I'm not trying to remark about what is or isn't good for program design. I actually like functional programming. I'm criticizing the author's claims about mathematics which are clearly a justification for his views.

If you're reading a paper with theorems and proofs and algorithms and the author says at the beginning that the algorithms in the paper will be described using mutation (or even if the reader has to figure this out on the fly) then I argue you can't use this as a reason to say what you're reading somehow isn't math. You can criticize it if you think it's unclear, sure, but it's still math.