That's the *definition* of physics: how mathematics applies to observations of nature! If it has no mathematical underpinning, it is not physics. It is not possible to do physics without some form of mathematics. Now, that mathematics can be approximative, and one can use intuition instead of calculations, but it is still "mathematics". For instance, saying that "pressure rises with the amount of gas in a container" is still a mathematical statement (even though it is not an equation, it specifies something about the functional relationship between two quantities (real numbers).
Well, unfortunately, that IS science. Science is the confrontation of a theory (a set of hypotheses, with their logical, hence mathematical, deductions) with observations (hence some form of quantitative assessment).
You cannot confront these if there's not some form of mathematical relationship between quantities (even inprecise, as stated above). And if you cannot confront them, then the theory is "non-falsifiable" and hence "non-scientific".
It's the very definition of science.
No, you can use old mathematics too, with new hypotheses.
But that's about as interesting as saying that "you professional scribes should be willing to let us, who have never learned the alphabet or any grammar or vocabulary, also write our works of literary art...", in other words, you should also consider our meaningless scribbles on paper.
