Goddamn I love freaky misfit mathematical geniuses. They're even better than their nerdier cousins, the chess geniuses. The ones from Central/Eastern Europe and South Asia always seem to be the most fun.
Make for good stories too... Wait, I saw this coming! There's also something about a black box, a blind guy, passports, and a guy who looks like he spent a little too much time in prison.
It looks like the trolls have taken over moderation *again*. Why is this moderated offtopic? TFA is about a quirky mathematical genius who solved an obscure math problem. I guess you don't need reading comprehension to moderate. Hint, moderators.. my post is about moderation so it is off topic. The parent post is about the East European math geniuses from the article... that *IS* the topic!
Nothing extraordinary really. In USSR, mathematics (as well physics) was just one of the top prioritized subjects. As one of my german friends compared me and his son, we soviet pupils have had about twice more mathematics during our school times.
Mathematics is not about numbers and problems - it teaches brain to think. Nothing more.
Haha.. oh that's rich. "Please Mr. Perelman--flee from the military-industrial complex. Come to a sanctum of human rights and democracy. Come to... [wait for it]... America!"
The reason they can't find him in Russia is because he's already living in Sweden.
but at least on the positive side he'll have access to great health-care, low-crime, respectful co-citizens and one of the highest standards of living on the planet
We should be quite concerned about Grigori Perelman since he returned to Russia.
Nice bit of jingoistic xenophobia there, but that's about all that's nice about your post.
Gang Tian, who has co-wrote a guide to Perelman's proof, said in 2004: "He certainly has no interest in material things. If he gets the Fields Medal, there is the issue of whether or not he will accept it." He also refused a prize from the European Mathematical Society many years before that.
There's nothing remotely Flamebait or Troll in that message. TrollMods spew cosmoturf to suppress discussion of growing Russian backsliding towards tyranny. Slashdot's mod system really is disgusting sometimes when it's abused by political operatives.
So rabbits have a hole, eh? Which means that topologically they form rings? OK, so what do three rabbirs forming Borromean rings [wikipedia.org] look like?
Reputedly, there exists a book with a picture of Borromean humans.
If I were known for proving Poincare Conjecture, I wouldn't give a damn to be known as a Fields medal winner. (They'll give it to him anyway, whether he's there personally to receive it.)
Is Einstein known for winning the Nobel? Is Madam Curie well known cause she won the Nobel? Is Neils Bohr well known cause he won the Nobel? Is Dirac well known cause he won the Nobel? Is Watson/Crick famous cause they won the Nobel? The point I am trying to make is that GP is 100% right. Nobel/Fields doesnt come anywhere near, if I were to prove the Poincare Conjunture.
Maybe I can put it across in another way. Is Ramanujan any less well known since he did not win a Fields? Is Mahatma Gandhi any less a person since
Google your friend. ANAM (I'm not a matematician), but I'll try.
According to string physicist Lubos Motl [blogspot.com] the proof indeed important to string theory. The proof based on the flow on the manifold (surface), analogous to heat dissipation - Ricci flow [wikipedia.org]. This flow deform metrics (distance between points of the surface). But this process also describe renormalization [wikipedia.org] of worldsheet - how the physics of the worldsheet [wikipedia.org] (surface which string drawing, moving in space and time) change with changing of the observation scale. That is how phisics of string change then the scale of calculation changed.
I'm not a geometer, but here is my understanding of the proof:
The Ricci Flow [wikipedia.org] was defined by Richard Hamilton in 1981 as a step towards classifying topological compact 3-manifolds. Classifying 3-manifolds would certainly decide The Poincare Conjecture, as it states that all simply connected compact 3-manifolds are homeomorphic to the sphere. This is an important special case: most proofs of the classification of compact 2-manifolds start out by proving the an analogous statement for the 2-sphere. The Ricci Flow is a differential equation which defines how the shape of a manifold changes in time: given an arbitrary manifold M(0), you can apply the differential equation to it to get manifolds M(t) for (some) positive t, which gradually change shape. However, the Ricci Flow is not volume preserving, so you "renormalize" so that M(t) has constant volume.
The Ricci Flow has the useful property that it tends to make manifolds smoother and smoother. For example, if you started out with a lumpy ball, you would eventually get a smooth ball. It was hoped that it could be proved that if the initial manifold was a compact simply connected 3-manifold, then as t increased, the manifold would tend towards a 3-sphere. Unfortunately, while locally solutions to differential equations always exist, they don't necessarily exist for all time, and for some starting manifolds, eventually you would get to a road-block: a t for which M(t) could not be defined. What Perlman (hopefully) showed was that all road-blocks were of certain types, and that a surgery could be formed that would modify the manifold but not it's topological nature, and then you could again apply the Ricci Flow, until the manifold became a sphere.
Note that this method is useful beyond proving the Poincare Conjecture, as it (again, hopefully) describes all road blocks to extending the Ricci Flow, so that the same tools can be applied to any 3-manifold, and not just simply connected ones. In this manner, assuming Perlman made no mistakes (or that any mistakes can be corrected), it is possible to apply the same arguments to prove the Geometrization Conjecture of Thurston, which classifies 3-manifolds.
I'm trying to glean what some of the practical implications could be of this discovery.
It seems to me at this Ricci Flow differential equation could be quite useful practically. For example, in pattern recognition, if a computer could build a 3d model of an object using multiple vantage points, then simplify the object to one of the handfull of object types described by Perlman using the Ricci Flow, then this simple catagorization might help in the identification of complex objects (e.g. a donut really is a donut, even if it's been heavily frosted).
