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First, let me highlight what I agree with:
>But I hate how math and physics are taught, it should always be taught from a spirit of exploration as if you are discovering new islands or continents and you get to name the things you discover.
Absolutely.
>Who are you to say that I have to use that particular symbol or term to describe this math? [..] they are just arbitrary drawings that people invented to name stuff that they found in nature.
Indeed, the notation is just a choice - and a tool.
>It's a cycle of lies.
It's an open secret :)
>Every math class should start with something like "This is the symbol for addition: '+'. This was invented by some person, you could use something else,
Absolutely. Old texts didn't have the "=" sign, people would write "eq." or something like that -- "=" is a relatively modern invention.
And in math papers notation is often invented on the spot. That's why papers often start with defining all the symbols - otherwise, there's might not be a way to know what "a * b" means. It can mean whatever the author felt like that day. Maybe it's quandle product! Maybe multiplication. Who knows.
>you could try to find some other way to add numbers but the way we teach you to think has proven to be fairly fast and convenient so we teach it."
Absolutely. I would like to add: "..and here are five other ways you could do the same thing - can you find a sixth?".
>There were cultures that did math with a completely different set of symbols, not just symbols but even way of thinking.
That's why we teach different notation: it encourages a different way to think. For example, in Calculus, we have Leibniz's "d/dx" and Newton's dot notation for the same notion of derivative.
> Math should be seen like a weird natural phenomenon that we observe, from the getgo
That's one perspective that many mathematicians do have. We do teach it -- in philosophy; it's the Platonic Universe. "Is mathematics invented, or discovered?" is a never-ending debate.
>Fields of math stack on top of each other because they happen to work together but in reality we don't know why. They just do and it's interesting that they do so we keep doing it that way because it works and hasn't broken yet and it's useful.
More of the same - yes, that's the view that is quite common.
>Yet our current way of doing math is taught to us as dogmatic, accept it or you are a troublemaker. No wonder people dont like math, nobody wants to be a slave to somebody else's ideas and value system. That in my opinion is how you make people interested in math because you treat them as equals instead of subjects to be trained in your favorite cultural way of doing math.. From childhood on. Explain it like that and I believe kids (and adults) will love to discover more about it.
Yes, sadly, that's the problem with the way mathematics is often taught -- by people who either don't know better or are forced to teach it that way because they are a part of a system.
That's not how math professors are teaching it to their kids, I guarantee you that.
You would greatly enjoy reading Mathematician's Lament[1], which shares your sentiment.
------------------------------ Now, my main point:
> Try getting a math professor to admit that he doesn't actually have an intuitive understanding for any of the stuff he teaches. I believe the vast majority probably don't have any such understanding but they are understandably scared to admit it.
First, no need to be aggressive.
Secondly, that's quite an accusation!
I am not going to refute it other than by saying that it's plainly false -- at least by the time you get to college.
At a high school level and earlier.... The problem is that one often doesn't get to do mathematics unless they are in a research program for math. That is too sad, but we end up with people who teach math and never got to do it -- because doing it is just doing what you are writing about: playing, exploring, being surprised by the fuckery of the universe.
What is true even for universities, though, is that the administration sets requirements on the curriculum and how it should be taught - and there's, sadly, little place in it for the intuition, vision, play, experimentation - which are the only things that should be taught.
Many people are fighting to change this.
Finally:
>Disclaimer, I'm really bad at math.
You are not. You have the right perspective. Armed with it, you are equipped to learn it far better than many others. Let us (the professors, teachers, random people who know some math that you don't yet know, etc.) help you.
Ask any professor about any math concept in this way: "What's a way to look at it? How should I really see it?" - and their answer will go into everything you are talking about.
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[1]https://www.maa.org/external_archive/devlin/LockhartsLament....