Artificial intelligence and undecidibility
No.  The Post correspondence problem is undecidable.  That means that no computer program can solve it (in all cases).  "Artificial intelligence" is just a computer program. Actually, "artificial intelligence" is a name for something that we're not even sure how to do with a computer program; but even if we knew how to achieve it, it would still be a computer program.  Artificial intelligence isn't magic -- anything that can be done is still constrained by the laws of physics and mathematics.