Russian May Have Solved Poincare Conjecture 527
nev4 writes "Reuters (via Yahoo News) reports that Grigori Perelman from St. Petersburg, Russia appears to have solved the Poincare Conjecture. The Poincare Conjecture is one of the 7 Millenium Problems (another is P vs NP, also covered on /. recently). Solving a Millenium Problem carries a reward of $1M, but apparently Perelman isn't interested..." nerdb0t provides some background in the form of this MathWorld page from 2003.
He'd post AC (Score:5, Insightful)
Take the case of Paul Erdos [wikipedia.org] who was essentially homeless, but published over 1500 papers and is considered one of the all time greats in the field.
Perelman just casually posted his solution out to the web in much the same way that some of the most brilliant posts on
Re:He'd post AC (Score:5, Insightful)
Einstein's original paper on Special relativity was named "On the electrodymanics of moving bodies".. It was not named "Revolutionary new discovery by me, Albert Einstein which will revolutionize the world of physics".
I guess there are several reasons for this.. one is simply manners. Boasting is unpolite. Scientific papers rarely have exciting titles, even when the results are exciting.
The second is of course, that a good scientist realizes the if a result may be revolutionary. A good scientist also always leaves room for doubt.
So the natural behaviour would of course to be careful and discreet, and not go confidently telling the world of your revolution until it has been verified. Otherwise, you'll end up with a lot of egg on your face.
Conversely, most scientists are highly sceptical of 'revolutionary' results which are announced in the press before being published. In fact, most pseudoscientists are very good at publicizing themselves and their 'revolutions', probably because they are totally convinced of their own theories, and are lacking the 'self-doubt' bit.
Re:He'd post AC (Score:5, Insightful)
Only us self-actualized "Anonymous Coward" guys rise above this with insightful and informative posts such as this one without whoring for karma.
Re:He'd post AC (Score:4, Insightful)
Oh please. What is this? The 60s? Apparently the guy is able to find enough time to work on these problems. That kind of freedom is what money buys. If he didn't have enough money to do that then it would suddenly become much more important.
"Money" is not some stack bills in your wallet. It represents some tangible effort that had value, and that value is now stored in a convenient form, ready to be exchanged for something else of value.
Just like Linux configuration forums (Score:3, Insightful)
Okay, so tell me how this is any different from every l33t user that tells me how to get my dual flat panel setup working under Xandros without editing the X files manually? Sounds like these kids just tried their hands at mathematics, too.
Wake me up when it's peer reviewed and accepted (Score:2, Insightful)
Editors, I'm talking to you.
Racist title (Score:4, Insightful)
Re:He'd post AC (Score:5, Insightful)
Re:He'd post AC (Score:2, Insightful)
I meant to say is that we'd all be happier if we didn't have to worry about money. However, a lot of people are living paycheck to paycheck and the little things in life (broadband, it's a joke) make the effort meaningful.
Your reply was dead on though, and insightful.
Re:He'd post AC (Score:5, Insightful)
However, I've seen many intelligent people work hard without stopping because it was the right thing to do, not because of the monetary gain. That is what I'd hope to highlight.
Re:He'd post AC (Score:2, Insightful)
In truth, money is a loan from a central bank to a government, that due to interest can never be repaid. Think about it a moment, if you get a $100,000 home loan, you don't walk away with a brief case of bills (and even if you did, they can't be exchanged for gold), the bank assigns some numbers to your account briefly, which gets assigned to someone else's account who then lets you have a house.
All money is, is slavery to a bank, which gives permission for someone to transfer real property to you.
tr/Russian/Grigori Perelman/ ..? (Score:5, Insightful)
"Grigori Perelman May Have Solved Poincare Conjecture"
I've noticed that these kinds of announcements often make a point of appending a nationality to the name of the person involved in the discovery. Surely this proof builds on mathematical knowledge from around the world. Or was Grigori Perelman standing solely on the shoulders of "fellow Russian" mathematicians? I highly doubt it...
Re:Getting Maried Bad for Math? (Score:3, Insightful)
Re:He'd post AC (Score:4, Insightful)
Contrast this lack of fanfare with another recent publication, Stephen Wolfram's A New Kind of Science [amazon.com]. This 'new' science seems to have been met with mixed reviews at best, and not the paradigm shift that the author seems to have been hoping for. Of course only time will tell who is right... But in the event that Perelman's is incorrect, his humility and lack of hubris regarding his solution definitely earns him my respect, and undoubtedly that of many others in the field.
