You can’t prove anything.
You can’t prove the world is real. You might be dreaming or hallucinating or in The Matrix.
If the world is real, you can’t prove that your senses are telling you the truth about it. Or that your mind is.
You can’t prove that I am conscious. On the outside it looks like it, but on the inside I might be just a void.
You can’t prove that what’s worked for you in the past will keep working for you tomorrow.
You can’t prove that the past ever happened. (Try going there to check.) You can’t prove that your memories are accurate.
You can’t prove that the people of the future won’t look at us as monsters because of what we do. Or as gods.
You can’t prove that the author of this blog intended it to mean what you think it means.
You can’t prove you won’t be hit by a bus tomorrow.
You can’t prove your wife truly loves you.
You can’t prove that everyone isn’t laughing at you behind your back. You can’t prove they’re not out to get you. You can’t prove they won’t be waiting for you when you get home.
You can’t prove your wife isn’t one of them.
You can’t prove that there isn’t a massive government conspiracy that has concocted all the conspiracy theories so as to make anyone who uncovers their conspiracy look silly, and that’s why conspiracy theories are so ridiculous.
You can’t prove that God exists. You can’t prove that the Scientologists didn’t get it right. Or the atheists. Or the good folks at ISIS.
You can’t prove that any of the following are real in any sense: free will, meaning (as in purpose), meanings (of words), your mind, morality, mathematics.
You can’t prove that your modern Western mindset isn’t acting as a sort of ideas cage, preventing you from seeing the truth.
You can’t prove that human logic works. You can’t prove that this sentence makes sense. You can’t prove that “this sentence” makes sense.
You can’t prove that your mind would have passed quality control at a mind factory.
You can’t prove that the world makes any type of sense at the most basic level.
You can’t prove that science tells you the truth about the world. (It assumes much of the above.)
You can’t prove that any scientific theory you can think of won’t fail a replication study tomorrow, or be contradicted by new evidence.
You can’t prove that science tells us about all of reality. (“Science tells us about all of reality” is not a scientific hypothesis.)
You can’t prove that if super intelligent aliens landed tomorrow, they wouldn’t dismiss our science and mathematics as being limited or wrong or missing the point somehow. (“Your pathetic human languages do not allow me to express the depth of my contempt for your stupid ideas”, says Zxxcxcc from the planet Kvzzxrrk. )
This is why some people go insane.
 I was granted an audience with Zxxcxcc the other evening. “You humans are so ridiculous” he said, his eye pulsating as he twirled his antennae with his left trunk. “You vote for people you know are idiots, but you still think you have the intelligence to unravel the deepest mysteries of the cosmos.”