The Poincaré Conjecture

The Poincaré Conjecture is a famous problem in mathematics. It concerns the nature of three-dimensional spaces and whether they can be "simply connected" or not.Simply connected means that any loop drawn in the space can be continuously shrunk to a point without leaving the space.

Poincaré conjectured that any closed, simply connected three-dimensional manifold is topologically equivalent to the three-dimensional sphere. In other words, any such manifold is essentially a "rubber ball" that can be deformed into a perfect sphere.

It remained unsolved for over a century, until it was finally proven by Russian mathematician Grigori Perelman in 2002. His proof was widely considered one of the most significant mathematical achievements of the 21st century and earned him numerous accolades.

In simple words -

The conjecture asks whether any 3-D shape that doesn't have any holes in it ("simply connected") is basically just a ball. The answer is yes-any simply connected 3D shape is essentially the same as a ball that can be stretched and squished into that shape.