Some of their language is unfortunate but they pulled through with the sharing part. It is quite hard to share maths with others however. How can I share that feeling inside my brain algebraically closed fields give me?
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.
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