The Poincaré conjecture

The Poincaré conjecture is a famous problem in mathematics about the shape of three-dimensional spaces. It states that if a space is like a three-dimensional version of a sphere—meaning it's simply connected (any loop can be shrunk to a point)—then it is essentially a 3-sphere, the three-dimensional analog of a regular sphere. In essence, the conjecture claims that the only 3D shape with these properties is the 3-sphere, and proving this confirms that such spaces are uniquely shaped like a 3-sphere. This was proven by mathematician Grigori Perelman in 2003.