We all know Pythagoras discovered the equation for determining the long side of a right angle right? Wrong. Ancient Babylonia did, 1000 years before.
3700 year old tablet named, Plimpton 322, has the calculations written in stone. We also know there is a connection to the ancient Egyptians, prior to the pyramids.. Babylonians were also tracking celestial objects like Venus and Jupiter. So it leaves one to wonder, how much did ancient civilizations know about math?
There is little doubt that the Babylonians, Egyptians, and other great ancient civilizations were preceded by people we know nothing about. You don't go from subsistence farming to building cities in one leap. For instance, look at Gobekli Tepe. Those people didn't wander home one day from hunting and decide to build a city. There had to be a fairly long period of time before them as small villages evolved into more complex cities. I believe one day we will learn our ancestors knew much more than we give them credit for and our history stretches farther back in time than we even dream of today. There is no telling what has been hidden under water on the continental shelves around the world as sea levels rose after the last ice age.
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I agree, our ancestors (and Neanderthals) were alot more sophisticated than purely 'savage hunters'- and this appears to go back alot further than the advent of agriculture.
WRT 'maths' there is evidence of counting going back at least to 44K years ago with the Lebombo bone and Ishango bone (~20K).
Gobekli Tepe- AFAIK there is no evidence of 'living spaces'- but it does show considerable organisation to gather and feed the numbers of people to build it (and continue to add to it over a period of time). Catalhoyuk though is pretty certainly a settlement as would be Natufian settlements such as Jericho