What we have is Applied Intelligence and as far as the Artificial kind of AI that becomes a big philosophical debate. Even so, what is Intelligence? If you start to define it in a way where you can build upon it logically, you end up with obvious conclusions where for example, your house thermostat is intelligent.
The domain or context is essential to the consideration too. So, the house thermostat is intelligent and within it's tiny world it performs quite well adapting and making decisions with it's simple stimuli. It is easy for us humans to think since we can write describe that intelligence in code or as a math function that there is no intelligence, just mechanically defined cause/effect. It is arrogant to define intelligence in terms of capabilities of humans... or just some subset of humans; plus practically speaking, it constrains us to only a select few to be the judges. The thermostat will not perform intelligently playing chess; just as human experts out of their depth do not perform intelligently either.
So lets say we have some math that is powerful enough to describe the problem of winning at Jeopardy. Do you honestly think that we or any math genius will be able to fully grasp that solution? So then do we call that Intelligence? It's "mechanical" but it does a better job than our human solutions. But why is that not intelligence? Because it can be described in some way and copied between machines? (we can't do that with our expert Jeopardy players.) No.
Lets go to a common fall back position: Humans can teach themselves without as much help a broad range of tasks. We have teachers, books etc... but why should we consider that way of learning the only way? Again, we are constraining it to humans. So... how far from "Idiot Savant" do we have to get before we consider it Intelligent? Again still constraining it to humans... What about mentally limited humans, like children? Do we let them off the hook simply because they grow up?
Getting back to the "some math:" What if you could describe incredibly complex real world problems found in life as complex math approximations? Well, that is just what we have been doing and the whole process of finding those mathematical non-linear equations is beyond our intelligence but for some problems our brains somehow do approximate solutions (unless you can find a perfect chess player, etc.) The amazing thing is that the math derived from theories on how our brains work is how we have algorithms which find approximate solutions - these are described as complex non-linear approximations (far better than human descriptions.) It is an iterative discovery process akin to our learning. So you might again say that this math is mechanical... but as we keep getting closer to mirroring human approximation abilities or surpassing them doesn't the trend make you wonder if everything in life can be described mathematically? Humans can describe solutions as math for simple problems but the machines do the work quicker. Is it unfair if a human teacher helps describe the problems and types of math (approaches) needed to learn the best solution to the task? Is it unfair that you learned your alphabet in a linear order? as a song? So do we give up at the point where we have automated the teacher?
Perhaps life is a non-linear approximation of 42... Do we know what the question was? no. does it matter? probably not. But we live in the process of approximating it. ;-)