RIP Alexander Grothendieck (d. 2014)

I just learned that Alexander Grothendieck died in November last year.

Who is Alexander Grothendieck? He was perhaps the finest mathematician of the 20th century, whose work in algebraic geometry have given birth to one of the most illuminating, productive and ambitious mathematical developments in the 20th century.

He was a colorful character who led an eventful life. His father perished in Auschwitz. He taught a prestigious mathematical seminar at IHES Paris. He was involved in radical leftist activism, which made him a pariah in Parisian academe. He gave math lectures and preached pacifism in the jungles of Vietnam during the war while Americans bombs were exploding all around him. He won the Fields Medal, the highest honor in mathematics. He decided later in his life to give up mathematics totally. Finally, in 1990, he gave up on society in general, and left behind everything he had, to live alone in the Pyrenees.

After that, his reputation took a romantic turn: popular accounts talk of a genius mind, disillusioned with worldly honors and insincere colleagues, who sought enlightenment in solitary life. He wrote screeds against what he viewed as a reactionary society, and became somewhat of a mythical figure of the French Left (Fortunately he didn’t become like the other brilliant mathematician, who stopped doing mathematics and went to live alone in ramshackle cabin in the Montana woods).

During his self-imposed exile, Grothendieck would write letters to his former departmental colleagues, to ask them to destroy anything he had ever written, whether published or not. We are lucky that they collectively decided to ignore his request, lest we would be deprived of some of the most sublime mathematical ideas ever concocted by our species.

Now that Grothendieck had passed away, mathematicians the world over are working on a mammoth task: translating the whole Grothendieck oeuvre into the major languages, so that his mathematical ideas and programs can be disseminated outside the French-speaking world. Not that these are easy to read; it is estimated that the number of people who understand his whole work is no more than ten, that including his most brilliant and most devoted proteges, like Rene Deligne.

I’m happy to see that Grothendieck is not totally forgotten, although response to his death in the English speaking media was a bit muted. I can imagine science editors the world over asking “Alexander who?”. His obituaries appeared in some major English newspapers like The New York Times, The Independent, and The Telegraph (no BBC?). There is no such problem in France. In a country that places mathematics as a source of historical pride, Grothendieck is considered a national hero. Now if only we can locate his autobiography that is rumored to exist somewhere…

alexgrothendieck

He is the bald one

 

The best write-up on the life and work of Grothendieck that I can find online is by Pierre Cartier: http://inference-review.com/article/a-country-known-only-by-name/ .

Quote from The New York Times obituary:

He avoided clever tricks that proved the theorem but did not develop insight. He likened his approach to softening a walnut in water so that, as he wrote, it can be peeled open “like a perfectly ripened avocado.”

“If there is one thing in mathematics that fascinates me more than anything else (and doubtless always has), it is neither ‘number’ nor ‘size,’ but always form,” he wrote in a long memoir in the 1980s, “Reapings and Sowings.” “And among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other and continues to fascinate me, is the structure hidden in mathematical things.”

Softening walnut in water: a brilliant heuristic. RIP, AG.

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