I love the puzzle of it. It's really fun developing your own solutions and methods (even if they were already discovered hundreds of years ago)There's all kinds of puzzles, and weird patterns. And you have to solve the puzzle of why those patterns exist.
Plus, you can build stuff!
Nope. Why try and prove something which everyone knows is true already, and has been proven by other people before in the same/ different ways. Its a complete waste of time. Its only useful if its proving/ discovering something new, but I doubt that's ever going to happen again with pure maths, for anything really significant anyway.
For realsies, there's a lot of big new math discoveries! Fermat's last theorem was only discovered in 1994. The poincare' conjecture was also proven in 2006.
There are lots of big math problems like Riemann's hypothesis, P vs NP, etc; that still need solving.
Math is all about puzzles. Some of those puzzles have huge implications for things like physics, computer science. Some of them are just interesting in their own right.
Some of them are interesting in their own right, then 50 years later we find out they have applications in other fields.
Making connections is fun, regardless of who did it before you.