SB

This is the only such essay/post I've found and I really enjoyed reading it. I might go away and think a lot more about it, so thank you for writing it. If I come up with a rejoinder, I'll let you know.

There are a few aspects which are presented as dichotomous with respect to natural language and mathematics.

there is an important difference between mathematical reasoning and "informal" reasoning: the latter virtually always involves a component that is not conscious and that cannot be easily verbalized. So, although thinking always involves models, a lot of the time these models are fully or partially hidden, encoded somewhere in the neural networks of the brain.