I wonder if their is any technological implementation from solving poincare conjecture outside the mathematics. I am not a mathematician but I suspect their is.
Any practical application of solving poincare conjecture
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Re: Any practical application of solving poincare conjecture
#2No. The proof itself is totally useless, the technological consequences of it are nonexistent.
The interesting part are the tools developed to solve it and a better understanding about the geometrical properties of the euclidean space.
Mathematics is interesting and useful because it gives us tools for investigation abstract problems. The proof of one particular theorem is rarely more interesting then the mathematical foundations behind it.
Behind the Riemann hypothesis you will find a century of deep investigation into the structure of 3D space and its foundations, with incountably many applications. The proof of the theorem was a prestige object, demonstrating that the proover had a very deep grasp on the subject matter. But even in this case, the Ricci Flow is probably a far more interesting object from a technological perspective.