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While Googling something or other, I came across Nine Chapters on the Semigroup Art , which is a leisurely introduction to the theory of semigroups. (While the document is labelled “lecture notes”, the typography is quite beautiful.)

Happy New Year! The publicity in the wake of Grothendieck’s death has left a certain number of non-mathematicians with the question of what it was exactly that he did. I wrote an answer elsewhere that people seemed to find informative, so I’m saving it here for posterity.

This post is as untechnical as I could make it. Grothendieck’s work is incredibly technical, even by modern standards of abstract mathematics, so my description is, if you’re being charitable, highly impressionistic, and if you’re not, wrong in many major details. I also only discussed schemes and the Weil conjectures, which is only part of what Grothendieck is famous for.

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