This Top Ten List comes to us courtesy of Wikipedia, with contributions from several other websites for their sources and citations for all discoveries and achievments listed here!
1) 2002 – Yasumasa Kanada, Y. Ushiro, Hisayasu Kuroda, Makoto Kudoh and a team of nine more compute π to 1241.1 billion digits using a Hitachi 64-node supercomputer.
2) 2004 – The classification of finite simple groups, a collaborative work involving some hundred mathematicians and spanning fifty years, is completed.
3) 2004 – Ben Green and Terence Tao prove the Green-Tao theorem.
4) 2007 – a team of researchers throughout North America and Europe used networks of computers to map E8.
5) 2009 – Fundamental lemma (Langlands program) had been proved by Ngô Bảo Châu.
6) 2013 – Yitang Zhang proves the first finite bound on gaps between prime numbers.
7) 2014 – Project Flyspeck announces that it completed proof of Kepler's conjecture.
8) 2015 – Terence Tao solved The Erdös Discrepancy Problem.
9) 2016 – Using Alexander Yee's y-cruncher Peter Trueb successfully calculated π to 22.4 trillion digits.
10) 2019 – Using y-cruncher v0.7.6 Emma Haruka Iwao calculated π to 31.4 trillion digits.