Poincaré conjecture
The Poincaré conjecture can also be extended to higher dimensions: this is the generalised Poincaré conjecture. Surprisingly, it was easier to prove the fact for higher-dimensional spheres: In 1960, Smale proved it to be true for the 5-sphere, 6-sphere and higher. In 1982, Freedman proved that it was also true for the 4-sphere, for which he was awarded a Fields Medal.