> A process of invention as far as deciding which axioms to assume (...) Possibly, but I think what mathematicians find is that they end up having little choic

> A process of invention as far as deciding which axioms to assume (...) Possibly, but I think what mathematicians find is that they end up having little choice about what sets of axioms (when taken together) are useful, fertile, and/or interesting and which aren't - when studying various mathematical systems. Which leads us to consider that trip down to what those essential various groupings of axioms to once again feel more like discovery than invention. Further, abstract math tries to shave concepts down to only what is logically essential. Arriving at what's left at that point is more akin to discovering a rare diamond or gold nugget buried deep beneath the surface, and inherent to the basic "construction" of the universe (philosophically, that which might exist beyond/before/after/without us).