Calculus is just beautiful.
It is so simple.
It amazes me that I didn't think of it myself one day, because after it is shown to you it appears to be so obvious.
There must be other things about math that are so obvious that we do not currently see?
There must be dozens of directions of thought that are just there, like low hanging fruit waiting for someone to turn things upside down.
I've wondered for a long time: WHAT IS MATHEMATICS? I have also wondered if I could unlock the secrets to the universe if only I could understand math. I gave up on understanding the universe, but I think i found out what math is....
Math is just a way to express logical thought.
So, you create a game by making up rules and regulations. You say that in your game you are going to have a circle and that the circle is going to be placed on an x and y graph and that the radius of the circle is going to be 1. Then you play. You turn things upside down, sideways, and you shake it all about looking for more stuff. Hey - look if you stick a triangle on this circle, a right triangle, then you can say that the point is represented by x,y and x = cos theta and y = sin theta and then you make more rules and you make up objects ad definitions like radians and angles.
Then you change the game, you say ok - now we're on an x,y graph but we have different objects. These objects are vectors and in order to add them you must do this - and to multiply them you must do this.
So, you create objects and rules and playing fields and definitions and then you just look for things. You play the game and you make logical arguments and deductions and proofs and you look to see how one playing field and game compares to another. You just keep doing this and after thousands of years you have a lot of games and rules!
Oh - and of course you look for how these games can be used in real life. Like how trig can help you measure distances or how vectors can model how airplanes move in the sky.
That is what mathematics is....