Has the Poincare Conjecture Finally Been Solved?

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    Conjecture Poincare
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SUMMARY

Grigory Perelman has solved the Poincare Conjecture, with a proof expected to be published soon in the arXiv under Differential Geometry. This breakthrough is anticipated to have significant implications in both mathematics and physics. The discussion highlights the excitement surrounding this development and compares it to other unsolved problems, such as the P=NP problem and the Riemann hypothesis. The emotional impact of such discoveries is also noted, referencing Andrew Wiles' experience with Fermat's Last Theorem.

PREREQUISITES
  • Understanding of Differential Geometry
  • Familiarity with the Poincare Conjecture
  • Knowledge of major unsolved problems in mathematics, such as P=NP and the Riemann hypothesis
  • Awareness of the implications of mathematical proofs in physics
NEXT STEPS
  • Read Grigory Perelman's papers on the Poincare Conjecture in the arXiv
  • Explore the implications of the P=NP problem on computational theory
  • Study the Hodge Conjecture and its significance in algebraic geometry
  • Investigate the historical context and impact of Andrew Wiles' proof of Fermat's Last Theorem
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Mathematicians, theoretical physicists, and anyone interested in the latest developments in topology and unsolved mathematical problems.

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Mathematicians are now saying that Grigory Perelman has really solved the conjecture and the proof will be in a paper he will post in the near future. His previous papers on this subject are in the arxiv specal topic Differential Geometry (under mathematics). Keep your eyes on this space!
 
Physics news on Phys.org
This story even http://edition.cnn.com/2004/US/West/01/07/math.mystery.ap/index.html

Any thoughts from the number-theory experts here?
 
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Heck! Now i only have 6 problems to achieve the million of dollars.
Which I will choose? The P=NP problem? The Hodge conjecture? The Riemann hypothesis not, for sure it must the most investigated by now of the 6.
It's a pity that I don't understand completely the statement of the Poincare conjecture. It surely must be a very beautiful sensation to achieve to understand the prove of the conjecture. and I think that the prove will have repercussions in the world of physics
 
Originally posted by meteor
Heck! Now i only have 6 problems to achieve the million of dollars.
Which I will choose? The P=NP problem? The Hodge conjecture? The Riemann hypothesis not, for sure it must the most investigated by now of the 6.
It's a pity that I don't understand completely the statement of the Poincare conjecture. It surely must be a very beautiful sensation to achieve to understand the prove of the conjecture. and I think that the prove will have repercussions in the world of physics
The P=NP problem; the ramifications could boost the world's GDP by several % in one fell swoop (or not; depends on what you prove :wink: ).

Did anyone else see the TV program on Wiles and Fermat? In it, Wiles attempted to explain what it felt like; as good a practical demonstration of 'rapture' as any, I feel.

More exciting than proving the 4-colour theorem, that's for sure. :smile:
 
Well, we don't know how the computer felt.
 

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