Do you know if Perlman's technique for handling the singularities will help with the numerical implementation of this process? Or are these issues numerically simple to solve - but only challenging to solve in proof?
For pattern (image) recognition the geometry is quite important, since usual applications are essentially trying to mimick the human behaviour, and humans in practical life are more geometers than topologists.
The incredulity that this mathematician might have been more interested in the challenge of the work than fame and fortune in the Western world practically oozes from each sentence.
I'm all for capitalism and the idea of "prizes" to encourage research, but have we really become so jaded that it's a complete shock when someone does something worthwhile merely for its own sake? Perhaps he's gone on to other challenges, or he's wrapped up in some research that has his complete attention. Heck, perhaps he just enjoys math for its own sake and doesn't want to deal with all the side-effects of notoriety.
Are you sure it's not just delight rather than incredulousness? Tone is rather hard to pick out with just text so you're assuming a lot in your conclusion...
I'm all for capitalism and the idea of "prizes" to encourage research, but have we really become so jaded that it's a complete shock when someone does something worthwhile merely for its own sake?
It isn't a shock that he did it for its own sake at all. Look at the thousands of open source programmers. The shock is that he's been given a million dollars and seem uninterested. Linus Torvalds does Linux for its own sake but if someone gave him a million dollars, he'd take it. Even someone who is not materialistic might think: "hmmm. A million dollars might help many Russian orphans or deliver AIDS drugs to Africans or..." It is strange for a single person to be neither greedy, nor ambitious nor altruistic... merely obsessed.
Yes, that's strange. It's rare and therefore strange.
Oddly enough, people tend to form their expectations based on past experiences. Is it so unreasonable for the tone of the article to be incredulous when the situation is unprecedented?
Where you see value judgments and a jaded reporter, I see a pretty reasonable surprise. I don't see anything in the article where the reporter suggests that Perelman "should" do anything other than what he is. Surprise, and remarking on an unusual behavior, is *not* approbation.
I'm all for capitalism and the idea of "prizes" to encourage research, but have we really become so jaded that it's a complete shock when someone does something worthwhile merely for its own sake?
Lots of people do things for their own sake (as long as they can pay their bills and get some food). But when someone got a prize of a million dollar as a bonus (for what you enjoyed doing anyway), can you really imagine someone turning this down? Well, Perelman hasn't done this (yet), but lots of people could im
I think that never is this more amply examplified than when the people who manage 'rights holders' "explain" how, if it weren't for copyright, there would exist no art.
Sadly, yes, doing something for it's own sake rather than for monetary gain is frowned apon, and sometimes viewed with fear and confusion, not that I'm saying this review goes THAT far (if you don't believe me, try smiling at someone while in a subway one of these days: the person will generally check that you haven't got someone stealing their wallet while they are distracted. Or busk without a hat out: no one realises that an orchestral musician might just enjoy playing music in the sun in winter, and they search madly for a way to throw a coin into my closed music case).
Perhaps he sees the money as a complication rather than a useful item: instead of assuming he could donate it, there would be all the trouble of getting the money into his country, bank balances, taxes, and more questions and papers to fill out to get it donated, and all the rest of it. All of which is time he could have been spending on solving another interesting question, or gathering mushrooms, or whatever.
Coming into a fortune is not always fortunate.
OTOH, doing something openly for monetary gain is frowned on in academia. It just seems to me that everyone is behaving as their stereotyped role here.
Sadly, yes, doing something for it's own sake rather than for monetary gain is frowned apon
That is not correct. Look at the hoopla around both Gates and Buffett giving way their money. Look at the adoration of Mother Teresa. Look at the army of fans for Linus Torvalds and Richard Stallman.
and sometimes viewed with fear and confusion,
Sure: anything out of the ordinary will engender fear and confusion. There is a difference between suspecting that someone MAY NOT BE altrustic and "frowning upon" the
>The incredulity that this mathematician might have been more interested in the challenge of the work than fame and fortune in the Western world practically oozes from each sentence.
That and also while he did the hard work, that he didn't really contribute to the full proof, which is also weird.
the submitter seems to have misplaced the incredulity. the important thing is that other mathematicians are amazed that someone would throw around important parts of the proof, not wait for credit and leave it to others to write it up. then again, knowing perelman they are not incredulous.
in mathematics, the trend has mostly been to keep the insights of a big result under wraps until the proof is written down properly and checked for bugs. that is the way to get yourself into the hall of fame [st-and.ac.uk]. it is almos
Want to make a lot of money, do something the generates a lot of money. I can understand your point of view, but get real...
Innovation in math and science generates more money than any movie.
Consider something obviously fundamental to the way we live, like calculus or Fourier transforms.
It is very foolish to think that the direct and immediate monetary rewards a person receives are any real inidcation of the value their work provides to society.
Consider the impact that paid licensure of Fourier transforms would have on science and engineering. Or was the money supposed to come from the Magic Unicorn Cave?
So science and engineering don't make money, or they can't spare any for the poor mathematician that made it possible? Consider the impact of movie licensing on the poor theaters: do you know that the producers/distributers take 100% of the opening weekend box? We should just give it all to the theater ans let the people who produceed it go hang.
From your sarcasm it seems that you have no idea how free markets work... There is no such thing as innate value, the only value that something has is the demand for that thing. The demand for comedy is higher than the demand for mathematical proofs. The recompense for either has absolutely nothing to do with merit, even if you believe a mathematical proof has more innate merit than comedy. BTW, if you do believe that, please define for us exactly how a mathematical proof is better (has more value or merit)
A Scottish physicist two centuries ago sees a strange bump-like waveform in a canal. It persists for over three miles, moving at nearly constant speed along the canal trench. He writes a paper, calling it a soliton wave and two Dutch mathematicians find a nonlinear partial differential equation that describes its motion. The equation, the Korteweg-De Vries Equation, proves fiendishly hard to solve. Finally, the crew working on the hydrogen bomb, finish the job early, so Ulam decides to use ENIAC to help him solve the Korteweg-De Vries Equation. He attains the first analytic solutions, and the study of soliton waves begins in earnest.
