I think you are right, Amos. It seems perfectly possible there are things inherently beyond mathematics and science, not just beyond them at the moment. For the sake of clarity I do think you can apply the scientific method to anything you want to investigate. It is simply not self evident that the process will always produce coherent results however hard we try.

Please don't bother asking for examples as I accept there may be none. I am uncertain: if I had an example I wouldn't be!