Excellent response, and my only, not very important, objection is to the above.
There are many, "proofs," in both science and technology (think computer science) as well. Many proofs are actually applications of the abstract, "sciences," to the real world. In topology, for example, how various real physical configurations can or cannot behave can be proved (consider the Mobius band), not by observation, but by the application of topological principles.
Chemistry involves myraid proofs of both composition and behavior. (The double helix of DNA is not a hypothesis but a proven theory.) (The entire periodic table is a huge proof of many different hypotheses.) The laser is "proof" of certain quantum mechanics principles applied to nature of light.
Hank
I consider topology a branch of math, not science. I agree that mathematical truths are more secure than scientific ones.
Chemistry involves myraid proofs of both composition and behavior. (The double helix of DNA is not a hypothesis but a proven theory.)
I disagree. The double helix is a model of how genetics works, and it is consistent with all known observations on the subject. It is consistent with x-ray diffraction and why intercalating agents are so-called "frameshift mutagens" - they insert themselves inside the base pairs and cause a reading error by the tRNA. But, you can't directly see the double helix, and you can't prove it isn't all one big illusion foisted upon us by invisible creatures, determined to influence the outcome of our experiments so as to shape the way in which we believe the natural world works. As of now, there is no evidence that such creatures exist - but some experiment may be done in the future that shows the double helix is just an illusion. Consider how well Newtonian physics explained planetary motion - it predicted the position of unseen planets, for example. But, in light of relativity and QM, it's simply wrong.
(The entire periodic table is a huge proof of many different hypotheses.)
The periodic table doesn't "prove" anything - it's just an organized way of presenting what we believe are chemical elements.
The laser is "proof" of certain quantum mechanics principles applied to nature of light.
It is as much proof of QM as the discovery of Uranus and Neptune "proved" Newtonian laws of planetary motion.
Regarding science, it is widly believed that theories are never really "proven." They survive experimental testing, which are occasions for potential disproof, but in principle, any scientific theory is subject to disproof if some new test, or some new evidence comes along which is inconsistent with the theory. Our most successful theories certainly accumulate a lot of supporting evidence, but technically this isn't "proof," just confirmation that the theory is still viable as far as we have been thus far been able to determine. Any new evidence which throws a theory into doubt must in due course be incorporated into a revised theory that is itself consistent with all prior evidence.