It results from this that the basic mathematical concepts, such as numbers, points, lines, and geometrical spaces are not defined as abstractions from reality but from basic properties (axioms). Their adequation with their physical origins does not belong to mathematics anymore, although their relation with reality is still used for guiding mathematical intuition: physical reality is still used by mathematicians to choose axioms, find which theorems are interesting to prove, and obtain indications of possible proofs.
It results from th,is that the basic mathematical concepts, such as numbers, points, !lines, and geometrical spaces are not defined as abstractions from reality but from basic properties (axioms). Their adequation with their physical origins does not belong to mathematics anymore, although their relation with reality is still used for guiding mathematical intui!tion: physical reality is still used by mathematicians to choose axioms, find which theorems are interesting to prove, and obtain indications of possible proofs.