Are we picking nits, or are we trying to have a fruitful discussion?
The thread you point to clearly shows a difference of opinions, and that difference has nothing whatsoever to do with mathematics. We have a different opinion on the suitability of one suggested item for solving a particular problem, that can equally well be solved with what the OP in that thread already has on his hands. I don't think that a 90 mm macro or T/S lens would behave a lot differently from a 70-200 zoom at the same distance with the same aperture, which is why I made the statement that the lens will not [automagically] solve the problem, no maths required. The actual problem involved throwing the background sufficiently out of focus. That is entirely a matter of opinion, not mathematics, even if applying the latter may help in resolving the problem.
And frankly, I think it is not relevant to this discussion. I fully appreciate that we can have different opinions, and you're entitled to yours. However, mine differs vastly from yours in the example you linked to. You did not disprove my claim (actually opinion), my claim (opinion) was not as bold as purported, and I did not try to belittle your opinion on the matter, neither am I doing so now. I just point out, that you yourself just tripped over what your key phrase expresses, that it is easy to make bold statements, but not so easy to back them up.
And maybe we indeed have a case of arithmetic (not mathematics) blurring our vision here? I usually don't care a lot about the formulae regarding depth of field or bokeh, as from my point of view, it is more a matter of opinion, just how much sharpness or blur might be required. The DOF equations have one random factor, which is based purely on opinion, neither physics nor mathematics. The example in the other thread, Foucsing and DOF, shows a mismatch of opinions regarding just how much of each is desired.
I did not make a bold statement to disprove your opinion, neither was it a claim of scientific proportions, only a declaration of my view on a mostly opinionated matter, what degree of sharpness and what degree of blur is desired. In the post pointed to, there are passages accentuated in bold by you, but I did not boldface them.
There is a huge difference in our reasoning in that other thread. I am unlikely to suggest to anyone to get an expensive piece of equipment to fulfill a particular task, if it is not necessary. A tilt lens is a major investment, while a close-up lens is not. If the task is such that stacking is needed to achieve the result, tilt is overkill. Stacking is a method that for still objects provides great control over optimal sharpness as well as blur. Controlling depth of field with aperture and tilt also are methods that can be used, and all those methods have limitations, advantages and disadvantages. Those matters surely fit somewhere within the topic of this thread, as they regard technical properties that can be more or less well understood and used for creative photography. And just as the matter of correct exposure, depth of field is largely a matter of opinion, of how we see the image and what we want it to look like. Those are artistic considerations, based on opinion, and not purely within the realm of physics and related mathematics/arithmetic, even if knowledge of the latter may help in understanding the underlying problems and to solve them.
My take on it is that the physics/mathematics are not essential to the artistic vision, but they are helpful tools when we know how to use them. Vision and visualising however is essential to the creation of images, no matter what tools we are using. Rembrandt did not have a DSLR, but he had the vision and made images with the tools at hand.
And please: These scribblings are not intended to serve as "proof" of anything. They are nothing but a discussion on some particular matters regarding photography, a discussion based mostly on opinion. I have opinions about how sharp is sharp enough, and how blurred is blurred enough for my taste. I also know that other opinions are fully valid on such matters. In the referred case, I used the phrasings: "I am afraid it would not solve the problem" and "from my point of view". I thought those formulations would reveal that I present my opinion on the matter and not a physical or scientific standpoint on a matter that can be proven or falsified. Should I always boldface such statements?
You are free to try to disprove my opinion with arithmetic if you like, but I think it might be fruitless, as it is only an opinion. I still respect yours, which is why I never challenged it.