Alexandre Eremenko's answer is all good, but here are some extra things :
Mathematics did sort of develop independently several times in history, I believe basically three times during the Iron Age : Greece (as mentioned above), India and China. Before then, people didn't care all that much about proofs and mostly had ad-hoc formulas and big tables of values (Sumerian math is famous for giant tables).
China had such works as "The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven" during the Zhou dynasty (1122–256 BCE), which contains a proof of the Pythagorean theorem, and the Mo Jing in 330 BCE.
Edit : Some more things, I guess :
I cannot find much in the ways of sources indicating foreign origins of chinese mathematics, except perhaps babylonian (Chinese mathematics was pretty tied to astronomy). For dates, a comment from Mathematics across cultures :
"On the whole, if Greek and Chinese mathematical astronomy are compared from a merely technical and non-historical point of view, as an abstract catalogue of isolated results, it clearly appears that Chinese developments, such as those connected with the discovery of the precession, or the solar and lunar inequality, occur much later than the former, usually five or more century"
As for Indian mathematics, the oldest geometry texts are the Sulbasūtras, parts of religious texts used for altar construction. The seven big ones are the Bodhāyana, Āpasthamba, Kātyāyana, Mānava, Maitrāyana, Varāha and Vidhūla, written between 800 and 500 BCE. They include the proofs of such theorems as :
- The diagonal of a rectangle divides it into equal parts
- The diagonals of a rectangle bisecting each other and opposite areas are equal
- The perpendicular through the vertex of an isosceles triangle on the base divides the triangle into two equal halves
- A rectangle and a paralleloram on the same base and between the parallels are equal in area
- The diagonals of a rhombus bisect each otbher at right angles
- The pythagorean theorem