A recent major breakthrough is announced here (Emory University's site, eScienceCommons). Looks like ultimately periodic sequences made the news. Also see here a recent article by Ken Ono (The Last Words of a Genius, Notices of the AMS Volume 57, Number 11, 1410-1419), and here a relevant abstract by John Webb (An improved “zoom rate” for the Folsom-Kent-Ono l-adic fractal behavior of partition values).
Image source.
A relevant video - Ken Ono talk (Emory University YT Channel):
http://youtu.be/aj4FozCSg8g
New Theories Reveal the Nature of Numbers