The Poincaré conjecture is listed as one of the Millennium Prize Problems and has received significant attention from the media a few years ago when Grigori Perelman presented a proof of this conjecture. But why is this interesting at all? What practical and interesting questions can be answered now that this conjecture is proven?
What is the importance of the Poincaré conjecture?
22
$\begingroup$
general-topology
manifolds
low-dimensional-topology
-
8The Poincare conjecture was not deemed interesting because of practical questions -- it won't help you build a more efficient washing-machine, if that's what you're after. If you want to understand why people care about the Poincare conjecture you should start with a more elementary question "why do people care about manifolds?" – 2010-11-05
-
1The various Wikipedia pages describing "Manifolds" would be a good start. – 2010-11-05
-
4My answer to this would perhaps be a combination of my answers in these two threads: http://math.stackexchange.com/questions/8808/why-the-interest-in-locally-euclidean-spaces/8863#8863 http://math.stackexchange.com/questions/2755/2771#2771 – 2010-11-05