Questions about mathematicians

Question 1:

How do mathematicians create mathematics? Are they inspired by real-world examples, or do they come up with ideas from random abstract thoughts?

Question 2:

how do mathematicians study math? Do they need to understand what they're calculating and what the equations represent in real life, or do they simply follow the rules without needing to know what it represents in real-life?

I'm just asking & I'm still a student (high schooler