Im a brazillian historian...

So yea, if anyone wants to know something about South American history, shoot, but let me warn you that our history is rather dull and boring.(I majored in classical studies, but I still know a good deal about LA history).

  Hmmm... its not as much that they mysteriously disappeared, but like other illeterate people from the "Old World", we know very little about them because either they left no written records, or we´re not able to translate them. Unfortunetly, we haven´t found a "Rosetta Stone" for a lot of those populations, so their history are left for archaelogist to ponder.

 The most notable pre-columbian civilizations are the:

 Olmecs(1.600 B.C.E/900 B.C.E) - Precursors to pretty much every central american civilization that came afterwards, they are the first western civilization to have devoloped a comprehensive writting system and were also responsible for creating the pantheon of anthropomorphics Gods that would become standard for the region for the next 2.500 years (Serpent God, Sun God, Chamaleon God, Jaguar God etc...).
   The Olmecs are also responsible for creating the first meso-american calendar, called "the long count", from whitch the mayans would borrow from heavilly thousands of years later.  Their calendar is extremly accurate, way more than the Babylonian calendar that was standard for Eurasia at that time. They even accounted for bissextus years, adding one day every 4 years which they called "The day outside of time". They also built temples, aqueducts, sacrificed people to the Gods etc...
    VERY broadly speaking, you can think on them as the "sumerians" of pre-columbia America.

  In South America, the Nazca Culture(100 C.E/800 C.E) deserves a shout. They are one of the precursors to the Inca, and like them they never developed a writting system, which makes their study extremly problematic. We do know that they made beautiful pottery, statues, and other nice works of art. They are also responsible for creating the breathtaking "Nazca Lines", which has archaeologists to these days still scratching their heads to figure out 1-) How they made them and 2-) What do they mean. They seemed to have worshiped a "Sun God", an "Orca God", a "Spider God", a "Puma God" and other anthropomorphic Gods.
  They probably disappeared due to volcanic Global warming, which made their region suffer from terrible floods. Their civilization was also situated on a region of strong tectonic activity, so its likelly they suffered a couple of 8+ Ritcher Scale earthquakes. Such earthquakes are still terribly common on the region.

Dear Alcebiades, is this writing familiar to you ?

Alcibiades, what do you know about the ancient city of Tiwanaku, said to date back to 1500 BC?