Just the last days I learned about the Grothendieck topology, which is a moral equivalent of an open covering in a category.
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(Physicists would put an extra point at 9, and Grothendieck himself would put an extra point at 57.)
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One of the best Grothendieck obits I've seen in terms of making his work comprehensible to us mere mortals.
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I can't speak to topos theory (which I have not really studied, and understand only in terms of a link between category theory and logic), but I can say a few words about grothendieck topologies.
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Grothendieck topologies are a way to recover this nice topology in the classical case, an also to fix the topology more generally so that one can do algebraic topology with schemes and get useful results.
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Grothendieck topologies can be defined for arbitrary categories and some of the computations in schemes only uses this categorical data, which allows one to think of a category with a topology as a (collection of) geometric object(s).
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David Mumford did an excellent obituary of Grothendieck for Nature.
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lowballing physicists never gets old and poor grothendieck.
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Ultimately, Grothendieck.
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is grothendieck locked in as one of them?
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Cool, but where do Grothendieck topologies and topos theory come into play?
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Why are people so obsessed with ranking people against Grothendieck?
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In my opinion, Godel and Turing were both greater mathematicians than Grothendieck, and probably von Neumann too.
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Grothendieck for sure.
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The sheaves used are over Lawvere-Tierney topologies, which are more general than Grothendieck topologies.
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So, you do think that Einstein, Grothendieck and Freud (to name a few) faked their accomplishments?
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Einstein, Grothendieck, Freud ... you can't fake their achievements.
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Perhaps you should take a completely different route and write about Grothendieck.
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Interestingly, Grothendieck grew disillusioned with math and mathematicians.
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Grothendieck died late last year, very recently.
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There are some beautiful pieces written about Grothendieck.
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This can be seen in the legend of the so-called “Grothendieck prime”.
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In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number.
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“You mean an actual number?” Grothendieck asked.
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Algebraic geometry post-Grothendieck.
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i vote for Grothendieck as well.
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