jueves, 8 de julio de 2010

GRIGORY AND THE POINCARÈ CONJETURE

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

WHY HOLLAND AND SPAIN ? WHY NOT ARGENTINA AND BRAZIL ?

By: Felipe Argote



After the drawing everybody knew what numbers were going out. Those are the "Monday morning break office coach" that is, the technical experts on Mondays in the recess of the office in the morning. Never mind. As this is not a sports blog and we spent the last month writing about South Africa, we need to do the analysis, although superficial, of what happened in the world cup. What led to the final to the Netherlands and Spain, while Latin American teams where let behind in the middle of the road.

I will not analize all Latin American countries, because the publisher is strictly on the number of bands that I use on each item, so that they are not that long that takes readers to boredom. Enough is to say that Mexico simply did not have enough. It had no human material to go further than they arrived and the coach Aguirre, who likes to kick opposite players, also has serious limitations. Much less Honduras with the loss of their best players even though many do not know that Honduras had a better line up than Mexico. Nor Chile, that although they have good players and had a good qualifying stage, these figures are not first class. Mad Bielsa, their coach at least did a better global role than in 2004, when he led Argentina, a great team, favored to win the World Cup and was out in the first round winning only one game to Nigeria. Paraguay did what they could without their top scorer Salvador Cabanas, who although only playing in Mexico, he should have to be playing in Europe for years.

Consider Argentina. Despite having an overwhelming front led by Messi, the best player in the world, Iguain, scorer of Real Madrid in the Spanish league, Tevez and Aguero suffered from the spine: they didn’t have a creator. Maradona 's thesis was that the axis of the equipment was to be Juan Sebastian Veron, the leader of the Estudiantes de la Plata football club. This did not work as Leo Messi finished playing the role of creator, to seek the ball down to the lack of this driver, therefore limited in their ability to get goals. Messi did what he could, but remember that he is not Xavi or Iniesta. In the generally he receives at Barza club passes from Xavi and Iniesta but they were not there, because they were busy playing in the Spanish team.

The case of Brazil is sadder. Dunga, a defender, who captained Brazil in 1984 and was coach of the Brazilian team at the World South Africa, decided to disappear Brazilian style, the famous Jogo Bonito, he said they had to choose between the jogo bonito, or to win games as if they were contradictory. So he not called Ronaldinho to the team, I know he is not still the best player in the world, but he is one of the best. In contrast to its ranks was Julio Cesar Baptista who almost did not play in the Rome of the Calcio. It was sad to see Brazil lose to Holland trying to play a practice football against a team that historically has the patent for the practical football: the so-called the mechanic orange.

The jogo Bonito instead was brought by Spain and a little by Germany because of his good creation midfield with Xavi and Iniesta in Spain and Bastian Schweinsteiger in Germany. Who would have thought...?

The next World Cup 1914 will take place in Brazil. It is time for Brazil to retrieve the style against Dunga's philosophy because that style is what has led them to five championships. Argentina should in turn take four years to get at least two midfielders of creation, to retire Veron and Riquelme.