I came across a nice saying from a book named Linear Algebra: Ideas and Applications (3rd Edition) by Richard C. Penney, pg 13.
There is a fundamental difference between mathematics and science.

Science is founded on experimentation.
If certain principles (such as Newton’s laws of motion) seem to be valid every time experiments are done to verify them, they are accepted as ‘law’.
However, they will still remain a law only as long as they agree with experimental evidence.
Thus, Newton’s laws were eventually replaced by the theory of relativity when they were found to conflict with the experiments of Michelson and Morley.

Mathematics, on the other hand, is based on proof.
No matter how many times some mathematical principle is observed to hold, we will not accept it as a theorem until we can produce a logical argument that shows the principle can never be violated.”


That’s why I like mathematician.