How does this earn a quid? Well, solitons model the way that blips of light move down a fiber-optic cable. The military decides that DARPA-net could run on fiber-optic cables, and uses them in building the early internet. Cellular telephone companies begin using fiber-optic cables to pack 100,000 phone conversations into a single pipe in such a way that they all get separated on the other end of the pipe-- one of the great engineering marvels of our time. We owe the modern internet, cell phones, anything that uses fiber-optics, to the solution of the Korteweg-De Vries equation. There was a similar burst of technology earlier in the last century when some closed-form solutions of the Schrödinger Equation were found.
Truth is, when we solve a major math problem like the Poincaré conjecture, billions of dollars of revenue are generated by new technologies that spring into being because of the new scientific understanding that the solution affords us. A thousand Adam Sandlers will not generate the amount of capital that the solution of the Poincaré conjecture will generate, especially considering that Perelman has shown the world that the Millenium Prize Problems are actually solvable.
"Truth is, when we solve a major math problem like the Poincaré conjecture, billions of dollars of revenue are generated by new technologies" Ah. No... The money/capital isn't generated. It's simply moved from one place to another, from low performing areas to higher performing areas. Only the governments can print money. Are you trying to tell me that money invested in the telecoms industry inherently has more merit than money invested in the entertainment industry?
It's a philosophical question, is a society where everyone is connected instantly to every one else but constantly working "better" than a society where everyone is happy and relaxed?
I think you hit the nail on the head with that. If only I had mod points.
At some point in the unseen future that might change, the solution might on the other hand sit gathering dust on a shelf as a mathematical curiosity until the universe dies.
Exactly. Merely because something is learned doesn't mean it's valuable. All
You don't understand the free market. In any free market transaction, value is created. Both parties walk away from a trade feeling that they have something of greater value. Paper money is not value. The government does not create stocks, and most value in the world is represented by stocks. Please get your facts straight.
Then perhaps the solution is to allow mathematical proofs to be patented so that the original discoverer can benefit from the resulting technological innovations. Ultimately, we're a resource based society, if someone wants to be compensated for the abilities they have to produce a resource with those abilities that can be bought and sold (or licensed, at least). If you give away your knowledge for free, you really can't complain when other people become multi-billionaires because of your initial hard work.
Fair enough -- if making stupid people laugh is considered more important by society than fundamental mathematical discoveries, then it should be more highly compensated. It is. What's your problem with that?
Simply put, I believe that society is wrong. It is wrong to value the contribution of Adam Sandler as greater than that of Grigori Perelman
One day, probably many years from now, Adam Sandler will be a footnote in some obsolete database, and Perelman will be famous for his contribution to human kno
Simply put, I believe that society is wrong. It is wrong to value the contribution of Adam Sandler as greater than that of Grigori Perelma
But you have to realize that most of societys concerns are immediate needs. We need food, fuel, sex and something to make the time pass by. These things are valuable because they are needed in huge quantities. Adam Sandler might not be a great comedian, but his skill serves a huge need. Mr. Perelman might be making a great contribution to math and science, which perhaps
"Investing" in Mozart was a good choice at the time - his operas WERE the popular music of his time. Investing in a Mozart opera would be like investing in a successful broadway show today. He also put on live performances that sold enough tickets to be financially successful.
Since he lived a long time before the advent of recording technology, the type of success available to a popular musician (or more properly their record label) today just didn't exist.
In Eastern Europe we don't pick up mushrooms to get narcotic high. It is merely a popular ingredient in our cuisine. The guy got his priorities right. No matter how rich and famous you are, in the West you cant get exactly the same ingredients for East European food.
As mushrooms based meals are so delicious, I wouldn't be bothered to travel somewhere to get some stupid price when there is high season for mushrooms.
And both are equally valid ways of raising a child. Most western nations just don't care enough about mushrooms to risk picking them up. We just leave it to the experts (who preferably are growing them and not just catching them, it's a lot safer).
PS: Even the experts who know the mushrooms in their area have been known to get sick or die when they go to another country and assume that the species which look the same are the same.
"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!"
The curse of the gifted is that niggling worry in the back of the mind that if one accepts praise, one may lose his focus, drive or muse, if you will.
I think the greatness of the prize isn't the mercenary value people seem to think it holds. The money just shows importance. The prize's value comes from the dialogue and new paths of discovery that are opened up. Remember that in the end Fermat's last theorem (proof of which is what prompted this, at least in part) wasn't important in its result. It was important because the search for a proof resulted in huge new areas of research that are much more fruitful both in the purely abstract mathematical se
Now that the conjecture is proved, do they change the name to "theory"? Or does the name stay put because that's what everyone knows and refers to it as?
Now that the conjecture is proved, do they change the name to "theory"? Or does the name stay put because that's what everyone knows and refers to it as?
Things that are proven, are called theorems. They do depend on axioms, but those are defined as true. Sciences about the real world that can't put up axioms (because that'd require ex facto knowledge about the real world), so they can never be conclusively "proven". Hence well call them theories, like theory of gravity, theory of evolution. A few we've called "laws" as well because they have been so extensively tested, but it is not proven in a strict formal sense.
