system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How does one "invent new maths"? Like Isaac Newton inventing Calculus, or John Napier logs. How does one answer a mathematical question that's never been answered?
gpt
It's about seeing things in a different way (and studying math of course). You want to solve a problem, or even just see things in a different way... so you define new things and apply them (as long as they are consistent with known math) to see if something interesting pops out.

For example, Newton was trying to describe the speed of a falling object. Since gravity changes the speed of falling object, he *defined* the mathematical concept of "rate of change" (derivative) of a function. He also found out that you can *apply* this concept also if you want to compute the area under a curve.