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Russian Mathematician proves Poincare's conjecture, drops out of sight.

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NNadir Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 07:26 AM
Original message
Russian Mathematician proves Poincare's conjecture, drops out of sight.
Maybe the guy just wants to get some work done:

Grisha Perelman, where are you?

To a topologist, a rabbit is the same as a sphere. Neither has a hole. Longitude and latitude lines on the rabbit allow mathematicians to map it onto different forms while preserving information.
Three years ago, a Russian mathematician by the name of Grigory Perelman, a k a Grisha, in St. Petersburg, announced that he had solved a famous and intractable mathematical problem, known as the Poincar conjecture, about the nature of space.

After posting a few short papers on the Internet and making a whirlwind lecture tour of the United States, Dr. Perelman disappeared back into the Russian woods in the spring of 2003, leaving the worlds mathematicians to pick up the pieces and decide if he was right.

Now they say they have finished his work, and the evidence is circulating among scholars in the form of three book-length papers with about 1,000 pages of dense mathematics and prose between them.

As a result there is a growing feeling, a cautious optimism that they have finally achieved a landmark not just of mathematics, but of human thought...

...The conjecture is fundamental to topology, the branch of math that deals with shapes, sometimes described as geometry without the details. To a topologist, a sphere, a cigar and a rabbits head are all the same because they can be deformed into one another. Likewise, a coffee mug and a doughnut are also the same because each has one hole, but they are not equivalent to a sphere.

In effect, what Poincar suggested was that anything without holes has to be a sphere. The one qualification was that this anything had to be what mathematicians call compact, or closed, meaning that it has a finite extent: no matter how far you strike out in one direction or another, you can get only so far away before you start coming back, the way you can never get more than 12,500 miles from home on the Earth.

In the case of two dimensions, like the surface of a sphere or a doughnut, it is easy to see what Poincar was talking about: imagine a rubber band stretched around an apple or a doughnut; on the apple, the rubber band can be shrunk without limit, but on the doughnut it is stopped by the hole...

Grisha Perelman, where are you?

To a topologist, a rabbit is the same as a sphere. Neither has a hole. Longitude and latitude lines on the rabbit allow mathematicians to map it onto different forms while preserving information.
Three years ago, a Russian mathematician by the name of Grigory Perelman, a k a Grisha, in St. Petersburg, announced that he had solved a famous and intractable mathematical problem, known as the Poincar conjecture, about the nature of space.

After posting a few short papers on the Internet and making a whirlwind lecture tour of the United States, Dr. Perelman disappeared back into the Russian woods in the spring of 2003, leaving the worlds mathematicians to pick up the pieces and decide if he was right.

Now they say they have finished his work, and the evidence is circulating among scholars in the form of three book-length papers with about 1,000 pages of dense mathematics and prose between them.

As a result there is a growing feeling, a cautious optimism that they have finally achieved a landmark not just of mathematics, but of human thought...

In a series of postdoctoral fellowships in the United States in the early 1990s, Dr. Perelman impressed his colleagues as a kind of unworldly person, in the words of Dr. Greene of U.C.L.A. friendly, but shy and not interested in material wealth...





http://www.nytimes.com/2006/08/15/science/15math.html?p...
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whistle Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 07:31 AM
Response to Original message
1. So, is it faster to Peoria or by bus?
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Nay Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 07:35 AM
Response to Original message
2. I only know a tiny bit about topography--4-color map, etc., so can
someone expound on the real-world implications of this?
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NNadir Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 09:32 AM
Response to Reply #2
7. Here is a reference work on applications of topology.
http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471...

Topics include open sets, compactness, homotopy, surface classification, index theory on surfaces, manifolds and complexes, topological groups, the fundamental group and homology. Modern applications of topology have played an important role solving a diverse spectrum of applied problems. In this text serious attention is given to recent applications of topology in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, population modeling and other areas of science and engineering. Most applications are presented in optional sections, allowing an instructor to customize the presentation.


