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."

Religion and politics off the table? I think not.

[KingSkippus (799657)]

Our readers can relax this year: Religion and politics are off the table, and n-dimensional geometry is on instead.

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..."

Re:Religion and politics off the table? I think no

[Pedersen (46721)]

the vast majority of people who I argue with over the subject start from the premise, "It says in Genesis..."

I think I'm going to start my own replies to this sort of argument with this reply: Is this from the same Bible which is missing a whole book? Not just a testament, like Luke, but a whole book. After all, unless you're a Roman Catholic, you very likely do not have a bible which has the Apocrypha in it. And if your Bible is missing that entire book, how can you be sure of what is actually said in so much as a single chapter and verse?

Not that I expect to ever win such an argument, but it makes for some fun

Re:

[KingSkippus (799657)]

Well, I'm really pushing the karma, so I swear, I'll leave this thread completely alone after this, and feel free to mod it down if you want. (My preferred mod tag is "Off-Topic," because that's what this post is, as it's pretty much solely intended for its parent post. I'm not trolling, so get it right.)

Before I get into any sort of argument about evolution these days, I ask a pretty simple question that will determine whether or not it's worthwhile to go any further: Is there anything whatsoever, any

Re:

[c_forq (924234)]

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 l

Re:

[Creedo (548980)]

I believe only the Roman Catholic and Eastern Orthodox churches use it, but could be wrong

Heh, only the majority of all Christians use it, as Catholics and Orthodox comprise the majority of Christians in the world.

http://www.adherents.com/adh_rb.html#International [adherents.com]

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[GrumpySimon (707671)]

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.

that, and there's only four corners of the world [wikipedia.org]. Irenaeus argued that there should only be four gospels as those ones were good, but also because there are four corners of the world, four winds, animals have four legs, etc. The choice was really quite arbitary.

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[vertinox (846076)]

And if your Bible is missing that entire book, how can you be sure of what is actually said in so much as a single chapter and verse?

Personally, I though GP was being sarcastic, but you do have a very serious point about religion.

If one were to take religion seriously, you must really consider the problem of the nature of Holy Books and man's interaction with them.

Unless you believe much like Kings of the Medieval era that if god didn't want you to do something he wouldn't have made you king.

As in... If god

Re:

[TheDreadSlashdotterD (966361)]

So what if the Cathar's were right and that the Catholic Bible was simply a political tool of the Papacy to bring the incorrect version of God's word to man.

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.

OT:Religion and politics off the table? I think no

[Kjella (173770)]

Is this from the same Bible which is missing a whole book?

Every religion define their own truth. If it's not there, it's because it's not meant to be there. In a way, Christianity is very loosely defined because Jesus never made writings so anything authentic about his words or actions is fair game. You could actually invert that statment and say "Is this from the same Bible that included a whole false book?".

In contrast, you have the Qur'an, which there is exactly one definitie version of, written down at

Re:Religion and politics off the table? I think no

[vertinox (846076)]

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.

Clear? As in the Aramaic, Hebrew, Greek, Latin, or 15th century English version of Leviticus?

And are these African or European non-spherical loops?

The Origin of Species...

[by Anonymous Coward]

...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?"

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[fafalone (633739)]

The Origin of Species is not the absolute complete flawless manual for evolution. There's been plenty of huge breakthrough in evolution that weren't even touched on in Darwin's book. The biggest one is tracking evolution through molecular genetics; the mechanism of what Darwin observed. Not to mention models for evolution like punctuated equilibrium (long periods of little evolution, short periods of rapid change in response to some major change in environment)... that was not part of Origin. Major breakthr

Let me be the first to say it Homer-style

[Cr0w T. Trollbot (848674)]

"In your face, Shing-Tung Yau!" [newyorker.com]

Crow T. Trollbot

Its all way over my head

[Timesprout (579035)]

But I found this on the Wikipedia page

Similarly, the hairy ball theorem of algebraic topology says that "one cannot comb the hair on a ball smooth". This fact is immediately convincing to most people, even though they might not recognize the more formal statement of the theorem, that there is no nonvanishing continuous tangent vector field on the sphere.

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.

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[Stanistani (808333)]

>the next time hairy balls come up in conversation...

If this is a common topic in your conversational circle, please include me out - :)

Invisibility cloak

[szembek (948327)]

I think this one should take the cake! http://www.sciencemag.org/cgi/content/full/314/580 7/1850a/F4 [sciencemag.org]

It's runners-up, not runner-ups.

[isaac (2852)]

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

There's a podcast as well

[ahab_2001 (610339)]

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 [sciencemag.org]; to get access to the articles I believe you need to register with the site. There's also a podcast [sciencemag.org], which doesn't require registration.

Science and Mathematics are Not the Same

[pz (113803)]

While this is a wonderful recognition of some fantastic work, the Slashdot editors should bear in mind that science and mathematics are not the same thing. To call solving the Poincarre Conjecture a breakthrough in Science (breakthrough of the year, no less!) is disrespectful to both scientists and mathematicians.

There have been some breakthroughs in Mathematics that were simultaneously notable in Science (solving the 4 Colors Problem, for example, the first time a computer was used to experimentally and e

Pereleman isn't accepting for a reason.

[Starker_Kull (896770)]

He thinks that academia is littered with people who are more interested in promoting themselves than who are actually good at research, and this leads to a lot more politicing than researching, and the system is set up to promote that. This is the reason he is not interested in claiming prize money or prizes or other official recognition of his worth. I don't necessarily agree with that point of view, but perhaps it is worth considering if he has a legitimate gripe? There is a good article about him in the New Yorker Mag; here is the link and concluding paragraphs:

http://www.newyorker.com/fact/content/articles/060 828fa_fact2 [newyorker.com]

As for Yau, Perelman said, "I can't say I'm outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest." The prospect of being awarded a Fields Medal had forced him to make a complete break with his profession. "As long as I was not conspicuous, I had a choice," Perelman explained. "Either to make some ugly thing"--a fuss about the math community's lack of integrity--"or, if I didn't do this kind of thing, to be treated as a pet. Now, when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit." We asked Perelman whether, by refusing the Fields and withdrawing from his profession, he was eliminating any possibility of influencing the discipline. "I am not a politician!" he replied, angrily. Perelman would not say whether his objection to awards extended to the Clay Institute's million-dollar prize. "I'm not going to decide whether to accept the prize until it is offered," he said. Mikhail Gromov, the Russian geometer, said that he understood Perelman's logic: "To do great work, you have to have a pure mind. You can think only about the mathematics. Everything else is human weakness. Accepting prizes is showing weakness." Others might view Perelman's refusal to accept a Fields as arrogant, Gromov said, but his principles are admirable. "The ideal scientist does science and cares about nothing else," he said. "He wants to live this ideal. Now, I don't think he really lives on this ideal plane. But he wants to."

Interesting, but very esoteric...

[posterlogo (943853)]

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.

Re: Interesting, but very esoteric...

[Black Parrot (19622)]

> 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.

The actual breakthrough of the year was that a Slashdotter got laid back in February, but they couldn't include it in the list because they haven't been able to confirm the details. So this one is a sort of symbolic stand-in.

The Article

[Starker_Kull (896770)]

The Poincare Conjecture-Proved: The solution of a century-old mathematics problem turns out to be a bittersweet prize

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

Re:Update please

[Wooloomooloo (902011)]

He turned the prize down. In fact, he didn't even show up at the ceremony.

Re:

[modular_form (1042794)]

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.