You are wrong. This is true for other fields, but in mathematics, theories are more a like set of definitions, propositions and theorems used in a particular field. Remember, in mathematics everything is proved except conjectures (which are basically theorems you don't have proof for, but you can't find a proof of the contrary either). Mathematics are a purely virtual world governed by logic rules. There is no place for observation or rough suppositions like in physics or biology. For example, the category
There is no place for observation or rough suppositions like in physics or biology.
This is mildly incorrect. Theories also consist of a body of associated hard to solve problems. These problems often turn out to be observations and guesses or as you put it, "rough suppositions". For example, "Fermat's Last Theorem" has for centuries been a part of number theory even though it was proven only ten years ago.
What I meant is that in physics or biology, there are competiting theories on a given subject. If you read/., you know that a "no Black Hole" theory pops up regularly and some physicists propose their own theory to explain an *observation* of a natural phenomenon. In mathematics, you can prove things in different ways, but in the end a valid proof is a valid proof. Sometimes, it may be proven using intuitive logic so someone will want to re-do it using constructive logic, etc. There are different schools.
Actually, the terms "theory" and "law" are used in mathematical logic as well. In a given logic language, if you have a set of logic formulae called axioms, a theory is all that can be derived from these axioms by applying modus ponens. If the axioms eventually derive contradiction, then the theory is said to be the trivial theory, that is the theory that consists of all possible statements of the language. The smalles theory of the language is the one that contains only all taughtologies of the language. T
by Anonymous Coward writes:
on Wednesday August 16, 2006 @04:23AM (#15917390)
If any of you had read the article you would have noticed that the 1000 pages is actually a very rough figure for the sum page count of all 3 articles by various people each of which explains Perelmans result in context, thus duplicating the other 2. So in fact the full articles are about 315-470 pages each.
Also what Perelman infact did was show that using the Ricci Flow technique on the 3D shapes to solve the Poincare conjecture, an idea of Hamilton's from the 80's, can work. Up till now it was thought that certain structures might degenerate to singularities and fail, but Perelman showed that those singularities would in fact all turn out ok. Poincare's conjecture is for 3D shapes, and higher dimensional generalisations have previously been solved (5+ dim by Smale in 60's, 4 dim by Freedman in 80's, both got Field's medals).
It is said that the Poincare Conjecture proof is one of the most important proofs in Mathematics. But I never managed to understand why. What are the practical consequences of this proof? does it have any real-world applications?
The Poincare conjecture matters to basically any area of science where topology is important. i.e relativity and quantum mechanics. Also to the new(er) directions in physics like string theory, et. al.
Even if the PC has no direct bearing on some of these fields, the techniques used in the proof will probably end up deeply influencing their research methods.
That's stupid. He might turn money down. Now it's announced that proof is correct and that makes him candidate for that prize.
Even Russian newspapers do not have any official reaction of Perelman himself yet.
His (western) colleagues speculate that he might turn the award down. He is too far from normal life and money would distract him - so his friends say. That's speculation.
Would you blame him? He obviously poured a lot of time and energy into this. I'm sure there was no shortage of nose-thumbing, pride, and jealousy if my experience of SOME people has proven.
Is it thanks to receive some money and a medal after your peers roasted you for a couple of years?
Ten or twenty years' worth of academic wages ain't something to sneeze at, nor is the single most prestigious award in mathematics. I could see turning the Fields down just to make a point, but the million dollars can free you from financial obligation so you can distance yourself from your peers however long you want while doing what you love doing. Otherwise the money just goes back into feeding the system that you apparently hate.
TFA mentions he has distanced himself from others in the Math community because he has become disillusioned. I read into that my own experience, which involved professors trying to hit on me, others trying to get me to write/edit their papers and then taking the credit, others who weave tall tales with just enough truth to fool grant money providers. One of my colleagues now believes that Science is actually performing a random walk on the landscape of Truth. Occasionally, the walk stumbles over something
Something that's intrigued me since I noticed it, relating to hypersphere volumes. In 1D it's 2r, in 2D it's pi.r^2. 3D is 4/3 pi.r^3. The sequence continues: const.pi^2.r^4, const.pi^2.r^5, const.pi^3.r^6, const.pi^3.r^7 (can't remember offhand what the consts are but they can easily be found). Obviously you're going to get an extra r with each dimension, buy why do you only get another pi every other dimension?
While I'm at it, on a related subject it seems to me there are two possible ways of constructi
Obviously you're going to get an extra r with each dimension, buy why do you only get another pi every other dimension?
The Jacobian, or unit volume if you will, of a hypersphere [wikipedia.org] has a a highest term of sine, or cosine, which grows as you increase dimension. Specifically, for an n dimensional sphere, the highest power of sine or cosine will be sin^(n-2).
Anyway, to answer your question, integrals of sine or cosine to odd powers produce only functions of other sines and cosines. However, integrals of sine or cosine to even powers produce functions of sin(x), cos(x) and x. The x part gives you your pi, but only does so every second dimension, when the highest power is even.
I don't work in three-manifolds but my research has some connections with it so from time to time I'm at a conference or two in the area. Grisha Perelman is an interesting guy, even amoung the very driven math folks who tend to be an interesting lot, and his disinterest in the political/social aspects of his work is I believe genuine.
1) I met him at the Mathematical Sciences Research Institute in Berkeley at a workshop sometime around 1994 and he at that point had ridiculously long fingernails and was quite unkempt, even by the quite weak standards applied to research mathematicians. That was a while ago, of course and that was probably one of his first visits to the US. He gave an incomprehensible energetic talk so what most people commented on was his nails.
