Written: Feb. 7, 2017
G.H. Hardy famously (and stupidly!) said that `Mathematics is a young man's game'. I don't know how he defined young, but if you define it as `under one hundred years old', then he may have been right.
Here are some examples, of people that I know personally, in decreasing age
My late colleague, the great Israel Gelfand (1913-2009), who published until he was 93-years-old.
Added Feb. 23, 2017: Martin Andler kindly informed me that Yvonne Choquet-Bruhat, born in 1923, has two 2015 entries in Mathscinet, and several in 2011.
Added April 18, 2016: Read interesting comments by Igor Pak.
Opinions of Doron Zeilberger