Poincare conjecture is one of the mathematical theorems that has been
demonstrated recently passably to the point that it can be taken as a
full theorem. You can find various definitions for Poincare Conjecture
on different websites. For example, according to Wikipedia "In
mathematics, the Poincare conjecture (French, ) is a theorem about the
characterization of the three-dimensional sphere among three-dimensional
manifolds."
Poincare conjecture has been one of the seven Millennium Prize Problems and above all, this is the first ever and only Millennium Prize Problem that has been solved. The Poincare Conjecture states that if a compact 3-D manifold has no boundary and is simply connected, then it is said to be homeomorphic to a 3-D sphere. This conjecture is believed to have been formulated in 1904 by Henri Poincare, a French mathematician, as an elemental for achieving a perceptive of three dimensional shapes, 3-D sphere being the simplest one.
This conjecture was recently provided with a breakthrough proof by numerous new elements introduced by Perelman. He gained complete perceptive of singularity formation in Ricci flow, in addition to the manner of collapsing of the parts of a shape onto lower-dimensional spaces. He solved the problem by introducing entropy as a new quantity. This entropy measures the disorder in the space's global geometry instead of measuring the disarray at the atomic level. Besides, he also pioneered a related local quantity, the L-functional, which was used that proved that the time between the configuration of singularities could not become smaller and smaller.
Perelman has enriched mathematics by deploy his new ideas and methods with utmost technicalities and describing the obtained results with elegant succinctness.
The interesting fact is that Grigory Perelman declined the prize of one million dollars which comes with the Fields medal which is equivalent of the Nobel Prize for mathematics. Perelman is currently unemployed living with his mom in a small apartment near St. Petersburg. Interfax, a Russian news agency, quoted him as saying. "To put it short," he said, "the main reason is my disagreement with the organized mathematical community. I don't like their decisions; I consider them unjust."
Poincare conjecture has been one of the seven Millennium Prize Problems and above all, this is the first ever and only Millennium Prize Problem that has been solved. The Poincare Conjecture states that if a compact 3-D manifold has no boundary and is simply connected, then it is said to be homeomorphic to a 3-D sphere. This conjecture is believed to have been formulated in 1904 by Henri Poincare, a French mathematician, as an elemental for achieving a perceptive of three dimensional shapes, 3-D sphere being the simplest one.
This conjecture was recently provided with a breakthrough proof by numerous new elements introduced by Perelman. He gained complete perceptive of singularity formation in Ricci flow, in addition to the manner of collapsing of the parts of a shape onto lower-dimensional spaces. He solved the problem by introducing entropy as a new quantity. This entropy measures the disorder in the space's global geometry instead of measuring the disarray at the atomic level. Besides, he also pioneered a related local quantity, the L-functional, which was used that proved that the time between the configuration of singularities could not become smaller and smaller.
Perelman has enriched mathematics by deploy his new ideas and methods with utmost technicalities and describing the obtained results with elegant succinctness.
The interesting fact is that Grigory Perelman declined the prize of one million dollars which comes with the Fields medal which is equivalent of the Nobel Prize for mathematics. Perelman is currently unemployed living with his mom in a small apartment near St. Petersburg. Interfax, a Russian news agency, quoted him as saying. "To put it short," he said, "the main reason is my disagreement with the organized mathematical community. I don't like their decisions; I consider them unjust."
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