The difference between Science and Proof

There seems to be a difference between mathematicians and biologists and as Pharyngula writes:

"Scientists don't talk about "proof", period."

A mathematician is a person whose area of study and research is mathematics and there are differences:

Mathematicians differ from physical scientists such as physicists or engineers in that they do not typically perform experiments to confirm or deny their conclusions; and whereas every scientific theory is always assumed to be an approximation of truth, mathematical statements are an attempt at capturing truth.
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Unlike physical theories, which may be expected to change whenever new information about our physical world is discovered, mathematical theories are "static" - once a statement achieves the lauded position of a theorem, it remains true forever.
(Source: Wikipedia)

Over at the Talk Origins Archive I found a good explanation of what is meant by scientific evidence and scientific proof:

In truth, science can never establish "truth" or "fact" in the sense that a scientific statement can be made that is formally beyond question. All scientific statements and concepts are open to re-evaluation as new data is acquired and novel technologies emerge. "Proof", then, is solely the realm of logic and mathematics.

Everyone uses the word proof from time to time and in most cases everyone knows exactly what they mean and what proof means. "Evidence" and "proof" have become almost synonymous to most people.

But in the sense of Science those two words can't be associated too close.

The strict sense of the word "proof" is that it implies certainty and completion. When we say something has been "proved" we often mean just that evidence has been produced which is sufficient or adequate to support it.

But the Scientific method does not offer proof - it offers understandings of observations and reasons to not rationally doubt those understandings. The scientific inquiry is never completed. If we claim proof of a scientific inquiry - the theory is only as strong as the opposite theory allows.

If you are serious about the The scientific Case you will not use "proof" when you mean "evidence," especially when talking about matters of science. So if "proof" means "evidence" in other contexts, (by example in law the word "proof" is often used as a synonym for "evidence.") it's not legitimately interchangeable in science, and if people write about science they should use the right words.

Scientific Evidence may support a conclusion, but not strongly enough to establish proof.

And proofs are only for mathematicians.