Solving of the Poincare' Conjecture

In summary, the Poincare' Conjecture is a mathematical problem proposed by Henri Poincare' in 1904 stating that any three-dimensional object without holes can be deformed into a sphere. It is important because it is one of the biggest unsolved problems in mathematics and has implications in various fields. The conjecture was solved by Grigori Perelman in 2002-2003 using a technique called Ricci flow, and his proof was later verified by other mathematicians. The solution of this conjecture has led to advancements in various fields of mathematics and has opened up new possibilities for solving other problems. The Poincare' Conjecture has been officially proven, but Perelman declined to accept awards for his
  • #1
vincentm
323
3
Ok first i'd like to note that I'm not good at mathematics and have a vague understanding of the conjecture. What i'd like to know though is what comes now that this has been solved by Perelman? What implications does this have?
 
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  • #2
It is hopeless in a few words.

Read the "Shape of Space". You don't need any more than high school math and by its end you will an intuitive idea of what the conjecture is about. (Do all the problems too!)
 
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Related to Solving of the Poincare' Conjecture

1. What is the Poincare' Conjecture?

The Poincare' Conjecture is a mathematical problem that was first proposed by French mathematician Henri Poincare' in 1904. It states that any three-dimensional object that is topologically equivalent to a three-dimensional sphere is in fact a three-dimensional sphere. In simpler terms, it means that any object without holes can be deformed into a sphere.

2. Why is the Poincare' Conjecture important?

The Poincare' Conjecture is important because it is one of the biggest unsolved problems in mathematics. It has implications in various fields of mathematics, including topology, geometry, and differential equations. Its solution would also provide a deeper understanding of the structure of three-dimensional space.

3. How was the Poincare' Conjecture solved?

The Poincare' Conjecture was solved by Russian mathematician Grigori Perelman in 2002-2003. He used a technique called Ricci flow, which involves continuously deforming the shape of an object while preserving its essential properties. Perelman's proof was later verified by other mathematicians, and he was awarded the Fields Medal in 2006 for his achievement.

4. What are the implications of solving the Poincare' Conjecture?

Solving the Poincare' Conjecture has led to advancements in various fields of mathematics, including topology, geometry, and differential equations. It has also inspired further research and new techniques in these areas. Additionally, the solution of this conjecture has also opened up new possibilities for solving other mathematical problems.

5. Has the Poincare' Conjecture been officially proven?

Yes, the Poincare' Conjecture has been officially proven by Grigori Perelman in 2002-2003. His proof has been verified by other mathematicians, and his achievement has been recognized by the mathematical community. However, Perelman declined to accept the Fields Medal and other prestigious awards for his solution of the conjecture.

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