Language grammar is a complicated system, poorly understood.
Michael Halliday is the first and only that I know of to address this in a complete fashion.
You could say that grammar is mathematical but it’s rather the other way around.
What makes the grammars of mathematics so powerful is the system of axioms and the theorems built upon them. Building upon that, you have a grammatical system that is transparent and, once learned, is considerably less ambiguity prone than regular language grammars.
That said, it’s not always clear _which_ grammar is in use or is needed in a particular instance. There are MANY MANY rules of thumb / heuristics in mathematics that are simply understood and left unspoken / unwritten, just as you have with regular language grammars.
Could we have built computers upon english words instead of binary accumulator and registers and such?
Absolutely. It could produce perfect English sentences and work with that natively instead of mathematics.
But another BIG BIG advantage mathematics has over English? It’s terse Space-saving. You can fit a lot in a little space.
Oh, qubits aren’t so strange. Being able to work on 2 states instead of 1 is an immediate boost in speed. Plus, entanglement increases the speed even further as you only need to modify one part to benefit both.
Its problem is noise and distinguishing noise from signal.
Being able to be programmed to handle paraconsistent logics is probably the most exciting feature to me.
We already do that to a degree with a few analog chips in every computer but much more with quantum.