Proofs exist only in mathematics and logic, not in science. Mathematics and logic are both closed, self-contained systems of propositions, whereas science is empirical and deals with nature as it exists. The primary criterion and standard of evaluation of scientific theory is evidence, not proof. All else equal (such as internal logical consistency and parsimony), scientists prefer theories for which there is more and better evidence to theories for which there is less and worse evidence. Proofs are not the currency of science.
Proofs have two features that do not exist in science: They are final, and they are binary. Once a theorem is proven, it will forever be true and there will be nothing in the future that will threaten its status as a proven theorem (unless a flaw is discovered in the proof). Apart from a discovery of an error, a proven theorem will forever and always be a proven theorem.
In contrast, all scientific knowledge is tentative and provisional, and nothing is final. There is no such thing as final proven knowledge in science. The currently accepted theory of a phenomenon is simply the best explanation for it among all available alternatives. Its status as the accepted theory is contingent on what other theories are available and might suddenly change tomorrow if there appears a better theory or new evidence that might challenge the accepted theory. No knowledge or theory (which embodies scientific knowledge) is final. That, by the way, is why science is so much fun.
Further, proofs, like pregnancy, are binary; a mathematical proposition is either proven (in which case it becomes a theorem) or not (in which case it remains a conjecture until it is proven). There is nothing in between. A theorem cannot be kind of proven or almost proven. These are the same as unproven.
In contrast, there is no such binary evaluation of scientific theories. Scientific theories are neither absolutely false nor absolutely true. They are always somewhere in between. Some theories are better, more credible, and more accepted than others. There is always more, more credible, and better evidence for some theories than others. It is a matter of more or less, not either/or. For example, experimental evidence is better and more credible than correlational evidence, but even the former cannot prove a theory; it only provides very strong evidence for the theory and against its alternatives.
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