The hypothesis presented in 1887 by Henri Poincaré excited the public almost immediately after the appearance. “Every closed n-dimensional manifold is homotopy equivalent to an n-dimensional sphere if and only if it is homeomorphic to it” - this is how this hypothesis sounds.

Over it, scientists - geometers and physicists from around the world unsuccessfully puzzled. This went on for about 100 years. The disclosure of the secret of approval in 2006 was a real sensation. And most importantly - the proof of the theorem was presented Russian mathematician Grigory Perelman.

Questions related to the two-dimensional sphere were understood in the nineteenth century. The positions of multidimensional objects are defined in the 1980s. Complexity was created only by the definition of three-dimensional objects. In 2002, the Russian scientists used the equation of "smooth evolution" to prove it. Thanks to this, he was able to determine the ability of three-dimensional surfaces without discontinuities to deform into three-dimensional spheres. The definition presented by Perelman aroused the interest of many scientists, who confirmed that this is a solution of the modern generation, which opens up new horizons for science, providing ample opportunities for further discoveries.

The theory presented by Russian scientists had many shortcomings and required a number of improvements. In this regard, scientists took up the search for evidence of an explanation.Some of them have spent their whole lives doing this.

Poincare conjecture in simple language

Briefly, the theory can be deciphered in several sentences. Imagine a slightly deflated balloon. Agree, this is not at all difficult. It is very easy to give it the necessary shape - a cube or an oval sphere, a person or an animal. The affordable variety of shapes is simply impressive. Moreover, there is a form that is universal - a ball. At the same time, a shape that cannot be given to a ball without resorting to tears is a donut - a shape with a hole. According to the definition given by the hypothesis, objects in the form of which a through hole is not provided have the same basis. A good example is a ball. In this case, bodies with holes, in mathematics they are given the definition - torus, are distinguished by the property of compatibility with each other, but not with solid objects.

For example, if we want, then without problems we can fashion a hare or a cat from plasticine, then turn the figure into a ball, then into a dog or an apple. In this case, you can do without gaps. In the event that the bagel was originally fashioned, then it can make a circle or a figure eight, it will not be possible to give the mass the shape of a ball. The presented examples clearly show the incompatibility of the sphere and the torus.

Poincaré conjecture application

Understanding the meaning of the Poincaré hypothesis along with the definition of the discovery made by Gregory Perelman will allow us to deal with this statement much faster.The hypothesis can be applied to all material objects of our universe. At the same time, its fidelity and the applicability of the provisions directly to the Universe are perfectly acceptable.

It can be assumed that the beginning of the appearance of matter was an insignificant point of the one-dimensional type, which is now being formed into a multidimensional sphere. Accordingly, many questions arise - is it possible to find boundaries, to identify a single mechanism of coagulation of the object to its original state, etc.

It was mathematically proved to Russian scientists that if a surface is simply connected, it is not a donut, then as a result of deformation, which ensures complete preservation of the characteristics of the surface under study, it is possible to easily and simply obtain a watermelon or, more simply put, a sphere. It can be any round object, which without any difficulties can be pulled to a point. Wrapping a sphere can be done using ordinary lace. Subsequently, the cord can be tied into a knot. You can’t do the same with the bagel.

The simplest model representing a ball can be collapsed into a dot. If the Universe is a ball, it means that it can also be rolled up to one point, and then deployed again. Thus, Perelman shows his ability to theoretically control the universe.