Russian May Have Solved Poincare Conjecture

nev4 writes "Reuters (via Yahoo News) reports that Grigori Perelman from St. Petersburg, Russia appears to have solved the Poincare Conjecture. The Poincare Conjecture is one of the 7 Millenium Problems (another is P vs NP, also covered on /. recently). Solving a Millenium Problem carries a reward of $1M, but apparently Perelman isn't interested..." nerdb0t provides some background in the form of this MathWorld page from 2003.

Comments

Re:Duplicate?

[Disevidence]

RTFA. He published another paper on it recently.

Math?

[hunterx11]

1,000,000 USD is about equal to 560,000 GBP, not 5.6 million GBP.

$1 million USD?

[Anonymous Coward]

From the article:

A reclusive Russian may have solved one of the world's toughest mathematics problems and stands to win $1 million (560 million pounds) -- but he doesn't appear to care.

Heh. Last I checked, $1 million dollars was not quite equal to 560 million (British) pounds. (560 thousand, sure ...)

In an article on mathematics. Of all things.

The Millenium Problems

[shadowmatter]

Since a great deal of discussion and awe comes up anytime one of the millenium problems is mentioned (solved?) on Slashdot, I'd just like to say that any layman interested in learning more about the millenium problems should run to his/her library/bookstore and pick up The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time. Although, perhaps, for the layman, the end may become a bit tricky (the problems are explained simply in order of increasing difficulty), it's a book worth sticking with, and ultimately worth a read.

- sm

Re:Yes but...

[Anonymous Coward]

Makes sense, as I have no idea what the question is.

Hm... Let's see what the article tells us about it:

If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.

Ah. Poincaré understood to ask a simple question like "what is six multiplied by seven" in such a profoundly stupid way that it puzzled the world ever since if and why the answer was 42...

Hopefully he has better luck than de Branges

[DeepRedux]

A few months ago Louis de Branges published his proof of the Riemann Hypothesis on the internet. This is also a Millennium problem. Apparently, no mathematician has read it.

It is not that de Branges is unqualified: he settled Bieberbach's Conjecture. Interestingly, much of the validation of de Branges work on Bieberbach's Conjecture was done by a team at the Steklov Institute, referred to in the MathWorld link in the article.

Re:Riemann hypothesis reportadly also solved

[Anonymous Coward]

That's a great link, with a wonderful human-readable summary of the 7 problems.

For those too lazy to click:

Seven baffling pillars of wisdom

1 Birch and Swinnerton-Dyer conjecture Euclid geometry for the 21st century, involving things called abelian points and zeta functions and both finite and infinite answers to algebraic equations

2 Poincaré conjecture The surface of an apple is simply connected. But the surface of a doughnut is not. How do you start from the idea of simple connectivity and then characterise space in three dimensions?

3 Navier-Stokes equation The answers to wave and breeze turbulence lie somewhere in the solutions to these equations

4 P vs NP problem Some problems are just too big: you can quickly check if an answer is right, but it might take the lifetime of a universe to solve it from scratch. Can you prove which questions are truly hard, which not?

5 Riemann hypothesis Involving zeta functions, and an assertion that all "interesting" solutions to an equation lie on a straight line. It seems to be true for the first 1,500 million solutions, but does that mean it is true for them all?

6 Hodge conjecture At the frontier of algebra and geometry, involving the technical problems of building shapes by "gluing" geometric blocks together

7 Yang-Mills and Mass gap A problem that involves quantum mechanics and elementary particles. Physicists know it, computers have simulated it but nobody has found a theory to explain it

Re:Wake me...

[RedWizzard]

Wake me when someone verifies his work. I can claim to solve anything, but it doesn't mean much unless the community says I'm right. Right off the bat it seems fishy: no journal submission, just a web post? No referee? And he's not answering questions about his work? He's either a genius or a nutcase, possibly both.

The claim has been around for a while. From the referenced MathWorld article:

Almost exactly a year later, Perelman's results appear to be much more robust. While it will be months before mathematicians can digest and verify the details of the proof, mathematicians familiar with Perelman's work describe it as well thought out and expect that it will prove difficult to locate any significant mistakes.

That was in April 2003. It's now over a year later again and it hasn't been disproven.

Re:Confused

[xoran99]

A better analogy would be to continuously move a circle on the surface until it becomes a point. In the case of a donut, you could draw the circle through the middle hole and around again, so you can't "shrink it to a point" my continuously moving it anywhere; it goes around the donut anywhere you put it. With a sphere, though, you can continuously move the circle to a "pole," where it becomes a point. This property is called simple connectivity.

It's pretty easy to see that all simply connected 2-manifolds (in 3 dimensions, at least) are homeomorphic to the shell of a sphere, i.e. they may be stretched and contorted to look like it. The question answered here is whether the same is true in the next dimension.