Nominations for the 2017 Breakthrough Prize in mathematics and the New Horizons Prizes in mathematics are now open. In 2016, the Breakthrough Prize was awarded to Ian Agol. The New Horizons prizes are for breakthroughs given by junior mathematicians, usually restricted to within 10 years of PhD; the 2016 prizes were awarded to Andre Neves, Larry Guth, and Peter Scholze (declined).
The rules for the prizes are listed on this page, and nominations can be made at this page. (No self-nominations are allowed, for the obvious reasons; also, a third-party letter of recommendation is also required.)