[Jensson]

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.

[abraxas]

There has to be a happy medium between the tersness of the current notation systems and the verbosity of code-like expressions. We just need to rethink this so more people can learn it. Math still stands a bit like writing did in ancient culture. It's a domain reserved for a few high priests inducted into the craft and completely inaccessible to everyone else.

[gjulianm]

I wonder why so many people are under the impression that the notation is what is keeping them away and if only the notation was easier then the underlying concepts would be clear. For example, if you don't know what the pullback of a differential form is, it doesn't matter if I write it in clear text or if I write the common notation φ^* ω.

> 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.

[zwnow]

φ^* ω is just 2 weird symbols. There are tons of symbols to learn. I gave up trying to learn the Russian alphabet after a few days so why do u think I am capable of memorizing the Greek one?

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.

[gjulianm]

> why do u think I am capable of memorizing the Greek one

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.

[nyrikki]

The problem is that math is not some universal language, it is a broad field with various sub domains with their own conventions, assumptions, and needs.

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.

[zwnow]

Yea because hieroglyphs are more understandable than the name of a function

[Jensson]

That is exactly it, a long text is much harder to understand than a one liner, we see that time and time again in problem solving if you write the same problem as a long text many fewer students manage to solve it than if you write it as a one liner.

[SetTheorist]

There is an inherent complexity in a lot of mathematics. The compact notation makes it much easier (or even possible) to understand what is going on.

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.