Alexander Grothendieck died on Thursday at age 86 in Saint-Girons.

Grothendieck, who started his work in functional analysis, is known for his far-reaching (and still incomplete) program of creating new foundations for algebraic geometry, a work that he led at IHES in the 50s and 60s and that is documented in the thousands of pages of EGA and SGA. If modern algebraic geometry is built on schemes, has applications to number theory, has definitions given in a category-theoretic language, and is completely incomprehensible to the novice, it is all thanks to Grothendieck’s vision.

In his 40s, and the top of his game, Grothendieck left IHES over the issue of military funding, and progressively detached from the mathematical community, while embracing environmental and anti-war causes.

Grothendieck’s life story, from his escaping Nazi Germany, to his revolution in mathematics, to his radical politics and later hermit life, is spellbinding. Some of it is told in a great two-part article in the Notices of the AMS (part 1, part 2) and I would also recommend this more technical essay and this more philosophical one.

Grothendieck has a flair for effective naming, he had a way with words, and he liked elaborate metaphors. Here is his famous “how to break a nut” analogy describing his style of mathematical research

I can illustrate the second approach with the same image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible

through weeks and months—when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado!

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If you haven’t already heard of it, I’d like to bring to your attention an excellent biography by Winfried Scharlau – there is a fundraising effort underway to translate its 3rd volume to English (so far only the 1st volume has been translated): http://www.gofundme.com/7ldiwo. I think it’s worth contributing to and spreading the word about it.

I think the best way to remember Grothendieck is to read his own works.

For non-mathematicians, the moving, personal parts of Récoltes et Sémailles; for those in a hurry, his personal sketch on his Riemann-Roch theorem.

For experts in other fields, either the Tohoku paper on homological algebra or the Bulletin one on Chern classes.

Once I also raised some concerns about applying to military funding. A colleague pointed out that better I use those resources for my research in TCS. Otherwise they will use it for real military research and purposes.

planning to blog on this also. grothendieck epitomizes the formidable/ towering/ intimidating abstraction created in math in the 20th century. somebody said that the FLT proof by wiles would have been impossible without his work.

youve already found some of the best links. see also impact of grothendiecks program on TCS / tcs.se

Thanks for this post, Luca.

For those who read French, Le Monde and Liberation have article on the passing away of Grothendieck.

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