>which means she was still leading at the age of 72
The current US president is 71 and on average women have longer life expectancies so it doesn't seem that high an age to be leading a group like the AMS.
The current US president is the oldest US president to date, and it was even a thing that came up in the campaign (for multiple candidates, by the way).
I remember it being an issue in the McCain campaign but not with Trump. Anyway, it's not a young age but if it's only a discussion point for president of the whole country for presiding over the AMS it shouldn't be surprising at all.
Her writeup when receiving the National Medal of Science in 1998: http://www.ams.org/notices/199903/comm-morawetz.pdf