and breathtaking beauty of the Grothendieck revolution.