What is math?

Why does it exist, who invented it, and how do you know it’s correct?

Of course I’ve done math all my life in school but I never understood what it was for. I just had all these teachers telling me that it was important to learn all these crazy symbols but they never explained the big picture of why we were doing it.

I can understand why ancient people would invent a basic system for measuring things so that they could build houses or draw a map or count/add things…but the more complicated math, like huge formulas, I don’t get.

When you watch a movie like A Beautiful Mind or Good Will Hunting and Will is able to come up with some genius mathematical formula that no one else in the world has been able to answer, how does his teacher know that the answer is correct if the teacher couldn’t answer it himself? and what are they solving? are they solving something related to the real world that is actually useful to humans?