Progress is a luxurious goal.

Observing that something always holds and even having a formula for it is not the same thing as having a proof, and the proof is what makes it mathematics and geometry and not "just" engineering. The babylonians had a rule of thumb -- the greeks discovered the theorem -- and more than that, they seem to have invented the mathematical/geometrical proof as a concept, along with formal logic.

Without that mental framework, it's hard to say that the babylonians proved anything or had any theorems at all, only collections of rules of thumb. It's quite likely that lots of babylonians sort of independently and intuitively understood _why_ it must be true, but they don't seem to have ever written it down.

Not that there's anything wrong with having rules of thumb -- it's a huge achievement to even notice and collect and teach those things, all the stuff around you is built relying on them.

I encourage everyone to watch this series of videos.

https://www.youtube.com/watch?v=_ivqWN4L3zU

As I understand Greeks invented proofs because "universal thruths" they exported from Babylon and Egypt sometimes explicitly contradicted each other.

I believe such contradictions may be a great nuisance when you try to get shit done.

Egypt and Babylon were sufficiently "complex" societies for proofs, but their tradition treated mathematics as a bunch of useful facts about numbers and shapes. New generation just memorized them. We should think it worked for them in most cases, and when it didn't work it was not so often for them to start thinking a lot of reforming mathematics. Plus they were indoctrinated by the math they learned (authority of a teacher is above of anything else, i suppose) and to reform math was not a natural idea for them.