Mathematics is the language of physics. So what would the world be like if the initial assumptions of math, the grammar you can say is changed?

"Math is not a language, it's an adventure"  Paul Lockhart

Mathematics is nothing but a way of modeling patterns we see in the real world. If the model doesn't match up with reality to some degree, it's useless. Changing the basic assumptions of mathematics would just make mathematics useless, in which case, no one would use it, and people would have an incentive to invent models that actually do match up to reality. This is in fact what happens repeatedly any time a new area of mathematics is formalized. Someone takes a guess at the assumptions that will result in a usable model, and then they discover some shortcoming of the model, so they revise it until it fits. The original model for counting was not digits on paper, but rather a pile of stones. As sheep would leave the corral, the shepherd would add stones to a pile. As they came back, the shepherd would remove them again. If there were any stones left in the pile, he knew to go looking for the missing sheep. Much later, someone invented a way of marking on a clay tablet instead of piling up stones. It's a different model for the same pattern in reality. Any model that represents that same pattern in reality will have the same behavior as that pattern in reality, and so they all work the same, no matter how they are implemented, be it stones, marks on clay tablets, scribbles on paper, or bits in a computer's memory. Changing the model enough to change its behavior is equivalent to breaking the model. Nothing in the real pattern that is being modeled changes in the process.

Then you have to rewrite in your new language. Your just saying, suppose we describe it in english, now we want to describe it in portugese. Math isnt the only tool, but its the most efficent one.