Posted on 09/06/2004 3:06:46 PM PDT by Willie Green
For education and discussion only. Not for commercial use.
One of the seven great unsolved mysteries of mathematics may have been cracked by a reclusive Russian who is not remotely interested in the £560,000 prize his solution could win him, it emerged today.
The Poincare Conjecture involves the study of shapes, spaces and surfaces and makes predictions about the topology of multi-dimensional objects.
Basically, it says that a three-dimensional sphere can be used in an analogous way to describe higher-dimensional objects that are impossible to visualise.
Since Henri Poincare suggested the theorem in 1904, some of the greatest mathematicians of the 20th century have struggled to prove it either right or wrong.
All have failed. But now the world of maths is buzzing with the news that an answer might at long last have been found.
Dr Grigori Perelman, from the Steklove Institute of Mathematics at the Russian Academy of Sciences in St Petersburg, has published two papers offering a solution to a larger-scale problem called the Geometrization Conjecture.
This is also concerned with geometry, and experts say that contained within it is proof that the Poincare Conjecture works.
If Perelman can satisfy his peers that this is the case, he stands to win a one million dollar cash prize from the Clay Mathematics Institute in the United States.
The Institute is offering million dollar prizes for solutions to each of the mathematical conundrums it calls the Seven Millennium Problems.
But there is a more fundamental problem the general community of mathematicians needs to solve first. Perelman does not seem to be interested.
Dr Keith Devlin, a leading mathematician from Stanford University in California, explained: “He´s very reclusive, and won´t talk to anyone. He´s shown no indication of publishing this as a paper, and he´s shown no interest in the prize whatsoever.
“Has it been proved? We don´t know, but there´s good reason to think it has been. My guess is that in about 12 months people will start to say okay, this is right, but there´s not going to be a golden moment.”
Dr Perelman published his two papers in November, 2002 and March last year.
A third is yet to be published.
By all accounts, Poincare will come out of the first two papers, said Dr Devlin.
If the conjecture was proved it would have profound ramifications, he told the British Association Festival of Science at the University of Exeter.
Scientists working on the frontiers of cosmology and physics frequently dealt with hyperdimensions. A solution to the Poincare Conjecture would greatly increase their understanding of the shape of the universe.
Dr Devlin compared proving Poincare with setting off an avalanche. If you are on top of a mountain, and it is spring, and you jump up and down, a little bit of snow moves. But at the bottom a whole lot of snow comes down.
“It can´t fail to have enormous implications; it will just be huge.”
He said solving mathematical problems such as the Poincare Conjecture was more like writing a story than doing a sum, which was why it took so long.
“It´s just so damn complicated, he said. It really can take two or three years to certify the thing.”
Proving the Poincare Conjecture would be the first great mathematical breakthrough since Andrew Wiles solved Fermats Last Theorem in 1994.
This year, Professor Louis de Branges de Bourcia, from Purdue University in the United States, claimed to have proven another of the Millennium Problems called the Riemann Hypothesis.
The hypothesis is a 150-year-old theory about Prime Numbers – numbers that divide only by one and themselves and are considered the atoms of arithmetic.
De Branges claimed to have confirmed a conjecture made by the German mathematician Bernhard Riemann in 1859 about the way prime numbers were distributed.
But, unlike in the case of Poincare Conjecture, the worlds mathematicians are becoming increasingly convinced that he has got it wrong.
Marcus du Sautoy, Professor of Mathematics at Oxford University, said: “The mathematical community is sceptical whether the methods of Louis de Branges are capable of proving the Riemann Hypothesis.”
If de Branges turned out to be right, it would have a dramatic impact on both global business and national security.
Encrypted codes are based on the randomness of prime numbers. If a system could be found that made them predictable, no secret would be safe.
“What mathematics has been missing is a sort of maths prime spectrometer, like the machine chemists use to tell them what things are made of,” said Prof du Sautoy. “If we had something like that it would bring the world of e-commerce to its knees overnight.”
Yeah, me and the guys were arguing about this same thing over a couple of beers last night. Right after that, we got into our weekly "Ginger or MaryAnn?" debate.
See # 36
Question: The article briefly mentions that it may aid us in the understanding of higher dimensions in theoretical physics and cosmology, and some on this thread think it would aid those working with string theory. Would proving the Poincare Conjecture allow us to finally express in geometrical terms physical phenomena we formerly could only express statistically? Might this be one of the panels we have to open in the "Chinese Box" in which (maybe) hides a quantum theory of gravity?
Does that mean I'mm have to change all my combinations from 1 2 3 4 5 to something else???
Funny, she doesn't even look druish.
Mulder: Mr. Simpson, we want you to recreate your every move the night you saw the alien.
Homer: The evening began at the gentleman's club, where we were discussing Wittgenstein over a game of backgammon.
Scully: Mr. Simpson, it's a felony to lie to the FBI.
Homer: We were sitting in Barney's car eating packets of mustard. Happy?
Hey, maybe that's the answer! (sad to hear about the e-machines though)
I solved it years before you did, but some Russian guy stole my work and ran off with it.
Too bad it wasn't seared--seared--into your memory.
Penrose prefers twistor theory.
Not in Russia. They have the flat tax.
And then, there it was.
In promulgating your esoteric cogitations or articulating your superficial sentimentalities and amicable philosophical or psychological observations, beware of platitudinous ponderosity.
Let your conversational communications possess a compacted conciseness, a clarified comprehensibility, a coalescent cogency and a concatenated consistency.
Eschew obfuscation and all conglomeration of flatulent garrulity, jejune babblement and asinine affectations.
Let your extemporaneous descants and unpremeditated expatiations have intelligibility and voracious vivacity without rodomontade or thrasonical bombast.
Sedulously avoid all polysyllabic profundity, pompous prolificacy and vain vapid verbosity.
"And then here it is."
Interesting. But until we figure how to duplicate energy scales, mimicing those of the first second or so of the creation event, we'll ultimately be guessing.
ol hoghead
You are ruining a good story with the facts.
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Or 7.99999999998493, if you happen to have an old Pentium.
Taylor or Maclauren?
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