Topological methods are important in the study of relativity. The mechanisms of many important chemical reactions are understood topological.

Topography and topology are related by the way, but not identical.
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Richard Steele Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 07:40 AM
Response to Original message
3. Insert "rabbit hole" joke HERE. nm
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annabanana Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 07:45 AM
Response to Reply #3
4. but really, the rabbit would be a donut....
(It IS skin tissue that lines the digestive tract)
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Nay Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 08:29 AM
Response to Reply #4
5. I wondered about that, too. According to the docs, the alimentary
canal, through the stomach and intestines and out the anus, well, it's all "outside." Making the rabbit, and the human, really a donut.
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Richard Steele Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 09:31 AM
Response to Reply #5
6. So the rabbit is just a soft, wet variation of the "Klein bottle"...
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unpossibles Donating Member (1000+ posts) Send PM | Profile | Ignore Tue Aug-22-06 02:11 PM
Response to Reply #6
22. there's a mental image I didn't need....
wait, yes I did.

;)
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NNadir Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 09:56 AM
Response to Reply #4
9. So much for science reporting from the NY Times.
:toast:
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phantom power Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 10:06 AM
Response to Reply #4
10. It's worse, the rabbit has more holes than a donut...
The nasal passages connecting to the esophagus!
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NNadir Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 01:50 PM
Response to Reply #10
12. Without claiming proficiency in rabbit anatomy, I believe that the
sinuses of the donut-rabbit are continuous with the alimentary canal of the rabbit.

This, I believe, gives the rabbit donut status.

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bananas Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 09:27 PM
Response to Reply #10
14. What about the ear canals?

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hunter Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Aug-21-06 02:21 PM
Response to Reply #4
16. A sea anemone, on the other hand is a sphere...
What they eat they spit back out the same opening again once it is digested.
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screembloodymurder Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 09:54 AM
Response to Original message
8. Think 2-D.
Is there really any difference between a triangle and a circle?
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Igel Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 10:51 AM
Response to Reply #8
11. Discontinuities?
Or can those be done away with?
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Ready4Change Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Aug-21-06 10:47 PM
Response to Reply #8
19. I get your point.
Hey, wait a sec...
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Xipe Totec Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 08:53 PM
Response to Original message
13. 'scuse me, but to a topologist, a rabbit is not a sphere
it is a donut.
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valerief Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Aug-20-06 10:26 PM
Response to Original message
15. self delete
Edited on Sun Aug-20-06 10:28 PM by valerief
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hunter Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Aug-21-06 02:26 PM
Response to Original message
17. If I had a dime for every odd mathematician I've met...
My favorite always wore cowboy boots.
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NNadir Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Aug-21-06 08:55 PM
Response to Reply #17
18. Hopefully - or maybe sadly - he or she wore something other than
cowboy boots, like underwear and overwear.

I don't think I could deal completely with a naked mathematician dressed only in cowboy boots.
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dipsydoodle Donating Member (1000+ posts) Send PM | Profile | Ignore Tue Aug-22-06 08:10 AM
Response to Original message
20. He's back -well sort of any
Maths genius declines top prize

Perelman is said to shun self-promotion

Grigory Perelman, the Russian who seems to have solved one of the hardest problems in mathematics, has declined one of the top prizes in maths.

http://news.bbc.co.uk/1/hi/sci/tech/5274040.stm?ls
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NNadir Donating Member (1000+ posts) Send PM | Profile | Ignore Tue Aug-22-06 11:36 AM
Response to Reply #20
21. I wonder what he's living on.
He clearly just wants to be left alone though. It's his perogative. He doesn't owe anyone an explanation.
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NickB79 Donating Member (1000+ posts) Send PM | Profile | Ignore Thu Aug-31-06 03:37 PM
Response to Reply #21
23. He tried to live off the land
But his rabbit stew tasted like rocks and sticks for some reason....
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