Is abstract math only meaningful because of the concrete objects it captures?

Hello,

Whenever I ask about the intuition of some abstract math idea, People usually answer me by looking at concrete examples, and how the abstraction captures them.

I thought abstract math ideas do have an intrinsic conceptual value in their own rights, independently of any concrete cases.

I started to feel abstract ideas are only valuable because they can capture more concrete objects, leading to establishing relationships between different areas of Math.

What do you think?