Ethan Siegel in Forbes:
You've heard of our greatest scientific theories: the theory of evolution, the Big Bang theory, the theory of gravity. You've also heard of the concept of a proof, and the claims that certain pieces of evidence prove the validities of these theories. Fossils, genetic inheritance, and DNA prove the theory of evolution. The Hubble expansion of the Universe, the evolution of stars, galaxies, and heavy elements, and the existence of the cosmic microwave background prove the Big Bang theory. And falling objects, GPS clocks, planetary motion, and the deflection of starlight prove the theory of gravity.
Except that's a complete lie. While they provide very strong evidence for those theories, they aren't proof. In fact, when it comes to science, proving anything is an impossibility.
Reality is a complicated place. All we have to guide us, from an empirical point of view, are the quantities we can measure and observe. Even at that, those quantities are only as good as the tools and equipment we use to make those observations and measurements. Distances and sizes are only as good as the measuring sticks you have access to; brightness measurements are only as good as your ability to count and quantify photons; even time itself is only known as well as the clock you have to measure its passage. No matter how good our measurements and observations are, there's a limit to how good they are.