>>12621866In the past? I'd say to a large extent discovered, since it feels like there was some fundamental link between nature and the discoveries that people were making in calculus, geometry, and even to some extent algebra.
Two most popular views were either natural numbers (Peano) or geometry (Euclid), were the foundations. Both of these somehow feel intrinsic to nature.
Today? Almost 100% invented. If you base mathematics on an axiomatic, formalist system where you choose the axioms, and those axioms include the axiom of infinity or arbitrary choice functions, and almost nothing can be explicitly tied down to computations, you are essentially divorcing yourself from reality and just playing a logic game. Therefore, you have invented something and are just looking to see what logical conclusions you can derive.
