Timeline for Proofs that require fundamentally new ways of thinking
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jun 26, 2020 at 19:34 | comment | added | Łukasz Lew | @MinhyongKim Is there some source where I could learn about the reasons why equivalence classes of morphisms are relevant and in what way it is natural for computers (without studying what sieve and site is)? | |
| Jun 3, 2012 at 19:49 | comment | added | temp | According to Grothendieck-Serre correspondence, I think it is more appropriate to say it is an insight due to both of them. | |
| Dec 10, 2010 at 1:26 | comment | added | Minhyong Kim | That is, it's easier to refer directly to arrows $A\rightarrow B$ between two of the symbols rather than equivalence classes of them. In this framework, a computer might easily ask itself why any reasonable collection of arrows might not do for a topology. Grothendieck topologies seem to embody exactly the kind of combinatorial and symbolic thinking about open sets that's natural to computers, but hard for humans. We are quite attached to the internal 'physical' characteristics of the open sets, good for some insights, bad for others. | |
| Dec 10, 2010 at 1:20 | comment | added | Minhyong Kim | Obviously, I agree that this was fundamental. But since we're speaking only about Grothendieck topologies and not the eventual proof of the Weil conjectures, there could be a curious sense in which this idea might be particularly natural to computers. Imagine encoding a category as objects and morphisms, which I'm told is quite a reasonable procedure in computer science. You'll recall then that it's somewhat hard to define a subobject. | |
| Dec 9, 2010 at 18:46 | history | answered | Tim Dokchitser | CC BY-SA 2.5 |