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CC-Mathematics deals with PROOFS while Science deals in Probabilities.

Nope, both are based on axioms and both prove things on the provision that those axioms are true.

Science is intrinsically provisional, so the word “scientific” in the term “scientific proof” is a qualifier, which means that a proposition has been proved on the provision that the underlying scientific assertions are true.

Mathematics is an expanded form of logic, and is founded on some basic axioms that are not themselves proved, only asserted to be true and agreed upon by convention to be true for the purpose of building a system of logic upon them.  A mathematical proof is no more of an absolute proof than a scientific proof, because like science, mathematics rests upon and is derived from axioms, which are not themselves proved.

If the foundation is unproved then the conclusions are unproved outside of that closed system of reasoning, that is, not absolutely proved.

Science does scientific proofs, which obligates a rational person to reject the underlying science if one wishes to reject the scientific proof.  For example, it has been scientifically proved that the Earth is approximately spherical, and most closely approximates a spheroid, as opposed to a cube or a disc, or a 2 dimensional plane.  Some folks still deny this, but such people are then obligated to reject the truth of the science that led to this scientifically proven fact, which they are free to do, but at that point I no longer share a common language of meaningful communication with such people.  Theists are like that, but typically in more subtle ways compared to flat Earth kooks.