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][1]). 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".


  [1]: https://el.wiktionary.org/wiki/%CE%B5%E1%BC%B4%CF%83%CE%B5%CE%B9%CE%BC%CE%B9