What is the meaning of Text inside of AMS logo
ἀγεωμέτρητος μη εἰσίτω - Let no one untutored in geometry enter here
According to tradition this text was displayed in the entrance of Plato's Academy. (The tradition is of a late data, see this critical discussion.) Nicolaus Copernicus choose to print it on the cover page of the book De Revolutionibus.
image from 1938 (left) and from
2015 (right)
De Revolutionibus
The phrase «Μηδείς αγεωμέτρητος εισίτω μοι την θύρα» (or «Μηδείς αγεωμέτρητος εισίτω μοι την στέγη») is a phrase that supposedly was on the threshold of Plato's Academy and translates to: "do not let anyone ignorant of geometry through my door" (or under my roof). See for instance this discussion https://www.plato-dialogues.org/faq/faq009.htm
The phrase in AMS' logo translates to "Do not be ignorant geometry".
Edit: The above translation is not correct. The word "εισίτω" is a form of the verb "εἴσειμι" which means "to come into" (wiktionary). I initially thought that it was a form of "ειμί" which means "to be".
So finally the AMS' logo says: "Do not enter if you don't know geometry" or "You will not enter if you don't know geometry".