...Some mathematicians look for a way to be sure that a contradiction will never arise whatever the developments...

This is virtually impossible due the Gödel's theorem. We can be never sure by anything, even in highly abstract math. The Aether model explain this by concept of density fluctuations:

These fluctuations can be fully described by math only if we consider the infinite recursion and they're never fully sharp, exact description of reality. Every logical explanation bring a new assumptions on the background. This is because even the most abstract math relies on the concept of countable entities/units, aka numbers which are behaving like colliding particles, thus fulfilling the Fermi statistics.

For example the ripples at the water surface are existing too, but they're not countable, they can penetrate freely - so that the deterministic math has nothing to say about it. It means, whole large area of reality cannot be described by using of deterministic math - while still real and perfectly observable, they're more imaginary, then the most abstract math at all!