Nope, the article is not about that. It is one thing to clearly state assumptions and derive the conclusions from there (which is what your professor seems to h

Nope, the article is not about that. It is one thing to clearly state assumptions and derive the conclusions from there (which is what your professor seems to have done). This is not "mathiness": indeed, this is exactly how theory is supposed to work -- as long as the assumptions and the logic are clear, he can disagree with the assumptions and this way argue against the results. It is quite another thing to replace assumptions by handwaving, in which case the point of math and logic is lost, and the argument becomes non-falsifiable. This is what the article calls "mathiness" and argues against.