mathematical charters of dimensions?

*This is not just a question for those interested in applying mathematics to the physics of cause and effect, and not necessarily a question for mathematicians who are in search of the topological perfection of numbers itself, numbers when applied to one another (and indeed is that another debate).*

For instance could it be possible, while riding time's arrow in the here and now, to formulate a basis for how we measure reality with space and time using numbers for the measurements of space and time? Of course it is. That is what we do with mathematics, that is how we apply mathematics. But is this a charter itself of mathematics, of mathematical perfection?

Strictly speaking, is it a question for mathematicans to devise equations relevant to reality, or a need of physics to explain their reality with mathematics? It's a need of physics (?). But, although mathematics depends on "numbers" primarily to be "mathematics", as we know, fundamentally speaking though "mathematics" is a school of thought that aims to measure "what"? To measure itself as numbers? Pythagoras was shot down in measuring real numbers alone when irrational numbers became effective. But that process, as a process of mathematics, in realising irrational numbers, employed the need to use linear dimensions of space dividing within itself to accomodate for irrational numbers. It was a quantum leap of mathematics at the time, the recognition that numbers themselves can be "irrational"; the solution being the acceptance of infentismal subdivisions of space using irrational numbers.

The question I am asking thus is relevant to how innovative mathematicians can be in investigating the idea of "dimensions", space and time, while using numbers. Basically, is mathematics based on the idea of using numbers to link the idea itself of dimensions, of linking space and time with numbers? Or is mathematics merely..........

........."basic" curiosity with numbers?

.....to count coins.......? alone?