jueves, 8 de julio de 2010


By: Felipe Argote

Because I was watching the soccer World Cup I did not finish what I had been building for years and was about to end: to solve the Poincare conjecture. Due to my negligence Grigori Parelman, a Russian mathematician, 44 years old, was ahead of me solving the puzzle.

I would not worry too much if it were not for the Clay Mathematics Institute had offered a million dollars to whoever solved the conjecture.

It was not so difficult. In 1904, a Frenchman named Henri Poincaré conjecture that the result obtained for the sphere n = 2 dimensional space 3 was an analogue for the field n= 3 of the 4-dimensional space. In other words, in four dimensional space, any variety of dimension n = 3, closed and simply connected, it would be homeomorphic to the sphere of dimension n= 3. But Poincaré, the mathematician who developed the so-called theory of relativity by Einstein then developed his theory of relativity was born in Meurthe-et -Moselle, Nancy, France, failed to verify his guess. This was more than 100 years ago, in 1904. From that point nobody had been able to confirm the guess until it was solved by Parelman. Maybe not this would have been at the news if it were not for the eccentric doctor rejected the prize of one million dollars.

It is not the first time Parelman rejects an award. Already in 2006 had rejected the award from the International Mathematical Union to mathematicians less than 40 years old for his contribution to the discipline.

Grigori Perelman was born in St. Petersburg in 1966 into a Jewish family. In 1982, at the age of 16 years represented the Soviet Union in international math Olympics where she won the gold medal. At the end of the eighties he earned a doctorate at the University of Leningrad. His thesis: Areas chair in Euclidean spaces. Lectured at the Steklov Institute in Russia, then he moved to lecturing at universities in New York, Stony Brook and Berkeley. But in 1995 he returned to the University of Steklov.

Today is said to Grigori Perelman is unemployed, and he has retired of any activity related to mathematics because of his disappointment over the ethics of the mathematical community in general. Moreover the solution of the Pointcare conjecture was not published in any scientific journal but in a website.

To get an idea of what we are talking let’s say that there are commonly four dimensions, three spatial and one temporal. If we draw a square it is two-dimensional. If, however, we draw a cube it is three dimensional. The fourth dimension is time. Then let’s use a hot item today: a soccer ball. This is a two-dimensional sphere in a three dimensional space. It is wide and long but not deep. This is a two dimensional case. Each piece of the sphere is not nothing but a flat piece bent slightly related. The term used to sound more complicated is homeomorphism. Then there is only one homeomomorfic variety of dimension n =2 closed and connected: this is the sphere or soccer ball. Ok ?

To test surround ourselves imagine that something elastic like a big gum. If we can compress it to make it a point not to step out of the surface we have an area two and it is a related area.

The problem is that Henri Poincaré conjecture introduced in 1904 that this result obtained for an area two, a soccer ball for example, in a three-dimensional space, had an analogous four-dimensional space in a sphere of dimension 3. Of course this is complicated to the point that it is very difficult to draw, but I will try. This should be seen like this:

This became one of the biggest problems of mathematics course with implications in physics and geometry until at last our friend Grigori rid us of this heavy burden. We can relax from this problem and return to our peaceful lives. To St. Petersburg where he lives with his mother retired at the age of… 44 years, we say:

Thanks Gregory

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