> Well we do actually have a purely mathematical approach to AI worked out.

Supposedly with enough computer power and
enough data, a one stroke solution to
everything is stochastic optimal control,
but that solution takes, say, just brute
force to, say, planetary motion instead of
Newton's second law of motion and law of
gravity. Else, need to insert such laws
into the software, but we would insert only laws humans
knew from the past, or have the AI software
discover such laws, not so promising. This
stochastic optimal control approach is
not practical or even very insightful.
But it is mathematical.

> machine learning is making progress in leaps and bounds.

I looked at Prof Ng's machine learning course, and
all I saw was some old intermediate statistics,
in particular, maximum likelihood estimation (MLE),
done badly. I doubt that we have any
solid foundation to build on for any significantly
new and powerful techniques for machine learning.
I see nothing in machine learning that promises
to be anything like human intelligence. Sure,
we can write a really good chess program, but
no way do we believe that its internals are
anything like human intelligence.

> As is our understanding of the brain.

Right, there are lots of neurons. And if
someone gets a really big injury
just above their left ear, then we have a good
guess at what the more obvious results will be.
But that's not much understanding of
how the brain actually works.

It's a little like we have a car,
have no idea what's under the
hood, and are asked to build a car. Maybe
we are good with metal working, but
we don't even know what a connecting rod is.

> It wasn't that long after engines were invented that we got airplanes.

The rest needed was relatively simple, the wind tunnel,
some spruce wood, glue, linen, paint, wire, and
good carpentry. For the equivalent parts of AI,
I doubt that we have even a weak little hollow
hint of a tiny clue.

In some of the old work in AI, it was said that
a core challenge was the 'representation problem'.
If all that was meant was just what programming
language data structures to use, then that was
not significant progress.

Or, sure, we have a shot at understanding the
'sensors' and 'transducers' that are connected
to the brain: Sensors: Pain, sound, sight,
taste, etc. Transducers: Muscles, speech,
eye focus, etc. We know some about how the
middle and inner ear handles sound and
the gross parts of the eye. And if we show
a guy a picture of a pretty girl, then we can
see what parts of his brain become more
active. And we know that there are neurons
firing. But so far it seems that that's about
it. So, that's like my computer: For sensors
and transducers it has a keyboard, mouse, speakers,
printer, Ethernet connection, etc. And if we
look deep inside then we see a lot of circuits and transistors.
But my kitty cat has no idea at all about the
internals of the software that runs in my computer,
and by analogy I see no understanding of the
analogous details inside a human brain.

Or, we have computers, and we can write software for
them using If-Then-Else, Do-While, Call-Return, etc.,
but for writing software comparable with a human
brain we don't know the first character to type
into an empty file for the software. In simple
terms, we don't have a software design. Or,
it's like we are still in the sixth grade,
have learned, say, Python, and are asked to
write software to solve the ordinary differential
equations of space flight to the outer planets --
we don't know where to start. Or, closer in,
we're asked to write software to solve the
Navier-Stokes equations -- once we get much
past toy problems, our grid software goes
unstable and gives wacko results.

Net, we just don't yet know how to program
anything like real, human intelligence.