Nothing In Science Ever Proved

I often say nothing in science is ever proved, theories just survive long series of tests and observations in an attempt to disprove them. Most people, even most scientists, tend to not agree with me. At least at first. Eventually they realize I'm right but only up to a point; they claim I'm being too stringent on my definition of 'proof'. Well, I started reading Brian Greene's Elegant Universe and right there, smack on page one (ok, really page number three, but its the first page of the first chapter nonetheless) is perhaps the best example of unproved science I can think of (no link, I'm typing from the book, here):

The problem is this: There are two foundational pillars upon which modern physics rests. One is Albert Einstein's general relativity, which provides a theoretical framework for understanding the universe on the largest of scales: stars, galaxies, clusters of galaxies, and beyond to the immense expanse of the universe itself. The other is quantum mechanics, which provides a theoretical framework for understanding the universe on the smallest of scales: molecules, atoms, and all the way down to the subatomic particles like electrons and quarks. Through years of reasearch, physicists have experimentally confirmed to almost unimaginable accuracy virtually all predictions made by each of these theories. But these same theoretical tools inexorably lead to another disturbing conclusion: As they are currently formulated, general relativity and quantum mechanics cannot both be right. The two theories underlying the tremendous progress of physics during the last hundred years -- progress that has explained the expansion of the heavens and the fundamental structure of matter -- are mutually incompatible.

Proofs are the domain of math and logic, not science. Proofs require assumptions, definitions and postulates; one can think of science as that list of assumptions, definitions and postulates. Of course, sometimes science boils down to math, so some scientific papers are proofs. For example, scientists recently "proved a mathematical theorem that shows the pointer states do actually coincide with the states probed by indirect measurements of a system's environment," and thus, quantum mechanics actually is capable of producing an objective reality.