Pointcare Conjecture - Grigory Perelman's Proof

In summary, the conversation discusses Perelman's proof of the Pointcare conjecture and its potential repercussions in practical applications. A link to an article on Perelman and the conjecture is provided, as well as comments from mathematician John Morgan confirming the correctness of the proof.
  • #1
Chaos' lil bro Order
683
2
Greetings,

I'm far from a skilled mathematician and I was wondering what greater minds than mine thought of Perelman's proof of the Pointcare conjecture. Also, if you could offer a brief explanation of the conjecture it would be very much appreciated.

Here is a link to a bried article on Perleman and the conjecture:
http://www.shoutwire.com/viewstory/46760/Math_Solution_Tops_Science_Class


What reprecussions will proving this conjecture mean to you and me in terms of practical applications?
 
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  • #3
john morgan of columbia says the proof is correct, and he has written a more detailed version of it. if john morgan believes it then i believe it is correct.
 

1. What is the Pointcare Conjecture?

The Pointcare Conjecture is a mathematical problem that was first proposed in the 19th century by Henri Poincaré. It states that any closed three-dimensional manifold (a type of geometric shape) is topologically equivalent to a three-dimensional sphere. In simpler terms, it is asking whether any shape in three-dimensional space can be stretched and deformed into a perfect sphere.

2. Who is Grigory Perelman?

Grigory Perelman is a Russian mathematician who is known for solving the Pointcare Conjecture. He was born in 1966 and received his Ph.D. from the St. Petersburg State University in 1996. He is also known for his contributions to the field of geometric analysis and the study of Ricci flow.

3. How did Grigory Perelman solve the Pointcare Conjecture?

Perelman used a combination of complex mathematical techniques, including Ricci flow and geometric analysis, to prove the Pointcare Conjecture. He published his proof in three papers, which were later compiled into a single paper in 2003. His work was widely acclaimed in the mathematics community and he was awarded several prestigious awards, including the Fields Medal, for his achievement.

4. Is the Pointcare Conjecture now considered a proven theorem?

Yes, Perelman's proof of the Pointcare Conjecture is widely accepted by the mathematics community. In 2006, the Clay Mathematics Institute officially recognized his proof and awarded him the Millennium Prize for solving one of the seven most important unsolved mathematical problems. However, Perelman declined the prize and has also declined other prestigious awards for his work.

5. What impact has the proof of the Pointcare Conjecture had on the field of mathematics?

The proof of the Pointcare Conjecture has had a significant impact on the field of mathematics. It has solved one of the most important unsolved problems in mathematics and has opened up new avenues for research in geometric analysis and topology. It has also led to further developments and applications in other areas, such as physics and computer science.

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