>
The Greeks were ideologically opposed to the number zero.I don't think this claim is supportable, certainly not as such a broad generalization. Do you have a specific statement clearly attributable to an ancient Greek author to that effect?
> Greeks saw geometry and math as interchangeable
You're going to have to define these terms more explicitly. I don't think this statement is right. Ancient Greeks spent quite a lot of effort studying areas of what we now call mathematics but which were not geometrical per se.
> Greeks weren’t gonna give up their belief in Geometry because it provided them with social and political power
Any claim that geometers in general had social or political power owing to their mathematical work seems exaggerated. While a couple of geometers happened to incidentally also be local political leaders (e.g. Eudoxus), geometers explicitly lamented how little their contemporaries cared about their work and how few colleagues they could find to share it with.
> Aristotle outright refuses to acknowledge the existence of zero and of infinity.
This seems like a reductive summary. Aristotle had a pretty sophisticated idea about this which finds echoes in modern mathematics: here is Aristotle:
> Now there is no ratio in which the void is exceeded by body, as there is no ratio of 0 (οὐδέν) to a number. For if 4 exceeds 3 by 1, and 2 by more than 1, and 1 by still more than it exceeds 2, still there is no ratio by which it exceeds 0; for that which exceeds must be divisible into the excess + that which is exceeded, so that 4 will be what it exceeds 0 by + 0. For this reason, too, a line does not exceed a point-unless it is composed of points!
Alternate translation:
> But the nonexistent substantiality of vacuity cannot bear any ratio whatever to the substantiality of any material substance, any more than zero can bear a ratio to a number. For if we divide a constant quantity c (that which exceeds) into two variable parts, a (the excess) and b (the exceeded), then, as a increases, b will decrease and the ratio a :b will increase; but when the whole of c is in section a there will be none of c for section b; and it is absurd to speak of 'none of c' as 'a part of c.' So the ratio a: b will cease to exist, because b has ceased to exist and only a is left, and there is no proportion between something and nothing. (And in the same way there is no such thing as the proportion between a line and a point, because, since a point is no part of a line, taking a point is not taking any of the line.)"
Later, about motion in a vacuum:
> But if a thing moves through the thickest medium such and such a distance in such and such a time, it moves through the void with a speed beyond any ratio.
(The physical premise here is wrong, but the concept of division by zero is clear.)
See https://www.jstor.org/stable/pdf/2304187.pdf
Aside: anyone telling you what Pythagoras thought about numbers is pulling your leg. We have no idea about this whatsoever, only what various people claimed like 5+ centuries later, most of which is nonsense.