That's the same as my own example of explaining to people that dogs brains can do some pretty complex math. I throw a stick that's turning as it flies and the dog catches it every time, but it can't explain nor communicate the formula that went into that.

But this is really an optimization problem: representing your formula as a bunch of weights that are then used to drive a cascade of multiply-add rules to derive some output is an imprecise but roughly accurate way to model a problem. That there is a much more direct and analytical way of modeling that problem requires intelligence of a different order.

But a program like mathematica gets awfully close to that, so that's not a problem that is a good fit for being solved with a neural network even if it would work.

I'd prefer to use a neural network for problems that have a less well defined solution.