Alexander Grothendieck is 80 today. It’s truly surprising that his strange and marvelous biography — to put it all in one sentence, he rewrote much of the foundation of number theory and geometry in an immense burst of energy in the 1960s, then, over time, came to feel that the mathematical establishment had betrayed him and his ideas, and moved to the Pyrenees to be alone and herd sheep — is not better known.

Read the excellent biographical article by Allyn Jackson, “Comme Appelé du Néant — As If Summoned From the Void”: Part I, Part II. And if that doesn’t sate you, skim through the mass of scanned manuscripts, appreciations both technical and non-, and photographs at The Grothendieck Circle.

My own story: in my last year of grad school I came across Grothendieck’s famous late article, “Esquisse d’un programme” (actually an unsuccessful grant application.) My advisor saw me reading it, and, aware of its seductive effect, told me, “I forbid you from reading the Esquisse until your thesis is finished!”

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Nitpicking about spelling: it should be “Esquisse d’un programme” (programme is masculine)…

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Ed:fixed!)One should not forget that before turning his powers to homological algebra and algebraic geometry, Grothendieck first revolutionized the theory of topological vector spaces, thus taking his rightful place in the list of analysts, with Riemann and Langlands, who have utterly transformed even the most algebraic parts of number theory…

Another remarkable book to see him “in action” is the collection of letters between him and Serre, recently published in English-French version by the AMS. My favorite part is when Grothendieck naively asks Serre (in the 50’s or 60’s) if people know or not if the Riemann zeta function has infinitely many zeros on the critical line…

(Also, if I remember right, “Esquisse d’un programme” was not a grant application, since France didn’t then — or now –have individual grants in the US style, but it was a kind of research statement/proposal for an application to be (re)hired by CNRS, the French national research institute).

Grothendieck deserves a proper biograhpical treatment. I’ve read Jackson’s articles and they are excellent ,but too short. She could flesh them out and have a best seller on her hands a la Nasar’s “A Beautiful Mind”.

W. Scharlau has apparently started writing a full-length biography, and from what I’ve seen, the first volume is available, but it is in German.