22
$\begingroup$

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?

  • 8
    The 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
  • 1
    The various Wikipedia pages describing "Manifolds" would be a good start.2010-11-05
  • 4
    My 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#27712010-11-05

3 Answers 3