This was already implied in the statement, made when discussing the role of applied mathematics, that the laws of nature must have been formulated in the language of mathematics to be an object for the use of applied mathematics. The statement that the laws of nature are written in the language of mathematics was properly made three hundred years ago; [ It is attributed to Galileo.] it is now more true than ever before.
And as I've indicated in my own essay on why QM is so difficult, in such a case, the mathematics of QM is the main connection we have between it and what we already understand, even when there is no conceptual connection between classical and quantum mechanics. It is the bridge and thus, if one does not understand the mathematical formulism of QM, one hasn't understand QM at all but rather has a superficial idea of what it is.
If you haven't come across this yet, I would certainly highly recommend that you read it.