One thing that grates on me is when people say science "proves" X. Or and A/B test "proves" Y. Science never proves anything, it provides evidence for the existence of some phenomenon or relationship. People need to repeat this to themselves whenever they are tempted to say the word "prove": Some arbitrarily complex hypothesis can also explain all of my evidence. Said in plain language, there is always another possibility.
You're being prescriptive that we always treat "prove" as if it has the meaning as we use it in math and logic. That's not how language works. Words have different meanings in different contexts.
Top definition of "prove" according to Google: "demonstrate the truth or existence of (something) by evidence or argument." According to that definition, it seems completely reasonable to me to say that science can prove things.
I think colloquially, lay people may not know the ontological origins of the word but when they use the word "proof" they mean it as some indisputable fact. At least most people I know use it in that manner.
Evidence? The dictionary disagrees with you. Dictionaries are compiled from the ways that people actually use language in the real world. Also, the etymology of "prove" has nothing to do with indisputable facts:
Middle English: from Old French prover, from Latin probare ‘test, approve, demonstrate’, from probus ‘good’.
Edit: I feel I was being a bit forceful with my replies here. You airing your pet peeve triggered my pet peeve with linguistic prescriptivism. Sorry about that.
