Other societies, that I am a member of, have had the "Fellows" distinction (much) longer from INFORMS to The Econometric Society to SIAM to RSAI. I am a Fellow of the RSAI.
Needless to say, since AMS just introduced the Fellows recognition in 2012 the list is quite long with the goals of the Fellows Program being, according to the AMS website;
- To create an enlarged class of mathematicians recognized by their peers as distinguished for their contributions to the profession.
- To honor not only the extraordinary but also the excellent.
- To lift the morale of the profession by providing an honor more accessible than those currently available.
- To make mathematicians more competitive for awards, promotion, and honors when they are being compared with colleagues from other disciplines.
- To support the advancement of more mathematicians in leadership positions in their own institutions and in the broader society.
Since I have 3 degrees in Applied Math from Brown and also a degree in Russian Language and Literature (yes, I love languages of all sorts, including computer programming languages) I know and even had as instructors many of the faculty on the above list in Applied Math. Plus, Constantine Dafermos was Stella Dafermos' husband and she was my doctoral dissertation advisor at Brown.
Of course, on the list are individuals who already are Fellows of other societies that I mentioned above.
Congratulations to all the AMS Fellows!