The Greeks have been attributed with 'discovering' many mathemetical theorems, however a lot of evidence is present that shows this knowledge was present way before Greek times (e.g. Pythagorean triplets on Sumerian tablets). How old is such understanding of 'mathematics/geometry' truly?

by OotB_OutOfTheBox

We have classicly attributed many mathematical and geometrical discoveries with 'western' scholars. However, I've heard that there is a lot of evidence that more ancient cultures than the Greeks already knew about (estimating) pi, the golden ratio, or even the Fibonacci sequence - believed to have been discovered in ancient India already if I'm not mistaken. Also I've heard that this notion (that the Greeks borrowed most of their knowledge) was not controversial at all in ancient times.

How far back does human knowledge on these things go? For example, what is the earliest credible estimate of human discovery of the theory of Pythagoras? Did pre-columbian American cultures and ancient Chinese cultures show similar (or possibly even more advanced) understanding of mathematics and geometry (i.e. did they conceive of these theorems independently)?

Alkibiades415

I do not have the mathematics expertise to answer your question directly, but I can point you to an excellent recent source on this wide-ranging question: Luke Hodgkin, A History of Mathematics: from Mesopotamia to Modernity (Oxford, 2005). You can see a breakdown of the chapters and a brief description here. Chapters 1-4 address your question directly (and it is way too much to summarize here effectively). The book is available online if you belong to a participating institution (like a University).