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Poincare conjecture

 
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CNN - Russian solves historic math problem, shuns prize.
 
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It had proved a theorem about the nature of multidimensional space that has stumped people for 100 years.



I always wondered how do you know you proved something when that something is not observable. Of course, I am assuming the theorem is for more than three dimensions.

Henry
 
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Math has always confused me in that way. In science, something is "proven" if it cannot be disproved through experimentation.

In math, well...I guess that's why I gave up my math major around the time of Theoretical Calculus.
 
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This is one of the seven millenium problems. And now there are six unsolved. I think P = NP? is one of them...

Wow!
 
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Originally posted by Henry Wong:
I always wondered how do you know you proved something when that something is not observable.



It must be easy for you to prove something like "all diagonals in a square are equal". You just observe it.



 
marc weber
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Originally posted by N Kriplani:
This is one of the seven millenium problems. And now there are six unsolved. I think P = NP? is one of them...


Yes, as is the Riemann hypothesis. ( )
 
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well , the problem itself seems a bit difficult to understand(Maybe easier for the mathematicans),
isnt there a "poincare conjecture" for the dummies?

Like relativity for the dummies:
"When you sit with a nice girl for two hours, it seems like two minutes. When you sit on a hot stove for two minutes, it seems like two hours that's relativity."

And does it have a practical application?
 
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[Henry]: I always wondered how do you know you proved something when that something is not observable. Of course, I am assuming the theorem is for more than three dimensions.

I don't pretend to know how they prove it, but apparently the problem had already been solved for n > 3, as well as for n = 1 and n = 2. So solving it for n = 3 was the last remaining problem within the scope of the Poincare conjecture.

[Roger]: isnt there a "poincare conjecture" for the dummies?

Um, I'm not sure that relativity example contains much useful information. But you may be able to get at least that much info from the beginning of the description here.

[Roger]: And does it have a practical application?

Maybe, if you're say, creating a universe. Or seeking to understand the one you're in. Seriously, in discussions of general relativity and cosmology, when they talk about the universe being like a big sphere (or maybe something more complex, like a doughnut), that's the sort of thing that the Poincare conjecture is talking about. I think.
 
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Here is a more detailed account of the "Grisha Perelman, where are you?" problem. It also explains a bit about Poincare conjecture.
 
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I have always been thinking that in our era, is there somebody among the scientific commnunity who is as famous as a Newton or a Einstein so as to become household names. Of course there's always a Stephen Hawking, Roger Penrose...but still...

Perelman definitely falls under this category and after reading Map's link, it seems he has the all qualities of that genre - brilliant, shy, reclusive and to top it all - humble, a quality which I admire in great people.

I hope he accepts the awards ...
[ August 23, 2006: Message edited by: Raghav Sam ]
 
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Here's a recent (from next Monday) New Yorker article on the topic.
 
Mapraputa Is
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�Everybody understood that if the proof is correct then no other recognition is needed.�

I can understand why he rejected a million prize. If I solved problem, maybe I would be not interested in a million either.

Perelman�s father, who was an electrical engineer, encouraged his interest in math. <...> � Among the books his father gave him was a copy of �Physics for Entertainment,� which had been a best-seller in the Soviet Union in the nineteen-thirties.

"Physics for Entertainment" was a terribly popular book in the Soviet Union -- and not only in nineteen-thirties! I had a copy, and I loved this book. What the author forgot to say, is that the book was written by an author whose last name was Perelman. Consequently, if you search the Ruissian net, you will find arctiles that claim that Grisha Perelman is a son of Jakov Perelman, the author of the �Physics for Entertainment�. The fact that Jakov died in Leningrad's blockade in 1941-42, and Grisha was born in 1966 bothers nobody.
 
stara szkapa
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Originally posted by Mapraputa Is:
[QBI can understand why he rejected a million prize.[/QB]



Well; If he accepted the prize, he would have to move out of his mother place. It might be more difficult then solving the puzzle.
 
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whateveah, stara szkapa.
 
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Me: Consequently, if you search the Ruissian net, you will find arctiles that claim that Grisha Perelman is a son of Jakov Perelman, the author of the �Physics for Entertainment�.

What's worse, you will read that Jakov Perelman, when dying, asked his son "to solve Poincare conjecture"...
 
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From what I understand, the poincare conjecture deals in the subject of algebraic topology, in particular homology theory. These kinds of problems deal with space in a very general sense. This kind of thinker would assume, for example, that it is possible to draw a map outlining all the surface of ins and outs of your average hunk of swiss cheese; however, he would never bother to actually do it. He's more interested in whether or not his cheese has the same structure of holes as his coworker's cheese. Most of the nontrivial proofs that I've seen in homology involve reducing exotic shapes into collections of magic spheres, which you can bend and stretch any way you want, but you can't poke a hole in them. Then it gets complicated when you start thinking about spheres of different dimensions, for example the unit circle is considered a lower dimensional sphere. You have to start thinking about shapes in relation to their boundaries, and the boundaries as objects in themselves.

With all this in mind I still have to confess that I do not understand any proof of the poincare conjecture.

Chris Arthur
doctoral student, mathematics
 
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