What is the significance of the Poincaré conjecture?

[donglepuss]

TL;DR Summary

What is the significance of the Poincaré conjecture?

Namely, what does Perelman’s proof of it imply?

 

[fresh_42]

The proof of the Poincaré conjecture is an important contribution to the classification of all 3-manifolds. This is because Perelman actually proves the more general geometrization conjecture over closed 3-manifolds, which includes the Poincaré conjecture as a special case.

And it proved that Perelman is a very special person.