Happened to read a blog for poincare conjecture and its prove. This remind me of first impression of this conjecture long time ago, and think that this conjecture was not proved.

Yes, this is right, it is not proved, even its definition has some problem. For example, three dimension objects should have its correspoding surface defined as three dimensions as well, just as one dimension and two dimensions space define their surfaces as the same dimensions of their correspoding space dimensions. This will lead to the right connection definition. Connection problem is the core problem that need to be proved in the poincare conjecture. Wrong definition will lead to wrong conception of prove. The torus connection should change its definition and the band should go around the hollow circle which is the condition of violation. This can be the definition for axiomatized topological solid ball. Other topology connections should also be changed.

So, poincare conjecture could not have been proved. At least not properly proved.

I also read some Hamilton, and don't think he is a great mathematician. It seemed that he lacked the basic knowledge to be a mathematician. Other mathematicians like Hilbert etc. are not much qualified either.

Thanks everyone.