2) In 2003 or so, during a limited lecture tour about his proof of the Poincare Conjecture, he responded deftly and hilariously to a comment of Misha Gromov in the audience. Gromov is one of the most difficult people to have in a talk- he is a great mathematician with not much patience and has derailed or rerouted talks by many great researchers, who sometimes get quite flustered. I can't remember the exact wording of the exchange, which is too bad since it was precious, but Gromov asked something like "I don't see how that goes, I'd like to see some more details" and Grisha responded with something like "well, yes, you would" and carried on as he had intended.
First of all, I highly doubt that all of those 1000 pages are devoted to solving the Poincare Conjecture. Perelman, if I remember correctly, studies Ricci curvature flows which is a large area of mathematics in its own right. In the course of his research, he discovered some things that led to this proof of the Poincare Conjecture. I would expect that the 1000 pages referred to by this article deal with many different consequences of Perelman's work. Mathematicians like to do things in full generality, so they would have studied broader consequences instead of focussing for so long on only one result.
Secondly, I would invite you to write down a complete proof of some well-known mathematical fact, the Stone-Weierstrass [wikipedia.org] theorem say. You must prove this from first principles, starting with axiomatic set theory. I would be very surprised if you even managed to finish and even more surprised if the proof came in at under 1000 pages. This highlights what was mentioned by a sibling of mine: mathematics is divided into small steps and you would never dream of trying to prove something all at once.
Thirdly, this is the first ever proof of the Poincare conjecture. It is quite common in mathematics that a nicer proof of a known fact will be found.
Quite right. I was merely trying to illustrate that a proof can be extremely long, with many steps. And yet, the results can be widely accepted. I suppose my point would have been clearer had I replied to this [slashdot.org] post instead.
Yeah right. You tested the formula for one month. And you "found no conjecture" (whatever that means). And you don't have any paper records for it. And three people forgot anything about what the formula looks like. Anything else?
Unless/until somebody comes up with a suitably compressed notation. B-) Example: Maxwell's four equations were each about 1 1/2 to 2 1/2 pages long in a notebook when first formulated as differential equations. Expessed using the currently familiar "del" operator form they are each much less than a line of type, and have been fit onto T shirts. Sometimes along with additional text, as in:
And God said
(max)
(well's)
(equa)
(tions) and there was light!
The world is coming to an end ... SAVE YOUR BUFFERS!!!
Square Pegs in Round Holes (Score:2, Funny)
Re:Square Pegs in Round Holes (Score:2)
Make for good stories too... Wait, I saw this coming! There's also something about a black box, a blind guy, passports, and a guy who looks like he spent a little too much time in prison.
Hmm, lost it now.
Re:Square Pegs in Round Holes (Score:2)
Re:Square Pegs in Round Holes (Score:2)
Re:Square Pegs in Round Holes (Score:5, Insightful)
Mathematics is not about numbers and problems - it teaches brain to think. Nothing more.
Okay, so what you're saying is... (Score:5, Funny)
In Soviet Russia, mathematics teaches you.
Re:Grigori Perelman, please give us a sign! (Score:5, Funny)
The reason they can't find him in Russia is because he's already living in Sweden.
Re:Grigori Perelman, please give us a sign! (Score:3, Funny)
Re:Grigori Perelman, please give us a sign! (Score:2, Insightful)
Re:Grigori Perelman, please give us a sign! (Score:2)
Re:Grigori Perelman, please give us a sign! (Score:4, Funny)
Re:Grigori Perelman, please give us a sign! (Score:3, Informative)
Nice bit of jingoistic xenophobia there, but that's about all that's nice about your post.
Gang Tian, who has co-wrote a guide to Perelman's proof, said in 2004: "He certainly has no interest in material things. If he gets the Fields Medal, there is the issue of whether or not he will accept it." He also refused a prize from the European Mathematical Society many years before that.
He is not being threatened, he is simply a pe
Re:Grigori Perelman, please give us a sign! (Score:2)
Re:Grigori Perelman, please give us a sign! (Score:2, Troll)
30% Flamebait
30% Troll
30% Interesting
There's nothing remotely Flamebait or Troll in that message. TrollMods spew cosmoturf to suppress discussion of growing Russian backsliding towards tyranny. Slashdot's mod system really is disgusting sometimes when it's abused by political operatives.
Too Many Pages (Score:3, Funny)
Re:Too Many Pages (Score:3, Funny)
Trust me, 99.9999% of the folks will never follow the link if your short blather is at all close to an accurite summary.
Re:Too Many Pages (Score:3, Interesting)
A rabbit is a donut, not a sphere. (Score:4, Insightful)
Re:A rabbit is a donut, not a sphere. (Score:3, Funny)
Chocolate ones
Re:A rabbit is a donut, not a sphere. (Score:2)
Reputedly, there exists a book with a picture of Borromean humans.
a million, a thousand, roundness (Score:4, Funny)
Re:a million, a thousand, roundness (Score:3, Funny)
Re:a million, a thousand, roundness (Score:2)
7097556CL3 = CF93
who cares Fields medal? (Score:2)
Re:who cares Fields medal? (Score:2)
Is Madam Curie well known cause she won the Nobel?
Is Neils Bohr well known cause he won the Nobel?
Is Dirac well known cause he won the Nobel?
Is Watson/Crick famous cause they won the Nobel?
The point I am trying to make is that GP is 100% right.
Nobel/Fields doesnt come anywhere near, if I were to prove the Poincare Conjunture.
Maybe I can put it across in another way.
Is Ramanujan any less well known since he did not win a Fields?
