Mathematical definitions

When defining mathematical boundary cases, such as the question whether 1 or 2 are prime numbers, or what something ^0 should be, or /0, or the intersection or union of an empty family of sets, etc, one is confronted with the decision what such an operation should actually be taken to 'mean', even though one initially had the idea he/she already knew what the operation 'meant', and was just wondering to what answer these boundary questions would *compute.

At this point, then, one wonders what the entire point is again, to define one out of many possible operations. And it is, of course, a decision based on nothing so much mathematical, as it is on a desire or intended result. Which result is intended, one then asks? Why, it's describing impressions, and this has always been the case. Nothing new is under the sun: mathematics is and remains our best attempt at the simplest, most elegant, yet internally coherent, description of (the abstract nature of) reality.

And it is true, that when thinking of mathematics purely as this cognitively efficacious description of reality, that the problem of the relation between mind and reality is seen as more basic, elementary, or first, than the problem of the relation between distinct minds. Mathematics, then, is indeed firsly viewed in a Kantian / intuitionistic manner, or, hugely dependent on a mode of thought, beit personal or human or ...; and only secondly, as a description of the world *as it is, or, with the perspective that reality is shared perception, as a description of this shared perception, which is reality.

It is after this insight that one can remark that, as so far as mathematics had been succesfully applied to our shared world, and has the tendency to be able to be shared indefinitely, with other people, and future people, indeed mathematics 'gets at' inherent intersubjective structure. ... Can we learn anything from this?