The Poincaré Conjecture has Been Proved 307
Martin Dunwoody, a famous mathematician who works in the field of topology has a preprint that provides a proof of the Poincaré conjecture. This was one of the seven Clay Mathematics Institute millenium prize problems (reported on Slashdot here). The solution to each of the problems carries a monetary reward of 1 million dollars. However there are a number of conditions that still need to be met for the prize to be awarded in the case of the Poincaré conjecture.
Wierd Problem (Score:3, Interesting)
English please! (Score:2, Interesting)
Re:In related news.... 4 = 5 (Score:2, Interesting)
Re:Proof (Score:3, Interesting)
-- Albert Einstein
Really, we do have proofs in physics(for example) that are just as provable as those in mathematics. You just have to understand that proofs of any kind are made based on certain assumtions (axioms + rules of logic).
For instance, the quantum no-cloning theorom states that you cannot exactly duplicate an unknown quantum mechanical state. This is an absolutely proven theorom -- one of the axioms of which is the Schrodinger equation. If we ever find that quantum mechanics is not the correct description for our universe, the no-cloning theorom will still be entirely valid within the constructs of QM, as well as the regime of the universe under which QM is applicable.
Likewise, Euclid said the sum of the angles of a triangle is Pi, but this is only true for trinagles in spaces that have a certain structure, which is why we call it Euclidian. It turns out that in general, space is non-Euclidian, though unless you are near a black hole or a neutron star, the difference is hardly noticable.
Computer scientists have "proven" using very general methods, that there are no algorithms for computing certain things that are faster than a given bound -- There is no way to search an unordered list in faster than O(N) time, no way to sort arbitrary numbers in less than O(N*Log(N)) time, etc. However, this is based on a Turing machine model of computation, and the laws of quantum mechanics as we understand them allow computers intrinsically more powerful than a turing machine. We still don't understand much about what these quantum computers can and can't do better than a classical computer, but we do know that they can search unordered lists faster than any classical computer, though I think it has been shown that they cannot sort lists faster than a classical computer.
Re:...has been "PROVEN", ...has been "PROVEN" (Score:3, Interesting)
Main Entry: prove
Pronunciation: 'prüv
Function: verb
Inflected Form(s): proved; proved or proven
You can say it either way. It's standard usage. Idiot.