few mathematical theories so excited far from abstract geometric reasoning public, like this one.Poincare conjecture put forward in 1887 by the French mathematician Henri Poincare, more than a hundred years it haunted the scientists from different countries.She became interested in not only the geometry, but also physics, and even ... the security services.Therefore, such a sensation caused a message stating that the secret of the hypothesis on which to puzzle many bright minds, finally opened, and the Poincare proved.Fuel to the fire poured the national interest and the fact that prove the theory scientist - Russian mathematician Grigory Perelman - in 2006, refused to award him the Fields Prize mathematical (and its attendant million).He did not react to the awarding of a scientist and his Millennium Prize Clay Mathematics Institute.
However, - the reader will ask, far from mathematics - why is it such an interest in the Poincaré conjecture?And why is it proof of paying so much money?To do this, albeit in very general terms, it is necessary to characterize what is this hypothesis within such areas of mathematics as topology.Imagine a little inflated balloon.If his crush, you can give it different forms: the cube, the sphere and even oval shapes of humans and animals.But all this variety of geometric shapes can be converted into a universal form - the ball.Only in that it can not turn without tearing the ball - is to form a hole, such as a bagel.
Poincare conjecture claimed that all of the items that do not have the through holes have a base - ball.But the body having a hole (called the mathematics of the torus, but we will let the "donut") are compatible with each other, but with solid bodies.For example, if we blindly plasticine cat, we can umyat it into a ball and from the blind without using the breaks, hedgehog or rail.If we blindly bagel, we can deform it in the "eight" or circle, but in the ball will not succeed.Torus and Sphere incompatible - in mathematical language homeomorphic.
remarkable that evidence of this theory is not so much interested in mathematics as astrophysics.If the theory of Poincare applies to all material bodies in the universe, why not imagine for a moment that it is also true of the universe itself?What if the whole matter came from a small, one-dimensional point and now takes place in a multi-dimensional sphere?And where are its borders?And abroad?And what if you find the clotting mechanism of the universe back to the starting point?As proof of his hypothesis, the author made a mistake, a lot of mathematicians and physicists, have fallen under the spell of the Poincaré conjecture, selflessly began to work on her evidence.Several of them - DG Whitehead, Bing, K. Papakiriakopoulos, Smale, M. Friedman - put their lives on the proof of the Poincare theory.
But as a result of the laurels went to the Petersburg obscure scientist Perelman, although formally - in the pages of peer-reviewed journals - his testimony and did not see the light.Work Gregory Yakovich was posted at arXiv.org in 2002, but, nevertheless, made in the scientific world the effect of an exploding bomb.Since the eccentric mathematician did not even bother "polish" their evidence, some scientists have decided to seize the laurels of the discoverer.So, Chinese mathematicians Huaydun Zhu Xiping and Cao called Perelman's proof intermediate, and extending it.However, the award of the Millennium Prize Russia mathematician (although he refused to receive it) put the record straight "i": the Poincaré conjecture was proved by Perelman.When reporters still managed to interview a brilliant mathematician, asked why he declined the award of one million dollars, there was a strange answer: "If I speak of the universe, then why should I in that case a million?»
