Slashdot Mirror
Science's Breakthrough of the Year
johkir writes "Last year, evolution was the breakthrough of the year; We found it full of new developments in understanding how new species originate. But we did get a complaint or two that perhaps we were just paying extra attention to the lively political/religious debate that was taking place over the issue, particularly in the United States.
Perish the thought! Our readers can relax this year: Religion and politics are off the table, and n-dimensional geometry is on instead. This year's Breakthrough salutes the work of a lone, publicity-shy Russian mathematician named Grigori Perelman, who was at the Steklov Institute of Mathematics of the Russian Academy of Sciences until 2005. The work is very technical but has received unusual public attention because Perelman appears to have proven the Poincaré Conjecture (Our coverage from earlier this year), a problem in topology whose solution will earn a $1 million prize from the Clay Mathematics Institute. That's only if Perelman survives what's left of a 2-year gauntlet of critical attack required by the Clay rules, but most mathematicians think he will.
There is also a page of runner-ups. Many of which have been covered here on Slashdot."
I've got karma to burn, so let's use some up.
You stop right there, mister.
I don't care what kind of "proof" this seedy Perelman character says he has. In Leviticus, The Bible makes it clear that in a closed 3-mainfold, there non-spherical loops that can be continually tightened to a point. Who are you going to believe, Grigori Perelman, or God? If you even try to put this proof in my kid's math book, I'm going to demand more stickers! Slashdot obviously wants the terrorists to win!
Apologies to any real mathematicians out there, that was the best twisting of Poincaré Conjecture I could come up for the sake of this joke based on Wikipedia's article. And while I hope that while everyone realizes that I'm kidding, I also hope that some folks realize that I'm kinda not. The vast majority of people who insist that such things as evolution aren't true sound to me pretty much like I just did, because the vast majority of people who I argue with over the subject start from the premise, "It says in Genesis..."
...as I recall was published in 1859. Not only was it not a breakthrough of this year, it was a breakthrough of near 150 years ago. As they say, "What exactly are you smoking, sir?"
He turned the prize down. In fact, he didn't even show up at the ceremony.
Crow T. Trollbot
I am now gagging for an opportunity start making crap up about nonvanishing continuous tangent vectors the next time hairy balls come up in conversation.
Do not try to read the dupe, thats impossible. Instead, only try to realize the truth
What truth?
There is no dupe
In case you were sick that day in remedial English 101, noun-adjective compounds - attorney general, mother-in-law, runner-up - are made plural by pluralizing the noun: attorneys general, mothers-in-law, runners-up.
-Isaac
I am not a lawyer, and this is not legal advice. For Entertainment Purposes Only.
He turned down the Fields medal, but the million dollars is a separate thing. They won't even offer it until two years after his proof is published. I heard the man lives on $1 a day, so he's probably not interested in the money either.
This all comes from the 22 December issue of the journal Science, in case that wasn't clear from the original posting. All of the stories from the issue are indexed here; to get access to the articles I believe you need to register with the site. There's also a podcast, which doesn't require registration.
I think you are a little off. The Apocrypha isn't a book, it is a collection of books, and a couple different versions of books existing in the canonical bible. At the time of Jesus the Apocryphal books were debated in the Jewish community, and in the modern world, besides a couple of extremely small Judaism sects, I believe only the Roman Catholic and Eastern Orthodox churches use it, but could be wrong. The reason the Apocrypha is not included in the normal canon of the bible is usually accredited to lacking authenticity, or conflicting with established books.
