Poincare conjecture proven?

[akruppa]

Looks like Perelman won the Fields medal.

But according to this article on Heise (in German), he won't bother to go pick it up. It's the first time someone refused the Fields medal.

Alex

[ewmayer]

Yeah, I just read about Perelman's refusal of the prize in the New York Times - note that officially he will be considered a Fields Medalist, just like you'd still be considered an Olympic medalist even if you refuse to accept the medal:

http://www.nytimes.com/2006/08/22/sc...2cnd-math.html

Highest Honor in Mathematics Is Refused

By KENNETH CHANG
Published: August 22, 2006

Grigory Perelman, a reclusive Russian mathematician who solved a key piece in a century-old puzzle known as the Poincaré conjecture, was one of four mathematicians awarded the Fields Medal today.

But Dr. Perelman refused to accept the medal, as he has other honors, and he did not attend the ceremonies at the International Congress of Mathematicians in Madrid.

“I regret that Dr. Perelman has declined to accept the medal,” Sir John M. Ball, president of the International Mathematical Union, said during the ceremonies.

The Fields Medal, often described as mathematics’ equivalent to the Nobel Prize, is given every four years, and several can be awarded at once. Besides Dr. Perelman, three professors of mathematics were awarded Fields Medals this year: Andrei Okounkov of Princeton; Terence Tao of University of California, Los Angeles; and Wendelin Werner of the University of Paris-Sud in Orsay.

Dr. Perelman, 40, is known not only for his work on the Poincaré conjecture, among the most heralded unsolved math problems, but also because he has declined previous mathematical prizes and has turned down job offers from Princeton, Stanford and other universities. He has said he wants no part of $1 million that the Clay Mathematics Institute in Cambridge, Mass. has offered for the first published proof of the conjecture.

In June, Dr. Ball traveled to St. Petersburg, Russia, where Dr. Perelman lives, for two days in hopes of persuading him to go to Madrid and accept the medal.

“He was very polite and cordial, and open and direct,” Dr. Ball said in an interview.

But he was also adamant. “The reasons center around his feeling of isolation from the mathematical community,” Dr. Ball said of Dr. Perelman’s refusal, “and in consequence his not wanting to be a figurehead for it or wanting to represent it.”

Dr. Ball added, “I don’t think he meant it as an insult. He’s a very polite person. There was never a cross word.”

Despite Dr. Perelman’s refusal, he is still officially a Fields Medalist. “He has a say whether he accepts it, but we have awarded it,” Dr. Ball said.

Beginning in 2002, Dr. Perelman, then at the Steklov Institute of Mathematics of the Russian Academy of Sciences in St. Petersburg, published a series of papers on the Internet and gave lectures at several American universities describing how he had overcome a roadblock in the proof of the Poincaré conjecture.

The conjecture, devised by Henri Poincaré in 1904, essentially says that the only shape that has no holes and fits within a finite space is a sphere. That is certainly true looking at two-dimensional surfaces in the everyday three-dimensional world, but the conjecture says the same is true for three-dimensional surfaces embedded in four dimensions.

Dr. Perelman solved a difficult problem that other mathematicians had encountered when trying to prove the conjecture, using a technique called Ricci flow that smoothes out bumps in a surface and transforms it into a simpler form.

Dr. Okounkov, born in 1969 in Moscow, was recognized for work that tied together different fields of mathematics that had seemed unrelated. “This is the striking feature of Okounkov’s work, finding unexpected links,” said Enrico Arbarello, a professor of geometry at the University of Rome in Italy.

Dr. Okounkov’s work has found use in describing the changing surfaces of melting crystals. The boundary between melted and non-melted is created randomly, but the random process inevitably produces a border in the shape of a heart.

Dr. Tao, a native of Australia and one of the youngest Fields Medal winners ever at age 31, has worked in several different fields, producing significant advances in the understanding of prime numbers, techniques that might lead to simplifying the equations of Einstein’s theory of general relativity and the equations of quantum mechanics that describe how light bounces around in a fiber optic cable.

Dr. Werner, born in Germany in 1968, has also worked at the intersection of mathematics and physics, describing phenomena like percolation and shapes produced by the random paths of Brownian motion.

The medal was conceived by John Charles Fields, a Canadian mathematician, “in recognition of work already done and as an encouragement for further achievements on the part of the recipient.”

Since 1936, when the medal was first awarded, judges have interpreted the terms of Dr. Fields’s trust fund to mean that the award should usually be limited to mathematicians 40 years old or younger.

[ewmayer]

Excellent and very interesting New Yorker article about the story - lots of juicy (and to no small degree dismaying) stuff about some of the mathematical infighting and politics swirling around the proof. As ever, nationalism and science make for a bad mix:

http://www.newyorker.com/fact/content/articles/060828fa_fact2

[mfgoode]

Originally Posted by ewmayer

Excellent and very interesting New Yorker article about the story - lots of juicy (and to no small degree dismaying) stuff about some of the mathematical infighting and politics swirling around the proof. As ever, nationalism and science make for a bad mix:

http://www.newyorker.com/fact/content/articles/060828fa_fact2

By the way that article from New yorker was contributed by me in my original thread, and I was notified that it was shifted to this older thread.
I would expect to have at least been acknowledged as the original contributor! Not that it matters to me in the least, but Im wondering if such 'infighting and politics swirling around' and even worse, for Poor Perelman in his term in the U.S., made him disgusted to the extent of refusing a worldly honour which another would have gladly accepted ,if not for the honour, but for the money! Yes the Love of money is the root of all evil!

