Leaving aside where you draw the line of what classifies as intelligence or not , you seem to be invoking some kind of non-materialist view of the human mind, that there is some other 'essence' that is not based on fundamental physics and that is what gives rise to intelligence.
If you subscribe to a materialist world view, that the mind is essentially a biological machine then it has to follow that you can replicate it in software and math. To state otherwise is, as I said, invoking a non-materialistic view that there is something non-physical that gives rise to intelligence.