News: Poincare's Conjecture Finally Proved (?)
- Well, it might be the case that this problem is finally solved by
Dunwoody. Check out this link and download the paper:
It's only 5 pages long! Gee, this guy could be a millionaire (and
some people say that Maths doesn't pay).
Briefly, for those of you who don't know about this conjecture:
Poincare has conjectured that every simply connected closed 3-
manifold is homeomorphic to the 3-sphere. Actually, what is now known
as Poincare's conjecture is a generalization of the previous
statement for any dimension. It has been shown for all n except 3!
And now, Dunwoody claims he's got a 5 pages proof for the (original)
n=3 case. The Clay Institute offers a Million Dollars reward for the
mortal who proves it (but imposes many conditions too!).
His prospective proof is based on an algorithm (by Rubinstein) which
shows how to recognize a 3-sphere (Thompson).