Is Mahatma Gandhi any less a person since
nytimes is more realistic (Score:2, Informative)
http://news.xinhuanet.com/english/2006-06/04/cont
Re:nytimes is more realistic (Score:2)
Did these two guys have ANYTHING to do with solving the proof?
How does this relate to string theory? (Score:2)
Re:How does this relate to string theory? (Score:2)
Re:How does this relate to string theory? (Score:5, Informative)
According to string physicist Lubos Motl [blogspot.com] the proof indeed important to string theory. The proof based on the flow on the manifold (surface), analogous to heat dissipation - Ricci flow [wikipedia.org]. This flow deform metrics (distance between points of the surface). But this process also describe renormalization [wikipedia.org] of worldsheet - how the physics of the worldsheet [wikipedia.org] (surface which string drawing, moving in space and time) change with changing of the observation scale. That is how phisics of string change then the scale of calculation changed.
Re: (Score:3, Funny)
Re:How does this relate to string theory? (Score:5, Interesting)
The Ricci Flow [wikipedia.org] was defined by Richard Hamilton in 1981 as a step towards classifying topological compact 3-manifolds. Classifying 3-manifolds would certainly decide The Poincare Conjecture, as it states that all simply connected compact 3-manifolds are homeomorphic to the sphere. This is an important special case: most proofs of the classification of compact 2-manifolds start out by proving the an analogous statement for the 2-sphere. The Ricci Flow is a differential equation which defines how the shape of a manifold changes in time: given an arbitrary manifold M(0), you can apply the differential equation to it to get manifolds M(t) for (some) positive t, which gradually change shape. However, the Ricci Flow is not volume preserving, so you "renormalize" so that M(t) has constant volume.
The Ricci Flow has the useful property that it tends to make manifolds smoother and smoother. For example, if you started out with a lumpy ball, you would eventually get a smooth ball. It was hoped that it could be proved that if the initial manifold was a compact simply connected 3-manifold, then as t increased, the manifold would tend towards a 3-sphere. Unfortunately, while locally solutions to differential equations always exist, they don't necessarily exist for all time, and for some starting manifolds, eventually you would get to a road-block: a t for which M(t) could not be defined. What Perlman (hopefully) showed was that all road-blocks were of certain types, and that a surgery could be formed that would modify the manifold but not it's topological nature, and then you could again apply the Ricci Flow, until the manifold became a sphere.
Note that this method is useful beyond proving the Poincare Conjecture, as it (again, hopefully) describes all road blocks to extending the Ricci Flow, so that the same tools can be applied to any 3-manifold, and not just simply connected ones. In this manner, assuming Perlman made no mistakes (or that any mistakes can be corrected), it is possible to apply the same arguments to prove the Geometrization Conjecture of Thurston, which classifies 3-manifolds.
Re:How does this relate to string theory? (Score:4, Interesting)
It seems to me at this Ricci Flow differential equation could be quite useful practically. For example, in pattern recognition, if a computer could build a 3d model of an object using multiple vantage points, then simplify the object to one of the handfull of object types described by Perlman using the Ricci Flow, then this simple catagorization might help in the identification of complex objects (e.g. a donut really is a donut, even if it's been heavily frosted).
Do you know if Perlman's technique for handling the singularities will help with the numerical implementation of this process? Or are these issues numerically simple to solve - but only challenging to solve in proof?
Re:How does this relate to string theory? (Score:3, Interesting)
The tone of the summary is typical (Score:5, Insightful)
I'm all for capitalism and the idea of "prizes" to encourage research, but have we really become so jaded that it's a complete shock when someone does something worthwhile merely for its own sake? Perhaps he's gone on to other challenges, or he's wrapped up in some research that has his complete attention. Heck, perhaps he just enjoys math for its own sake and doesn't want to deal with all the side-effects of notoriety.
Re:The tone of the summary is typical (Score:2)
Re:The tone of the summary is typical (Score:5, Insightful)
I'm all for capitalism and the idea of "prizes" to encourage research, but have we really become so jaded that it's a complete shock when someone does something worthwhile merely for its own sake?
It isn't a shock that he did it for its own sake at all. Look at the thousands of open source programmers. The shock is that he's been given a million dollars and seem uninterested. Linus Torvalds does Linux for its own sake but if someone gave him a million dollars, he'd take it. Even someone who is not materialistic might think: "hmmm. A million dollars might help many Russian orphans or deliver AIDS drugs to Africans or ..." It is strange for a single person to be neither greedy, nor ambitious nor altruistic ... merely obsessed.
Yes, that's strange. It's rare and therefore strange.
Re:The tone of the summary is typical (Score:4, Insightful)
Where you see value judgments and a jaded reporter, I see a pretty reasonable surprise. I don't see anything in the article where the reporter suggests that Perelman "should" do anything other than what he is. Surprise, and remarking on an unusual behavior, is *not* approbation.
-b
Re:The tone of the summary is typical (Score:2)
Re:The tone of the summary is typical (Score:2)
Lots of people do things for their own sake (as long as they can pay their bills and get some food). But when someone got a prize of a million dollar as a bonus (for what you enjoyed doing anyway), can you really imagine someone turning this down? Well, Perelman hasn't done this (yet), but lots of people could im
Re:The tone of the summary is typical (Score:4, Insightful)
Maybe he... (Score:2, Funny)
Re:The tone of the summary is typical (Score:5, Insightful)
Re:The tone of the summary is typical (Score:2)
Re:The tone of the summary is typical (Score:3, Insightful)
Sadly, yes, doing something for it's own sake rather than for monetary gain is frowned apon
That is not correct. Look at the hoopla around both Gates and Buffett giving way their money. Look at the adoration of Mother Teresa. Look at the army of fans for Linus Torvalds and Richard Stallman.
and sometimes viewed with fear and confusion,
Sure: anything out of the ordinary will engender fear and confusion. There is a difference between suspecting that someone MAY NOT BE altrustic and "frowning upon" the
Re:The tone of the summary is typical (Score:2)
That and also while he did the hard work, that he didn't really contribute to the full proof, which is also weird.
