[bluetomcat]

> but I think that there are many mathematicians who would not describe your characterisation as the core of what they do professionally.

Those mathematicians are certainly doing something much more intellectually-challenging than counting things and measuring space, but I would argue that those basic activities represent the basic problems upon which most of the low-level math abstractions are built. "Serious" math is about operating at much higher abstraction levels, but it is not disconnected from those low-level foundations.