-_- what do you intend to accomplish by cutting out most of my post that explains the difference between the common use of the term "proof" and what proof is from an academic perspective?
There are other possibilities for how your hand got burned, or how you ended up mistaking it for burned. As long as there are other possibilities, no matter how unlikely they are, you haven't "proven" that it was the stove that burned your hand. Again, this is why asking for "proof" is asking for a standard impossible for science to meet, no matter how good the evidence is. To obtain proof is to not only support a particular conclusion, but it is also to exclude all other possibilities... including ones you aren't personally aware of.
It isn't that we don't have to "prove" evolution. It is that "proof" isn't what you are acting as if it is. You can't even prove to me that you exist, and I am talking to you right now. Additionally, you may have confusion as to what the difference between the theory of evolution and the phenomenon it attempts to explain. Evolution the theory isn't literally that populations of organisms change over time and generations. Evolution the theory is an explanation of HOW and WHY populations of organisms change over time and generations.
As for the process itself, there are plenty of opportunities to observe it if you want. Just Google search "evolution experiment".
Actually, you have it backwards. Science doesn't determine what a "fact" is, facts determine the course of science. Facts are gleaned through observation. For example, we can factually determine that your hand was damaged by it not being in a healthy state. The scientific theory relevant to you burning your hand would be the most evidenced explanation as to how and why it happened, but no scientific theory could guarantee that it is a fully correct explanation. Could get 99.99% certain, but never 100% certain. After all, someone could have cast an evil spell to burn your hand, because magic hasn't been disproven. A ridiculous conclusion? Sure, given the lack of evidence supporting it, but as it hasn't been disproven, it is a possibility nevertheless and has to be recognized. Proof narrows down possibilities to just 1, which is why it only applies to math.
As for the common use of the term "proof", I have no idea what your personal standard of evidence is, so trying to cater to it would be silly. But, I'll provide some evidence for evolution any time you like, as long as that's actually what you are requesting. If you insist on "proof", I'll take it as an unwillingness to learn.
You must have missed it, because it is brought up from time to time, and I am not the only person that brings it up.