Re: "what it is that makes us human when computers and machines can educate themselves"
There was a computer program that "discovered" prime numbers all by itself.
It was not really AI. It was a goal-seeking algorithm that could apply the rules of symbolic algrebra. It had the axioms of arithmetic hard-coded, and its goal was to prove hypotheses with high values of interestingness, where interestingness was a heuristic based on the relation of a hypothesis to other hypotheses and theorems and their interestingnesses (ie, if we can prove this, then we get that and that and that ... )
ISTR it got as far as inventing and trying to prove Goldbach's conjecture (every even number greater than two can be expressed as the sum of two prime numbers). It failed to prove it, which is not very surprising ... the best human mathematicians of the last 250 years or so haven't been able to prove it either!
There's also the proof of the four-colour theorem which is too complex for any human unassisted by a computer to comprehend. So it it proved, and if so what is it proved by?