Those are used since it makes things easier, if you write everything out basically nobody would manage to learn math, that is how it used to be and then everything got shortened and suddenly average people could learn calculus.
> It's a domain reserved for a few high priests inducted into the craft and completely inaccessible to everyone else.
It's a domain reserved for people who want to learn it, and there's ton of resources to learn it. Expecting to understand it without learning it does not make any sense.
The theories are learnable, making sense of all the weird symbols is what's breaking my brain. I tried to get into set theory thrice now, not happening with all the math lingo, hieroglyphs and dry ass content. Learning can be incredibly fun if it was designed fun. Math is a dry and slow process. Make it fun, make it readable and people will be capable to learn it easier.
No one memorizes the Greek alphabet. We just learn it as we go because it’s useful to have different types of letters to refer to different types of objects. That’s it.
> I tried to get into set theory thrice now, not happening with all the math lingo, hieroglyphs and dry ass content.
That sounds like you’re trying to learn a specific field without actually having any of the prerequisites to learn it. I don’t know what you’re specifically referring to when you say “set theory” as that’s an incredibly wide field, and depending on what you’re trying to learn it can be quite technical.
> Learning can be incredibly fun if it was designed fun. Math is a dry and slow process.
This sounds like someone complaining that getting to run a marathon is tiresome and hard. Yes, teaching mathematics can always be improved and nothing is perfect, but it will still be hard work.
Polysemy vs Homonymy vs Context Dependency will always be a problem.
There are lots of areas to improve, but one of the reasons learning math is hard is that in the elementary forms we pretend that there is a singular ubiquitous language, only to change it later.
That is why books that try to be rigorous tend to dedicate so much room at the start to definitions.
Abstract algebra is what finally help it click for me, but it is rare for people to be exposed to it.
Compare something like
equals(integral(divide(exponentiate(negate(divide(square(var),2))),sqrt(multiply(2,constant_pi))),var,negate(infinity),infinity),1)
vs
$$\int_{-\infty}^{\infty}\frac{e^{-x^2/2}}{\sqrt{2\pi}}dx = 1$$
(imagine the actual generated mathematical formula here :-/ )
it is infinitely easier to grok what is going on using symbolic notation after a minimal amount of learning.