My favorite part of algebraic geometry is that I heard one time (from one of my fellow grad students studying algebraic geometry so I assume it's true, but who really knows) that much of the fundamental basic theory isn't really in textbooks, or even papers for that matter, it's just algebraic geometers telling other algebraic geometers that some guy gave a talk 15 years ago in which he proved some theorem, so go ahead and use that theorem.
(I think there's a bit of this in just about every field. I, for example, once spent a few hours trying to find a statement of "Andreev's Theorem", and came up with like 4 different theorems, saying different things, all of them citing a paper by Andreev that doesn't seem to exist anymore before I finally just gave the fuck up and now I take on faith that circle packing a sphere works because of some result on fucking polytopes that people call Andreev's Theorem, except, of course, everyone gives contradictory statements. It's maddening.)
having studied algebraic geometry in and out of school, this explains some of the overwhelming confusion at where the textbooks leave off. there's kind of a massive gulf between what's in the textbooks and what anyone is writing papers about, which makes them incomprehensible.
This is honestly one of my main gripes with mathematicians. Maybe everyone else is actually a super genius who doesn't need anything spelled out for them, ever, and wants to put in hours trying to dig through incomprehensible papers with incompatible and confusing notation to try and figure out what the fuck is even happening, but I really doubt it. I think as a field a little more emphasis needs to be placed on making papers comprehensible and textbooks should be written more often and, more importantly, more clearly, with as many examples as possible.
Ah well, I'm just angry about this today. It's fine, I'm leaving the field anyway because there are no jobs and it turns out I actually hate research, actually.
When they say that it's called proof by intimidation lol
To be fair sometimes it is a little obvious or not necessary for education to really dive into the details (unless you're in senior courses about those details but then they handwave all the "simple stuff"). Sometimes it's better to start with the view from 10000 feet and then zoom in on the relevant stuff, then for the people who are into the details you can let them try to work it out - which will really help them learn too. I agree, modern papers and textbooks do have a readability problem even still.
So, there's a concept in physics called Cherenkov radiation, and that happens when some particle with charge is moving faster in a medium than light can. There was a Russian guy back in the day named Askaryan who came up with a clever argument that while this normally gives you blue light to detect, you can have situations that also emit significant amounts of radiation. I was trying to understand this for a class a few years ago so I read the original paper....
It was three pages long and didn't actually bother to lay out the math that proved their argument. Had to find a much later, much longer paper of people actually showing all the details.
Haha yeah, that's just classic, really. Chances are good that a similar thing would happen to me if I ever did manage to find Andreev's paper. Maddening.
Oh! I just remembered another fun one! I once ran across a theorem which according to the paper I found it in was proven in this other paper. So I go to the other paper, and they say "your proof is in another castle (paper)", so I find that one, and it's in german, shittily typed on a typewriter, with the most arcane notation I've ever seen. So what do I do? You guessed it! I just cite the first paper where I found the theorem, which isn't great, because now anyone who reads my dissertation gets to go down exactly the same rabbit hole! Neat!
I mean, yeah, but this kind of thing makes it much, much more difficult to actually learn anything new in math, which is quite annoying. Just write stuff down where people can read it, even if they don't know someone who knows someone who was at the original talk 15 years ago, god damn it!
Yeah, I think that is a thing in a lot of different fields, probably to different degrees. All the people in the field have already trudged through the fundamental examples themselves, so why write it down? The interesting stuff is the cutting edge, not that baby stuff.
Nah for real though, it's quite frustrating. Honestly the whole field (and academia at that rate) is, I don't blame you at all for bailing. I'm sunk-costing myself through at this point.
related
My favorite part of algebraic geometry is that I heard one time (from one of my fellow grad students studying algebraic geometry so I assume it's true, but who really knows) that much of the fundamental basic theory isn't really in textbooks, or even papers for that matter, it's just algebraic geometers telling other algebraic geometers that some guy gave a talk 15 years ago in which he proved some theorem, so go ahead and use that theorem.
(I think there's a bit of this in just about every field. I, for example, once spent a few hours trying to find a statement of "Andreev's Theorem", and came up with like 4 different theorems, saying different things, all of them citing a paper by Andreev that doesn't seem to exist anymore before I finally just gave the fuck up and now I take on faith that circle packing a sphere works because of some result on fucking polytopes that people call Andreev's Theorem, except, of course, everyone gives contradictory statements. It's maddening.)
having studied algebraic geometry in and out of school, this explains some of the overwhelming confusion at where the textbooks leave off. there's kind of a massive gulf between what's in the textbooks and what anyone is writing papers about, which makes them incomprehensible.
Might as well be carved on a mathematician's tombstone.
Also, if you like math history, read "The Man Who Loved Only Numbers", the biography of Paul Erdos. He was a cool dude.
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This is honestly one of my main gripes with mathematicians. Maybe everyone else is actually a super genius who doesn't need anything spelled out for them, ever, and wants to put in hours trying to dig through incomprehensible papers with incompatible and confusing notation to try and figure out what the fuck is even happening, but I really doubt it. I think as a field a little more emphasis needs to be placed on making papers comprehensible and textbooks should be written more often and, more importantly, more clearly, with as many examples as possible.
Ah well, I'm just angry about this today. It's fine, I'm leaving the field anyway because there are no jobs and it turns out I actually hate research, actually.
When they say that it's called proof by intimidation lol
To be fair sometimes it is a little obvious or not necessary for education to really dive into the details (unless you're in senior courses about those details but then they handwave all the "simple stuff"). Sometimes it's better to start with the view from 10000 feet and then zoom in on the relevant stuff, then for the people who are into the details you can let them try to work it out - which will really help them learn too. I agree, modern papers and textbooks do have a readability problem even still.
So, there's a concept in physics called Cherenkov radiation, and that happens when some particle with charge is moving faster in a medium than light can. There was a Russian guy back in the day named Askaryan who came up with a clever argument that while this normally gives you blue light to detect, you can have situations that also emit significant amounts of radiation. I was trying to understand this for a class a few years ago so I read the original paper....
It was three pages long and didn't actually bother to lay out the math that proved their argument. Had to find a much later, much longer paper of people actually showing all the details.
Haha yeah, that's just classic, really. Chances are good that a similar thing would happen to me if I ever did manage to find Andreev's paper. Maddening.
Oh! I just remembered another fun one! I once ran across a theorem which according to the paper I found it in was proven in this other paper. So I go to the other paper, and they say "your proof is in another castle (paper)", so I find that one, and it's in german, shittily typed on a typewriter, with the most arcane notation I've ever seen. So what do I do? You guessed it! I just cite the first paper where I found the theorem, which isn't great, because now anyone who reads my dissertation gets to go down exactly the same rabbit hole! Neat!
Why isn't "schollarly rewriter" a job:(
Reality is based on consensus? :thonk:
I mean, yeah, but this kind of thing makes it much, much more difficult to actually learn anything new in math, which is quite annoying. Just write stuff down where people can read it, even if they don't know someone who knows someone who was at the original talk 15 years ago, god damn it!
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Yeah, I think that is a thing in a lot of different fields, probably to different degrees. All the people in the field have already trudged through the fundamental examples themselves, so why write it down? The interesting stuff is the cutting edge, not that baby stuff.
Nah for real though, it's quite frustrating. Honestly the whole field (and academia at that rate) is, I don't blame you at all for bailing. I'm sunk-costing myself through at this point.
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