The Greeks wrote their mathematical ideas in a different way than other cultures, so the answers to these questions aren’t completely clear-cut.
The Sumerian/Babylonian style of written records did not match, say, Euclid’s Elements. (They didn’t write books full of precise definitions and proofs. They didn’t leave behind textbooks, only problem sets and worked examples.) But note that neither did the style of the Pythagoreans necessarily, and the notion that Pythagoras or his disciples made a proof comes from written records from hundreds of years later.
> Mesopotamian, Indian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases.
As humans we always lived a kind of ups and downs, regarding use of technology, relationships among countries, how open/closed the societies used to be, how travelling was seen and so on.
For example, in the ancient world there was already a kind of Erasmus, as Greek medicine students used to spend a few years with Egyptian doctors before getting back home and start practising.
But also, we can't trust geometrical diagrams: https://en.wikipedia.org/wiki/Missing_square_puzzle