A proof in mathematics is not like a proof in a court of law, where a high degree of probability is sufficient. In most scientific studies, it is enough to establish a plausible causal connection if the odds are sufficiently great against that connection occurring by chance, say 100 to 1 against. Mathematicians, on the other hand, have to be absolutely certain that there will never be a counter-example.
Proofs in mathematics make extensive use of deductive reasoning.
External link: A Collection of Beautiful Proofs