Yea, math is a crazy thing. just "a tool to solve problems" is a wild take. On one extreme, there's an edgy but logical / plausible hypothesis that we live in a universe of mathematical objects, and at the other, math also discovers a lot of questions, the exact opposite of solving problems.
You're right, but what I'm saying is that solving the problem isn't necessarily the primary goal and these new abstractions can be valuable in their own right.