Not only am I hoping you can answer my question, but perhaps refine my question itself. Unfortunately it is something I do not know how to ask, but I will give it my best attempt. Either I ask it, or it keeps pestering me.
A bit of history: I have little experience in mathematics, but want to harness this tool/language. I'm in early high school. Math seems different when I hear about it than when I'm doing it in my textbook.
My question is, how do people come up with formulas ? I understand when my teacher explains to me how something works, or asks me to test it with numbers e.g. draw a triangle and measure the sides, but how do people first come up with the formula? Do they do the same? Play around with numbers until they see a pattern and then write different ideas down and test them?
When math gets really complicated, how do people come up with it? Do they completely rely on algebra or do they just magically think formulas up (of course not but what is the alternative)?
I want to learn math, not just how to use a formula. If I start by learning my basic operations, and basic theorems, where do I go from there? How do I actually truly become acquainted with the way of thinking so that I can come up with formulas?
Thanks, I'm sorry if it seems naive. But I would appreciate if you tried to answer. I know there are seemingly many questions, but I asked them all in one post because the person who can answer the first set of questions, is the person who could answer the last set too. Please give me ideas for how to become better at mathematics. I know practice, which I have to start taking more seriously, but I feel like I am just practicing functions - orders of operations, algebra. I can't actually progress and do something myself. How do I get there?