What cultural contributions did the Maya and the Aztecs make?

The Maya civilization and Aztec Empire were, at the time the Spanish came across them in the sixteenth century, perhaps the most advanced and organized societies in North America, living in large cities that in many cases still partially stand to this day.
The Mayan people are most famously known for their astronomy, writing system, and use of zero in mathematics, all of which were highly advanced and entirely indigenous. The Mayan calendar was more accurate in determining the length of a year than the calendar used by the Spanish when they arrived, while elements of the Mayan writing system were adopted in modern systems. Mayan art and craftsmanship was particularly sought after by traders both before and after their conquest by the conquistadors, with a tradition of cotton-weaving and metalwork that continues in the region.
The achievements of the Aztec Empire reflect its leading place in the region; not only do most of their lasting accomplishments have to do with administering an empire, but they can be seen in modern Mexico. The Aztec Empire placed a high value on education, which was provided to their citizens not only irrespective of class, but of gender as well. Their collective farms, which formed part of the administrative bodies known as calpulli, can be seen in the Mexican ejido system. The name "Mexico" itself refers to the Aztecs, who can more properly be known as the Mexica, whose former capital Tenochtitlan is now Mexico City.
Perhaps most recognizable of all, the farms of these and other regional peoples produced crops many of us would know in our daily lives, including corn, cotton, and cocoa.