Mally

[Spherical Cow]

Originally Posted by ewmayer

Excellent and very interesting New Yorker article about the story - lots of juicy (and to no small degree dismaying) stuff about some of the mathematical infighting and politics swirling around the proof. As ever, nationalism and science make for a bad mix:

http://www.newyorker.com/fact/content/articles/060828fa_fact2

That is indeed an excellent article- I would love to see it expanded into an entire book. Thanks for pointing it out.

Norm

[mfgoode]

Originally Posted by Spherical Cow

That is indeed an excellent article- I would love to see it expanded into an entire book. Thanks for pointing it out.

Norm

Well thats the incentive- to write an article in a prestigious mag. and see how well it is received by the public. If the response is good then on with the book.
Sylvia Nasar is the author of 'A Beautiful Mind' - the life of the Nobel laureate John Nash, who for most of the time, was a psychizophrenic. I wonder if you have seen the movie as its a very touching story, with a slight departure to the book, though.
I think he is still active today.
It wont be long before she comes out with a book on Grigori Perelman, the Fields medallist.
Mally

[bdodson]

Originally Posted by mfgoode

By the way that article from New yorker was contributed by me in my original thread, and I was notified that it was shifted to this older thread.
I would expect to have at least been acknowledged as the original contributor!
...

Mally

The dates on the posts in this "older" thread are more interesting
than the math-as-soap-opera dug-up and spread around by the
author of the NY'er article. We have the NYT report on three
pre-prints/reprints that seem to have settled what was (accurately)
described as sketchy and/or incomplete over most of the more than
three years since Perelman's 2003 lecture tour. These are the
Kleiner-Lott preprint (on the same archiv as Perelman's original
three pre-prints), the Tian-Morgan manuscript that seems headed
towards being a (math) book, and the Cao-Zhu paper in AJM.
Anderson's conclusion about these papers serving as peer-review
of Perelman's work would have been a good place to end the topic,
if not for Fields_medal/Clay_prize bring a lot of attention from people
that hadn't heard about the 3-dim Poincare Conjecture before
it was solved.

Anyone in doubt could refer to the comment of the Clay Inst.
President referring to the 2-year interval for peer review before
awarding the prize (that'd be the $1M, not the Fields) --- they're
starting the 2-year clock from the appearance above three papers,
not from Perelman's 3rd internet post or lecture-tour. Clearly the
IMU (which awards the Fields) was able to determine somewhat earlier
that substantial progress had been made, sufficient for awarding the
medal.

As I was saying, you can check the dates in this thread yourself -
Dec 03, Dec 03, May 04 (2 posts), Sept 04 (4 posts). Then a
nearly two year jump to the NYTimes articles, Aug 06. If there was
anyone besides Perelman that believed they understood all of the
details needed for a complete proof a year ago, last August, they
were being extra-ordinarily quite. Cao, for example, didn't breathe a
word during his seminar here last year. -bd

[ewmayer]

Originally Posted by mfgoode

By the way that article from New yorker was contributed by me in my original thread, and I was notified that it was shifted to this older thread.
I would expect to have at least been acknowledged as the original contributor!

Mally, are you referring to this thread you started in the Math section? That's the only other one I saw about the Perelman story, and there is no New Yorker link in your post there - only one to the same New York Times article which I linked to and reprinted above, 2 days before you started the aforementioned thread.

Geez, I can't believe we're actually having a priority dispute about who posted the first forum link to this-or-that popular news article about a story about a proof of a famous conjecture and the attendant priority dispute...

[ewmayer]

On a more humorous note, Comedy Central's The Colbert Report had a funny segment about the Poincare' conjecture and Perelman's declining the Fields Medal last week - here's a copy of the synopsis I sent to a non-mathematical friend about that:

===

Well, here's the gist of it: the Poincare' conjecture is in the area of topology, which deals with the fundamental "shape" of objects in various-dimensional spaces. One of the key tools in topology is the idea that object A is topologically equivalent to object B if A can be deformed (in a mathematically precise sense, but basically without tearing a hole in it) into B (and v.v.). One of the classic analogies used here is that to a topologist a rabbit and a sphere are equivalent because both are objects without holes, unlike, say, a donut.

At this point, Colbert goes off on the silly mathematicians: "of course rabbits have holes - where do you think *baby* rabbits come from?"

Then to prove that all the math nerds are wrong and that a donut can in fact be transformed into sphere without tearing it, he pulls a powdered donut out of a cardboard box and smushes it with his hands into a ball, begins to eat it ("delicious!"), and starts pulling those powdered donut-hole thingies out of the same box (more proof that donuts can be spheres), tosses them into the audience, and then announces to the givers of the Fields medal, that clearly being the most deserving candidate, he's ready to accept the award which Dr. Perelman declined.

===

[akruppa]

Due to the digestive tract, should a rabbit not be equivalient to a doughnut (before mashing (the doughnut, not the rabbit))?

Alex

[grandpascorpion]

He deserves some kind of medal for the Steven and Melinda Gates foundation alone.