Great problems

20th century

1. 1904
   Poincaré conjectureTopology, Geometry. Every simply connected closed $3$-manifold is homeomorphic to the $3$-sphere $S^3$ — posed by Henri Poincaré in 1904 and proved by Grigori Perelman in 2002–2003 via Ricci flow with surgery, the only solved Clay Millennium Prize Problem.MillenniumGPGrigori Perelman, 2003