Computers allow humans to make mistakes at the fastest speeds known, with the possible exception of tequila and handguns
http://www.newyorker.com/fact/content/articles/060 828fa_fact2
This mathematical proof is clearly interesting from a mathematics-proofs-point-of-view. But I'm surprised it's considered the breakthrough of the year. Its very difficult for most people to relate to. I'm a scientist, and I try and keep up (at a basic level) with many fields of research other than my own (by reading articles in Science), but I think the nature of this proof is very difficult to keep up with. Not to mention it is difficult to even be sure that the proof works (since it can really only be evaluated by highly specialized experts). If this breakthrough pans out, mathematicians need to do a much better job of public relations, like most other sciences do. I for one think the data from the Mars Rovers, the Cassini spacecraft, and the comet material recovery mission represent (collectively) the breakthrough of the year. The amount we have learned about our solar system this past year is extraordinary. I say this even though I am a biologist, and we've done some marvelous things in biology this year. But the unmanned space program really came through this year, and is far more captivating than the math proof, no offense.
Perhaps you haven't been paying attention. Religion has always been a political tool. It's a convenient mechanism used to control people, and has worked beautifully for thousands of years. If you need an example, see the current U.S.A.
I have nothing to say.
TO MATHEMATICIANS, GRIGORI PERELMAN'S proof of the Poincare conjecture qualifies at least as the Breakthrough of the Decade. But it has taken them a good part of that decade to convince themselves that it was for real. In 2006, nearly 4 years after the Russian mathematician released the first of three papers outlining the proof, researchers finally reached a consensus that Perelman had solved one of the subject's most venerable problems. But the solution touched off a storm of controversy and drama that threatened to overshadow the brilliant work.
Perelman's proof has fundamentally altered two distinct branches of mathematics. First, it solved a problem that for more than a century was the indigestible seed at the core of topology, the mathematical study of abstract shape. Most mathematicians expect that the work will lead to a much broader result, a proof of the geometrization conjecture: essentially, a "periodic table" that brings clarity to the study of three-dimensional spaces, much as Mendeleev's table did for chemistry.
While bringing new results to topology, Perelman's work brought new techniques to geometry. It cemented the central role of geometric evolution equations, powerful machinery for transforming hard-to-work-with spaces into more-manageable ones. Earlier studies of such equations always ran into "singularities" at which the equations break down. Perelman dynamited that roadblock.
"This is the first time that mathematicians have been able to understand the structure of singularities and the development of such a complicated system," said Shing-Tung Yau of Harvard University at a lecture in Beijing this summer. "The methods developed ... should shed light on many natural systems, such as the Navier-Stokes equation [of fluid dynamics] and the Einstein equation [of general relativity]."
Unruly spaces
Henri Poincare, who posed his problem in 1904, is generally regarded as the founded of topology, the first mathematician to clearly distinguish it from analysis (the branch of mathematics that evolved from calculus) and geometry. Topology is often described as "rubber-sheet geometry," because it deals with properties of surfaces that can undergo arbitrary amounts of stretching. Tearing and its opposite, sewing, are not allowed.
Our bodies, and most of the familiar objects they interact with, have three dimensions. Their surfaces, however, have only two. As far as topology is concerned, two-dimensional surfaces with no boundary (those that wrap around and close in on themselves, as our skin does) have essentially only one distinguishing feature: the number of holes in the surface. A surface with no holes is a sphere: a surface with one hole is a torus; and so on. A sphere can never be turned into a torus, or vice versa.
Three-dimensional objects with 2D surfaces, however, are just the beginning. For example, it is possible to define curved 3D spaces as boundaries of 4D objects. Human beings can only dimly visualize such spaces, but mathematicians can use symbolic notation to describe them and explore their properties. Poincare developed and ingenious tool called the "fundamental group," for detecting holes, twists, and other feature in spaces of any dimension. He conjectured that a 3D space cannot hide any interesting topology from the fundamental group. That is, a 3D space with a "trivial" fundamental group must be a hypersphere: the boundary of a ball in 4D space.
Although simple to state, Poincare's conjecture proved maddeningly difficult to prove. By the early 1980's, mathematicians had proved analogous statements for spaces of every dimension higher than three - but not for the original one that Poincare had pondered.
To make progress, topologists reached for a tool they had neglected: a way to specify distance. They se