Purely intuitively, it seems like there should be a connection between the two (computation and intelligence). But I have not formally studied any relevant fields, I would be interested to hear thoughts from those who have.
The known laws of physics are computable, so if you believe that human intelligence is purely physical (and the known laws of physics are sufficient to explain it) then that means that human intelligence is in principle no more powerful than a Turing machine, since the Turing machine can emulate human intelligence by simulating physics.
If there's a nonphysical aspect to human intelligence and it's not computable, then that means computers can never match human intelligence even in theory.
If there's a nonphysical aspect to human intelligence and it's not computable, then that means computers can never match human intelligence even in theory.