i spent a little time thinking about math again because of the lovecraft thread and made a little progress articulating my criticism of what i saw in my time in grad school. basically i think pure math has become almost entirely highly technical bullshit
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not in the sense of indifferent to its truth value but in the sense of indifferent to its *significance*. almost nobody in pure math has a compelling vision of what kind of math would *matter* to do. if you read writing by mathematicians from 100+ years ago it's not like this
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people used to do math because they were trying to understand the *world*. there just was not a pure / applied distinction, or even much of a math / physics distinction. modern pure math is an almost totally closed system, people do math to understand *other math*
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i left grad school among other things b/c it became clear to me that my thesis work did not matter in the slightest, that i had in large part only been drawn to doing math because i was good at it, so once i hit a real difficulty i no longer had any real motivation to continue
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there are enormously more different kinds of math to do now than there ever have been, this huge proliferation of different subjects of study, and almost none of it matters in the slightest. it's DLC for the biggest puzzle game ever
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but it's felt to me for awhile like at some point in the last ~30-100 years mathematicians stopped trying to understand *the world* and i think that was bad actually. mathematics disconnected from the world is just a complicated and engrossing puzzle game
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the standard line is "well you never know what will be useful in 50 years" - this is bullshit, it's not about knowing what will be useful in 50 years, it's about paying attention *at all* to one's internal sense of *significance*, as opposed to being endlessly nerdsniped
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professionalization has, i think, been very bad for pure math and probably every other part of academia too. math was never meant to be something people crank out to keep their jobs. that's a perfect recipe for producing highly technical bullshit
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the good shit comes from people who are *mystically compelled to understand the mind of god* and nobody learns how to do that in grad school
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there was one research agenda i was really compelled by in grad school and it was to rigorously establish mathematical foundations for quantum field theory. but honestly i was too intimidated to actually try doing this. it just seemed too hard so i gave up before i even started
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i remember when i studied abroad at cambridge coming across math people who told me “yeah i’m doing this to get a bank job in london later” and i was kind of appalled. not how i would’ve put it at the time but like… “you mean this isn’t sacred to you???”
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I disagree very strongly with this point of view - but I must immediately admit that unlike the majority of similar critics you actually a lot of "technical bullshit".
It's bewildering to me because following your blog& writing you always went beyond surface technical details...
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To get to the (imho beautiful) core conceptual ideas in the maths you were explaining.
In my own experience I have almost always found that I would dismiss some area of mathematics as technical bullshit only to understand years later its particular beauty and place in the grand
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dude I think you would really, really like The Fabric of Reality by Deutsch if you haven't read it yet
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like his two books have me so fired up about technical understanding and problem solving, and he talks about quantum really enjoyably and he has an awesome view of what mathematics and proof theory are about
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