Exactly, we disagree and you are not alone in thinking this. You can use reason to do math, but your can't model reason with math.

I'm ignorantly curious of what type of math will work in your view. Genuine question, I just want to be educated.

There is no type of math that can model conceptual reasoning. You can use conceptual reasoning, however, to do math.

I think I know what math is, though I'm not sure. Logical systems of axioms and inference rules?

But I'm even less sure what conceptual reasoning is.