Perhaps he just hates parties (Score:2)
Quite.
Perhaps he just hates parties. It's not like he'd be the first mathematician to do so. I and many other Slashdotters can sympathise with this, surely.
Re:The tone of the summary is typical (Score:2)
-Eric
Re:The tone of the summary is typical (Score:2, Insightful)
in mathematics, the trend has mostly been to keep the insights of a big result under wraps until the proof is written down properly and checked for bugs. that is the way to get yourself into the hall of fame [st-and.ac.uk]. it is almos
TFA is well worth reading (Score:2, Funny)
Quite an interesting character, this Perelman, and his proof could turn out to be a real landmark for mathematics.
I liked this bit:
Whatever he's smoking, I want some!
Re:TFA is well worth reading (Score:3, Insightful)
Side note: the Millenium Prize is a cool million. Which is $24 million less than Adam Sandler makes per movie.
Hurray for the free market! The true value for a personal accomplishment has once again been properly determined and awarded!
Re:TFA is well worth reading (Score:2)
Re:TFA is well worth reading (Score:3, Insightful)
Want to make a lot of money, do something the generates a lot of money. I can understand your point of view, but get real...
Re:TFA is well worth reading (Score:3, Insightful)
Innovation in math and science generates more money than any movie.
Consider something obviously fundamental to the way we live, like calculus or Fourier transforms.
It is very foolish to think that the direct and immediate monetary rewards a person receives are any real inidcation of the value their work provides to society.
Re:TFA is well worth reading (Score:2)
Re:TFA is well worth reading (Score:2)
You misunderstand free markets (Score:2)
The demand for comedy is higher than the demand for mathematical proofs. The recompense for either has absolutely nothing to do with merit, even if you believe a mathematical proof has more innate merit than comedy. BTW, if you do believe that, please define for us exactly how a mathematical proof is better (has more value or merit)
On the contrary... (Score:5, Insightful)
A Scottish physicist two centuries ago sees a strange bump-like waveform in a canal. It persists for over three miles, moving at nearly constant speed along the canal trench. He writes a paper, calling it a soliton wave and two Dutch mathematicians find a nonlinear partial differential equation that describes its motion. The equation, the Korteweg-De Vries Equation, proves fiendishly hard to solve. Finally, the crew working on the hydrogen bomb, finish the job early, so Ulam decides to use ENIAC to help him solve the Korteweg-De Vries Equation. He attains the first analytic solutions, and the study of soliton waves begins in earnest.
How does this earn a quid? Well, solitons model the way that blips of light move down a fiber-optic cable. The military decides that DARPA-net could run on fiber-optic cables, and uses them in building the early internet. Cellular telephone companies begin using fiber-optic cables to pack 100,000 phone conversations into a single pipe in such a way that they all get separated on the other end of the pipe-- one of the great engineering marvels of our time. We owe the modern internet, cell phones, anything that uses fiber-optics, to the solution of the Korteweg-De Vries equation. There was a similar burst of technology earlier in the last century when some closed-form solutions of the Schrödinger Equation were found.
Truth is, when we solve a major math problem like the Poincaré conjecture, billions of dollars of revenue are generated by new technologies that spring into being because of the new scientific understanding that the solution affords us. A thousand Adam Sandlers will not generate the amount of capital that the solution of the Poincaré conjecture will generate, especially considering that Perelman has shown the world that the Millenium Prize Problems are actually solvable.
Re:On the contrary... (Score:2)
Ah. No... The money/capital isn't generated. It's simply moved from one place to another, from low performing areas to higher performing areas. Only the governments can print money. Are you trying to tell me that money invested in the telecoms industry inherently has more merit than money invested in the entertainment industry?
What makes a mathematical proof inher
Re:On the contrary... (Score:2)
I think you hit the nail on the head with that. If only I had mod points.
Exactly. Merely because something is learned doesn't mean it's valuable. All
Re:On the contrary... (Score:2)
Re:On the contrary... (Score:2)
Re:TFA is well worth reading (Score:2)
Fair enough -- if making stupid people laugh is considered more important by society than fundamental mathematical discoveries, then it should be more highly compensated. It is. What's your problem with that?
Simply put, I believe that society is wrong. It is wrong to value the contribution of Adam Sandler as greater than that of Grigori Perelman
One day, probably many years from now, Adam Sandler will be a footnote in some obsolete database, and Perelman will be famous for his contribution to human kno
Re:TFA is well worth reading (Score:2)
Re:TFA is well worth reading (Score:3, Insightful)
Re:TFA is well worth reading (Score:2)
Since he lived a long time before the advent of recording technology, the type of success available to a popular musician (or more properly their record label) today just didn't exist.
a perpetual copyright system would only serve to
Re:TFA is well worth reading (Score:2)
Re:TFA is well worth reading (Score:5, Interesting)
Re:TFA is well worth reading (Score:2)
Re:TFA is well worth reading (Score:2)
PS: Even the experts who know the mushrooms in their area have been known to get sick or die when they go to another country and assume that the species which look the same are the same.
Recognition = Worry (Score:4, Insightful)
The curse of the gifted is that niggling worry in the back of the mind that if one accepts praise, one may lose his focus, drive or muse, if you will.
