The ratification of the U.S Constitution is the correct answer.
Even though the 'Articles of Confederation and Perpetual Union' had been submitted for ratification in 1777, it wasn't until 1781 that a significant number of states approved it. The ratification of the U.S constitution was a very important event in the midst of the economic depression that the United States was going through.
An intellectual movement of the renaissance based on the study of humanities
Tecumseh was a tribal leader who thought all Native Americans needed to get together to force US to stop its expansion. Together the Native Americans were strong enough that US would stop to avoid an armed conflict.
I believe the answer is:
- Pure mathematics
Proven by the difference in knowledge on astronomy between aztec culture and the Castillian.
- Urban architecture
Proven by the superior irrigation system that Aztec civilization had compared to Castilian civilization at that time.