Tragic how colonization went down ... these people had larger cities than Europe, comparable organization, and stunning engineering skills. Unfortunately germs and viruses care little how advanced you are in those realms

I'm totally unfamiliar as to how much influence the Mayans had on our Caribbean Amerindian natives and what exactly their relationship was. But one thing I would imagine is that our relatively peaceful Tainos had to have been wary of the warlike Mayans. If my memory serves me right the Carib usually got the best of them in war, if I was a Taino I would be very wary of Mayans and their warlike culture of capturing victims for their massive sacrifices.
I'm not demonizing the Mayans, just being very real about them in the same way the Romans and Greeks had their good and bad aspects so did the Mayans.
Recall that the Aztec culture had many similarities in terms of capturing other Indians for sacrificing and this actually helped the Spaniards attract indian allys in defeating the Aztecs.
One thing history has shown is that all things being equal it was better for our Tainos to have fought the Spaniards tooth and nail, too bad they were the first to come in contact with Europeans and how relatively peaceful their culture was in comparison to say the Caribs or Apaches. Today, out of all the Caribbean natives it is only a handful of Caribs and their descendants that survive, the Tainos were either killed or absorbed into the general population.

The Ancient Maya discovered two fundamental ideas in mathematics: positional value and the concept of zero.

The Maya's had an extremely complicated method of keeping track of time, ... Also, they were able to predict every solar and lunar eclipse until this day.

The Maya particularly picked the date of December 21st 2012, an end date of this calendar rather than a start date because they had calculated that on that date the Sun would be in the 'exact center of the Milky Way Galaxy.

How did they manage to accomplish this achievements with the naked eye?

Columbus on the Tainos:
"They traded with us and gave us everything they had, with good will..they took great delight in pleasing us..They are very gentle and without knowledge of what is evil; nor do they murder or steal..Your highness may believe that in all the world there can be no better people ..They love their neighbours as themselves, and they have the sweetest talk in the world, and are gentle and always laughing."

Looking back I'm not sure that was necessarily a good characteristic to have. The Spanish had nothing but bad to say about the Caribs and there is still Caribs left on Dominica.

To me at least, it was demonstrative of how civilized the tainos where in sharp contrast to the barbarity that was Spain. History has shown time and again how barbaric peoples of a bellicose nature have brought down more civilized and hence more passive societies. The tainos may not have been grand architects but they obviously were well ahead of many other peoples in the world with respect to how they interacted with each other. That to me is a greater measure of enlightenment and progress than ten Giza pyramids or all of the cathedrals of medieval Spain.

Oh definitely, time and time again one see's supposed 'primitive' people being in a sense more 'civilized'. Even their personal hygiene was way ahead of the Spaniards of that time. On a seperate note, I've often heard from other LatinAmericans who've lived in Spain (mostly Cubans who left after Castro) comment on how little the Spaniards bathed and their lack of hygiene (in comparison). I'm talking about Spain from the 60's & 70's, it may be alot different now. The Spaniards would comment on how much water the Cubans used with their daily baths, lol. No offense to any Spaniards on here.

Indeed the the medieval Spaniard was a dirtbag in every sense of the word. We're talking about a society that viewed not bathing as being somehow holy (I'm not kidding. They associated bathing with the Moors and hence something to be despised so when someone went long intervals without bathing, meaning YEARS, Spanish commentators of the time would write about their "piety" ).

Cibao:

Years???? c'mon.......

From Crow's Spain: The Root And The Flower:

"The medicant Spanish monks, according to their practice of setting up a directly antagonistic principle, considered physical dirt as the test of moral purity and faith; and by dining and sleeping from year's end to year's end in the same unchanged woolen frock, arrived at the height of their ambition, according to their view of the odor of sanctity, the olor de santidad...it came to represent Christian dodliness, and many saints are pictured as sitting in their own excrement...the Princess Isabel, the "daughter of the eye" of King Phillip II, made a solemn vow never to change her clothes until Ostend was taken. The seige lasted three years, three months, and thirteen days. The royal garment acquired a tawny color, which was called Isabel by the courtiers, in compliment to the pious princess."

If that was their nobles I can't even imagine the stench emanating from the commoners back then..lol..no glimmer, I would not make such a claim unless it were true, which indeed it is.