Dr Feynman would agree:

    The principle is that you must not fool yourself, and you are the easiest person to fool.

Math and physics can describe juggling, but that description is not what helped discover juggling - holding a few balls in your hand suffices for that. Engineering and physics on the other hand to be math derived fields. In other words, the processes involved are sufficiently complex to be beyond the scope of even a rather clever human's intuition. Of course you might argue of success by mimicry, yet mimicry becomes exponentially more difficult as the complexity of a problem increases, to the point that I think we can all but disregard it for meaningful applications of engineering and most natural sciences.

You'd be surprised how much math can actually help get into advanced juggling. Similar to origami. Sure, basics don't benefit from math. Advanced practices, though, do.

Regardless of that, the point of the example was precisely the point you seem to be using against me. Most practices in many fields, including much of physics and engineering, don't actually need advanced math. They are helped considerably by it, though.

Yes Mathematics is hard.

I don't think being good at juggling makes you any better at describing the dynamics of juggling, nor the physiological characteristics that enable it.

Regarding Feynman (comment below), yes it is very important not to fool yourself, but knowing mathematics well makes it easier not to fool yourself.

But does it? Or is it just that the people you know that don't fool themselves happen to be good at math? :)

The juggling example was supposed to be an obvious example of people doing something that takes complicated math to analyze. I'm asserting it is not much different to many engineering jobs. Nor do I think that most physicists have a terribly strong intuition for math.

I confess to not having numbers to back this. :(