PhD in math here...I disagree that it is just a tool. I don't really give two cents about the usefulness of math. I only studied it as an art because I apprecia

PhD in math here...I disagree that it is just a tool. I don't really give two cents about the usefulness of math. I only studied it as an art because I appreciate its artistic beauty. For me, math is only interesting as an art, and practical problems aren't any motivation for me in that regard.