On the curious similarity between mathematics and imaginative design.https://twitter.com/tools_4_thought/status/1001966675451924480 …
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No, I haven’t. Must admit, I took a class on category theory, and didn’t get a lot out of it (almost the only math class of which that was true; certainly the only well-taught class of which that was true).
Interesting to see that Grothendieck apparently liked category theory. I wonder what he saw in it? (Many leading mathematicians seem rather skeptical it has much value; as you probably know it’s often referred to as “General nonsense”.)
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Most accounts I've heard say he used it to revolutionize algebraic geometry. Category theory is much more popular than this tweet lets on. I know many active professional mathematicians who say that category theory is a hard prerequisite for modern pure math.
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The accounts of Grothendieck I've heard made it sound like he and a few colleagues, over the course of a few months, rewrote algebraic geometry in category theory, while inventing new parts along the way, his colleagues furiously scribbling notes to keep pace.
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The term comes from category theorists themselves. And mathematicians will occasionally say things like "this bit follows by general nonsense". This is not meant to be disparaging. It's more an indication that machinery is used that's more general that the subject in hand.
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"architecture is frozen music, ... that means music is liquid architecture"https://www.youtube.com/watch?v=ET2UoTwwJuk&t=165s …
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tbh I haven't studied it in any great depth, & I suspect the bits that I find useful are some of the shallowest (high-level intuitions about structure-preserving maps between spaces, etc). a whole class on it might rapidly get into stuff with no intuitive use to me
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To be clear, terms like “general abstract nonsense” are also used playfully or otherwise without any negative connotation. Grothendieck used category theory to revolutionize math. He was singular in his seemingly natural ability to reason categorically and do so to great result.
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