Grigori Perelman proves, between 2002 and 2003, in three preprints circulated only on arXiv with no journal peer review, Thurston's geometrization conjecture formulated in the 1970s — of which the century-old Poincaré conjecture, posed in 1904, is a special case. Perelman decisively employs and refines the Ricci flow with surgery technique, originally developed by Richard Hamilton in the 1980s, resolving the technical obstacles (the so-called "singularities") that had prevented completion of the program for nearly two decades. Full validation of the proof required several years of collective work by the international mathematical community, given its extreme technical complexity. Perelman declined both the 2006 Fields Medal and, in 2010, the million-dollar Millennium Prize awarded by the Clay Mathematics Institute, withdrawing entirely from institutional mathematical activity.