Well, you have analog to digital converters in the digital world. This gives you binary and machine language. Higher up you have assembly language which is basic instructions like load byte, store byte. Very tedious but simple. And then you have higher programming languages where you don't have to worry about low level details, the ones on the bits and bytes level.

I suspect that we operate on a high level too, but the language we use in public, written and spoken, is lower than what we use in our heads. It's like assembly language or even machine language. I think it would be really hard to translate from English to French if that wasn't the case. Or from Python to Java. Obviously programming languages have some resemblance to mathematics. For instance the concept of functions. If you never learned the pure concept of functions, it's hard to understand it with all the other things that you have to deal with like programming tools, editor, and assignments. So I think there's a more abstract language inside ourselves, but it's part of our hardware, so we can't express it.