I think you are mostly correct but most people don't like this explanation and choose to believe in magic or spirits or whatever instead of physical reality. For some reason the brain is "magic" and non-physical unlike other organs (and everything else that exists) to most people. It's almost impossible to convince anyone of this though and it's not even worth trying.
> most people don't like this explanation and choose to believe in magic or spirits or whatever instead of physical reality.
You have it reversed. Math is a language tool to describe things, in a limited fashion (our current modeling). One is physical matter (even if it's antimatter). If you believe that there will be a language that can describe anything, it still doesn't manifest matter by speaking that language or describing it...unless you're into magic or spirits or whatever.
This disconnect has nothing to do with how well we do or do not understand physical phenomena. I think what the OP meant to say (and probably you support) is how the "mind" or how we think, can be described with mathematical models. Maybe one day we will have a full understanding, but we're not there yet and not currently in a way that is legally compelling.
