When prescriptivists tell you that naive is exclusively spelled naïve, they are in fact wrong: the former has a much higher usage and is equally correct. The word naïve (which I'm spelling this way because it is so cool anyway) is a direct loanword from French, which goes back to the Old French term naif, or "innocent". This derives from the Latin word nativus, or "natural", since innocence is supposedly natural. The word may sound a bit familiar because it is also the direct root of the current word natives, the natural inhabitants of a place. Both of these words are from nascor, or "birth", since something present at birth is natural, and this is from the Proto-Italic term gnaskor ("to be born"), ultimately from Proto-Indo-European genh, or "to produce", which also had undertones of "birth". When conquistadors described New World natives as naïve, they had no clue how right they were, linguistically speaking.
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.