The prize is important (Score:2, Insightful)
name change? (Score:5, Insightful)
Re:name change? (Score:2)
Re:name change? (Score:5, Informative)
Things that are proven, are called theorems. They do depend on axioms, but those are defined as true. Sciences about the real world that can't put up axioms (because that'd require ex facto knowledge about the real world), so they can never be conclusively "proven". Hence well call them theories, like theory of gravity, theory of evolution. A few we've called "laws" as well because they have been so extensively tested, but it is not proven in a strict formal sense.
Re:name change? (Score:2)
Re:name change? (Score:2)
This is mildly incorrect. Theories also consist of a body of associated hard to solve problems. These problems often turn out to be observations and guesses or as you put it, "rough suppositions". For example, "Fermat's Last Theorem" has for centuries been a part of number theory even though it was proven only ten years ago.
Re:name change? (Score:2)
Re:name change? (Score:2)
Has anyone read the actual article? (Score:5, Informative)
Practical consequences of the proof? (Score:2)
Re:Practical consequences of the proof? (Score:2)
Even if the PC has no direct bearing on some of these fields, the techniques used in the proof will probably end up deeply influencing their research methods.
He's turned down the money (Score:5, Interesting)
Re:He's turned down the money (Score:2)
Re:He's turned down the money (Score:2)
That's stupid. He might turn money down. Now it's announced that proof is correct and that makes him candidate for that prize.
Even Russian newspapers do not have any official reaction of Perelman himself yet.
His (western) colleagues speculate that he might turn the award down. He is too far from normal life and money would distract him - so his friends say. That's speculation.
Re:He's turned down the money (Score:2)
Is it thanks to receive some money and a medal after your peers roasted you for a couple of years?
Re:He's turned down the money (Score:2)
disillusioned with Academia (Score:3, Interesting)
TFA mentions he has distanced himself from others in the Math community because he has become disillusioned. I read into that my own experience, which involved professors trying to hit on me, others trying to get me to write/edit their papers and then taking the credit, others who weave tall tales with just enough truth to fool grant money providers.
One of my colleagues now believes that Science is actually performing a random walk on the landscape of Truth. Occasionally, the walk stumbles over something
After reading TFA . . . (Score:2)
[/lie]
A question about hypersphere volumes (Score:2)
Obviously you're going to get an extra r with each dimension, buy why do you only get another pi every other dimension?
While I'm at it, on a related subject it seems to me there are two possible ways of constructi
Re:A question about hypersphere volumes (Score:5, Informative)
The Jacobian, or unit volume if you will, of a hypersphere [wikipedia.org] has a a highest term of sine, or cosine, which grows as you increase dimension. Specifically, for an n dimensional sphere, the highest power of sine or cosine will be sin^(n-2).
Anyway, to answer your question, integrals of sine or cosine to odd powers produce only functions of other sines and cosines. However, integrals of sine or cosine to even powers produce functions of sin(x), cos(x) and x. The x part gives you your pi, but only does so every second dimension, when the highest power is even.
Here's the integrals of (sin(x))^n, for various n
n=0: x
n=1: - cos(x)
n=2: x/2 - sin(2x)/4
n=3: 1/3 * (cos(x))^3 - cos(x)
n=4: (sin(4 x) - 8 sin(2 x) + 12 x)/32
two Perelman anecdotes (Score:4, Interesting)
1) I met him at the Mathematical Sciences Research Institute in Berkeley at a workshop sometime around 1994 and he at that point had ridiculously long fingernails and was quite unkempt, even by the quite weak standards applied to research mathematicians. That was a while ago, of course and that was probably one of his first visits to the US. He gave an incomprehensible energetic talk so what most people commented on was his nails.
2) In 2003 or so, during a limited lecture tour about his proof of the Poincare Conjecture, he responded deftly and hilariously to a comment of Misha Gromov in the audience. Gromov is one of the most difficult people to have in a talk- he is a great mathematician with not much patience and has derailed or rerouted talks by many great researchers, who sometimes get quite flustered. I can't remember the exact wording of the exchange, which is too bad since it was precious, but Gromov asked something like "I don't see how that goes, I'd like to see some more details" and Grisha responded with something like "well, yes, you would" and carried on as he had intended.
Re:I remain skeptical (Score:3, Funny)
Re:I remain skeptical (Score:5, Insightful)
Secondly, I would invite you to write down a complete proof of some well-known mathematical fact, the Stone-Weierstrass [wikipedia.org] theorem say. You must prove this from first principles, starting with axiomatic set theory. I would be very surprised if you even managed to finish and even more surprised if the proof came in at under 1000 pages. This highlights what was mentioned by a sibling of mine: mathematics is divided into small steps and you would never dream of trying to prove something all at once.
Thirdly, this is the first ever proof of the Poincare conjecture. It is quite common in mathematics that a nicer proof of a known fact will be found.
Re:I remain skeptical (Score:2)
Re:I remain skeptical (Score:4, Funny)
Re:Ellipse in Highschool (Score:2)
Re:Ellipse in Highschool (Score:2)
Re:High Mips, Low I/O (Score:4, Insightful)
Next time you are in a meeting think about this..
Re:1000 pages?! (Score:2)
Example: Maxwell's four equations were each about 1 1/2 to 2 1/2 pages long in a notebook when first formulated as differential equations. Expessed using the currently familiar "del" operator form they are each much less than a line of type, and have been fit onto T shirts. Sometimes along with additional text, as in:
And God said
(max)
(well's)
(equa)
(tions)
and there was light!