Slashdot Log In
Science's Breakthrough of the Year
Posted by
CmdrTaco
on Fri Dec 22, 2006 12:12 PM
from the break-this-science dept.
from the break-this-science dept.
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."
Related Stories
[+]
Poincare Conjecture Proof Completed 222 comments
Flamerule writes "A New York Times article has finally provided an update on the status of Grigori Perelman's 2003 rough proof of the Poincaré Conjecture. 3 years ago, Perelman published several papers online explaining his idea for proving the conjecture, but after giving lectures at MIT and several other schools (covered on Slashdot) he returned to Russia, where he's remained silent since. Now, mathematicians in the US and elsewhere have finally finished going over his work and have produced several papers, totaling 1000 pages, that give step-by-step, complete proofs of the conjecture. In addition to winning some or all of the $1,000,000 Millennium Prize, Perelman now seems to be the favorite to receive a Fields Medal at the International Mathematics Union meeting next week, but it's not clear that he'll even show up!"
This discussion has been archived.
No new comments can be posted.
The Fine Print: The following comments are owned by whoever posted them. We are not responsible for them in any way.
Full
Abbreviated
Hidden
Loading... please wait.
Religion and politics off the table? I think not. (Score:5, Funny)
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 (Score:2)
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: (Score:2)
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: (Score:2, Informative)
Re: (Score:2)
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]
Re: (Score:2)
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.
Re: (Score:2)
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: (Score:2, Insightful)
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 (Score:2)
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 (Score:2)
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... (Score:5, Funny)
Re: (Score:3, Insightful)
Let me be the first to say it Homer-style (Score:4, Funny)
Crow T. Trollbot
Its all way over my head (Score:4, Funny)
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.
Re: (Score:2)
If this is a common topic in your conversational circle, please include me out -
Invisibility cloak (Score:2)
It's runners-up, not runner-ups. (Score:4, Informative)
-Isaac
There's a podcast as well (Score:3, Informative)
Science and Mathematics are Not the Same (Score:2, Insightful)
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. (Score:5, Informative)
http://www.newyorker.com/fact/content/articles/060 828fa_fact2 [newyorker.com]
Interesting, but very esoteric... (Score:5, Interesting)
Re: Interesting, but very esoteric... (Score:3, Funny)
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 (Score:4, Informative)
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 (Score:4, Informative)
Parent
Re: (Score:2, Informative)