Nice gatekeeping, friend. I've also personally never heard my math graduate student friends talk like this.
I think that the system has failed the author, and deprived them of fun.
If I met them, I'd tell them the same thing I'd tell you: come back to math! There's fun and beauty in it, and suffering is not a necessary component of that.
As far as your math grad friends go: the school, most likely, is failing them. Statistically, about half of them are depressed. Most have no job prospects that will allow them to keep doing what they are trained to do (simple matter of #students >> #positions). Ask them how often they considered suicide (not if), the answers may surprise you. Graduate school does make mathematics (amd life) a funless process way too often - and that's a problem. But that's not how things should and can be.
Please read Lockhart's Lament I linked to in order to understand my point better.
What I ultimately am saying is that what is being pushed onto people as math is way to often isn't really, in a way that a cheese product isn't cheese.
He is wrong in that painters and musicians tend to get rigorous instruction in the basics before they become independently creative. Picasso's realism phase. Musical theory etc.
They still get to do it: they get to paint, play, sing, etc. Most math students don't get to do math. They learn about it until a year or two into grad school sometimes.
>maths is one of the few arts that is actually taught in school.
His point is that what is taught is mathematics as much as the names of notes is music.
Poetry.
it was correct by construction
stretchy compactness
continuity
we wrote numbers in the sand
watched the glass dance of entropy
against tired eyes
until our vision blurred
remaining only feeling
legs crossed in a field
blade of grass
simplification is hard work
it's clear there is no enemy
but misunderstanding it's clear there is no enemy
but misunderstanding
That's kinda like returning home after a long day, because algebraically closed fields are about the nicest structure you can hope to find yourself working in!
Personally I'd posit finitely generated abelian groups as the nicest structures. Perhaps there is also something to be said for finite algebraically closed fields.
That you can't communicate a particular piece of math suggests that it has no tangible relation to physical phenomena. To me, that's a major red flag.
A lot of mathematics is that way, and there's nothing wrong with that.
Sometimes mathematical concepts do find tangible physical phenomena that demonstrate them - but sometimes, centuries after they've been invented.
Mathematics is often about what one can imagine. Our imagination can be inspired by the world around us, but it is not limited by it.
It's not a red flag that some concepts don't have short explanations. Sometimes you really just have to know the full joke to get the punchline.