Think of play-dough.
If you make a ball of play-dough then stretch it or fold it or pinch it, it is still basically a ball of play-dough -- until you either pull it in two or poke a hole through it -- than it isn't like a ball of play-dough is a very fundemental way.
Furthermore, this is true for every dimension.
Easier said than proved.
Though proving P != NP does not necessarily give any insight to heuristics for NP problems. The fact, in and of itself, has no value in engineering. But it would be a significant proof and highly newsworthy.
Since both the P vs NP problem and the Poincare conjecture are pesky and hard problems that have received attention in the popular press, I would imagine, like you, it is worthy of mentioning on slashdot -- indeed if it wasn't mentioned here, slashdot would be suspect.
Why read Shakespeare?
Why listen to music composed by some dead guy?
Why go to see art hanging on a wall?
The proof of the Poincare Conjecture offers new insights into the human understanding of the advanced mathematics of topology and geometry. To ask, "what do we care?" is the archetypal philistine question. If you don't care, than you're not interested in knowledge... that's fine. But those of us who have studied these problems see a thing of beauty.
The question is, why don't you see a thing of beauty? Because you do not understand it or because your eyes are shut?
Slashdot Mirror
Think of play-dough. If you make a ball of play-dough then stretch it or fold it or pinch it, it is still basically a ball of play-dough -- until you either pull it in two or poke a hole through it -- than it isn't like a ball of play-dough is a very fundemental way. Furthermore, this is true for every dimension. Easier said than proved.
Though proving P != NP does not necessarily give any insight to heuristics for NP problems. The fact, in and of itself, has no value in engineering. But it would be a significant proof and highly newsworthy. Since both the P vs NP problem and the Poincare conjecture are pesky and hard problems that have received attention in the popular press, I would imagine, like you, it is worthy of mentioning on slashdot -- indeed if it wasn't mentioned here, slashdot would be suspect.
Why read Shakespeare? Why listen to music composed by some dead guy? Why go to see art hanging on a wall? The proof of the Poincare Conjecture offers new insights into the human understanding of the advanced mathematics of topology and geometry. To ask, "what do we care?" is the archetypal philistine question. If you don't care, than you're not interested in knowledge ... that's fine. But those of us who have studied these problems see a thing of beauty.
The question is, why don't you see a thing of beauty? Because you do not understand it or because your eyes are shut?