I agree that some forms of intelligence must be able to be learned, in the sense that it may involve employing the right algorithm (NlogN rather than N^N). There must be a software component involved that can be updated and accelerated through experience. In fact, that seems to be what experience is.
Even if there is an absolute physical property of the brain that we could call intelligence, it would be foolish to think we could measure it through the results of a pencil and paper test.