The feature distinguishing science from other means of doing so is its characteristic method. Crudely, this consists of asking a question, formulating a hypothesis, testing it, and then, on the basis of the results, rejecting or provisionally accepting the hypothesis. One usually repeats the process after refining the question, the hypothesis, or one's ability to test it. In mathematics, however, the ultimate arbiter of correctness is proof rather than empirical evidence. For a mathematical statement to be accepted as a theorem, its conclusion must be known to always be true whenever its hypotheses are satisfied.
Empirical evidence does, to be sure, play an important part in doing mathematics.
Conjectures are usually formed by observing a common pattern in a number of examples, and are often tested on other examples before a proof is attempted. However, we cannot be sure it is true unless someone finds a proof. Until then, it is conceivable that someone might find a very big even number which is not the sum of two odd prime numbers. By an easy argument which is left to the reader, it follows that all odd numbers greater than one are prime. The mathematician is wrong by the standards of her field because a valid proof of the assertion that all odd numbers are prime has not been given.