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What is the importance of the Poincaré conjecture?

It is rather well known that Poincare conjecture was proved by Perelman in 2003 given the amount of coverage it received (for instance in the New York Times and Nasar and Gruber's highly controversial piece in the New Yorker). Furthermore was one of the Clay Millenium Prize problems.

Despite having known about this conjecture for awhile now I'm not really sure of its significance.

For instance one of the implications of the Birch and Swinnerton-Dyer conjecture is an algorithm that will allow us to compute the Mordell-Weil rank of an elliptic curve. The Riemann hypothesis will give us tight bound on the error term of $Li(x)$, which tells us something about the distribution of primes. The $P = NP$ conjecture will tell us that non-deterministic polynomial time algorithms are in fact polynomial-time algorithms (I'll stop here since I don't know the Hodge conjecture, Navier-Stokes or Yang-Mills).

So what is the significance of the Poincare conjecture (theorem now I guess) in math or outside of it?

Eugene
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