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Alexandre Grothendieck, the greatest mathematician for the twenties century, passed away on November 13, 2014 at the Saint-Girons hospital (Ariège) near the village Lasserre.
Alexandre Grothendieck spent about the last 24 years of his life in this village in Pyrenees range of mountains in a self-imposed retirement avoiding all contacts with the outside world and the mathematical community.
He had good reasons for this, but till now the mathematical community does not want to listen, or, rather, to read his extensive partially autobiographical, partially philosophical texts.
Alexandre Grothendieck, with help of his pupils, collaborators, and admires, completely transformed mathematics. His best known contribution is the proof of most of the Andre Weil conjectures (with the last step done by his pupil Pierre Deligne). Much more important is his transformation of the algebraic geometry from relatively obscure branch of mathematics to its central part. Even more important is his most intangible contribution, the concept known as th "rising sea", the idea that every mathematical problem should be immersed in a sufficiently abstract theory, which will made the solution trivial. This theory should be, in a sense, trivial too - it should not involve any tricks or convoluted arguments. This was a drastic departure from the mathematical analysis, the central branch of mathematics at the time, which was dominated by proofs demonstrating not so much the vision, but the "executive power" of the authors (the concept introduced by G. Hardy, who valued the executive power most). These ideas are still far from being internalized or even understood by the mathematical community.
Despite his tremendous influence, surpassing by a large margin the influence of any mathematician after David Hilbert, Alexandre Grothendieck was at least about 100 years ahead of his time.
His integrity and his concern about the perils people put each other into are hardly matched by any other contemporary scientist. He did not succeed much in this respect, apparently because his concerns only appeared to be left wing politics, but in fact were not of political nature.
With Alexandre Grothendieck passing away we lost the last living giant in mathematics.
Here is a link to a memorial article Alexandre Grothendieck, le plus grand mathématicien du XXe siècle, est mort in Le Monde, France (in French).
Next post: Where one can find an autobiography of Alexander Grothendieck? Part 1.
