Our universe seems to tell a story that is independent of the words in which we have always chosen to express it. – Kate Becker
I like to shorten it down to: The world works the same, regardless of how we speak about it.
Mathematical formulations also count as a way of speaking about it. Math is a human invention - it is a "language" - that we use to describe our world. Talking about the world in English or German does not change how the world works. Describing the world in some mathematical terms or in other mathematical terms, doesn't change how the world works.
But naturally, if you speak in German, others who listen to you must be able to understand German. If you reinvent another mathematical description of some phenomenon, then you will only be able to talk about it with people who know about this other description. This other description might cause derived formulas and expressions to be different than we are used to as well - you are here altering the "language" that everyone are used to.
This might be fine. This might even be smart and useful, if it eases the work. Such as when tensor notation was introduced to easier describe vector and matrix relationships e.g. when dealing with fields and distributions, or such as when quantum bra-ket notation was introduced to describe quantum states more compressed. Everyone who already know math and physics just must then learn this new notation and this new version of the math "language".
(Adding new forms of notation in this manner is quite different from changing already existing and well-known formulas. You might need good reasons to do this to make it catch on.)