Re:Poincare Conjecture link sucks! (Score:4, Insightful)
The Poincare Conjecture involves hypothetical 4-dimensional shapes with the same properties, and isn't very easy.
Re:He'd post AC (Score:2, Insightful)
Perhaps all of these years of fertilizing your organic garden with human feces has lead to some sort of spongiform encephalitus.
Money IS important. It may not be the most important thing in the world, but we all need to eat and have a safe place to sleep at night. Those things take money.
LK
Re:Getting Maried Bad for Math? (Score:2, Insightful)
Re:He'd post AC (Score:3, Insightful)
However, the last couple of years since I finished, I have lived very close to the official poverty limit of my city, and I know that is bad.... So, I need to do something to get a higher influx of cash. I find no motivation in doing it, though, to the contrary, it feels like I have to abandon the pursuit of interesting things to get it.
I just need to be fed, kept clothed when it is cold (and when it is warm too, I hear society demands it for some strange reason), some bandwidth and electricity, given a bit of sports equipment, and an occasional trip to interesting places on earth. Then, I need interesting and hard problems to work on, and I'll be a very happy creature.
I could probably do this at below average income, but right now, it seems very interesting stuff very seldomly pays even that...
Re:Just like Linux configuration forums (Score:2, Insightful)
the case of: it's too complicated, I'll just get a
Mac. This is a case of if you build it they will
come.
2. He probably wants the verification to happen
double blind, without his input which could make
things easier to understand but also could make it
easier to skip over errors. This simply is a way
to nudge each reviewer to think for themselves.
We know getting YetAnotherDistro to run SomeDriver
is possible, it's just a matter of how. Not so here.
3. Whether or not he is right, this guy _is_ 1337.
Think K&R writing a blurb on how some driver is to
be written letting you code up the rest.
Re:He'd post AC (Score:3, Insightful)
"A musician must make music." I'd strike the "If
Regarding the "homeless" Paul Erdos, who wouldn't go to more than a little trouble to have him as a house guest? Seems like he'd have the advantages of the very rich with many homes and none of the disadvantages.
To add a smallish fly to your ointment, somebody had to use a couple of mod points to bring your post up to the same level of visibility as this one.
Re:He'd post AC (Score:3, Insightful)
Humm, but what if the loan has been paid off, for long enough you've forgotten that you once made house payments?
You see, I wasn't about to be scratching to make a mortgage payment when my income was reduced to the social security (gawd, what an oxymoron that is for some folks) levels in my old age, so the house has been paid off for 8 years now, and I've been almost-retired for 2.5 years.
That little detail makes it so that I still have some "discretionary" income, keep 2 vehicles running and can play with a little woodworking (I found some cherry a few days ago for less than $1 a bd ft) and these damned computers, and still afford a couple of beers a day. And oh yes, take my boat out on the lake and fish if I get otherwise totally bored. It aint new, it aint fancy, but it keeps my butt dry unless its raining, and gets me around the lake at about 5mph with its 10hp motor.
Think about it... Its called managing your money for you, not some faceless loan shark or bank (is there a difference at the end of the day?).
But, it was easy to pay it off in a short time when both of us were working full time, so we didn't really miss a nearly $700 a month payment while we were paying it of in 7 years instead of 30, and we saved about 60,000 USD in interest doing it. Now all we owe are utilities and taxes.
Its a nice feeling, and those we can handle, or at least till oil hits $100 a barrel.
So no, you don't have to owe your soul to the money lenders. Way the hell and gone too many of you do though.
To those who will never get ahead because they owe their soul to the company store, I have sympathy, but the message is the same. Look at how you are handling your money now and see if there is any room to cut waste. Doing so will pay hundreds of thousands in future dividends once you get into the habit of making every dollar that comes out of your pocket buy something worthwhile. The "just gotta have it" attitude doesn't count at the end of the day if theres nothing left to invest in tomorrow at the end of the day.
Cheers, Gene
Re:He'd post AC (Score:4, Insightful)
So it would be like publishing a paper called "on datastructures" if you were the person that invented datastructures....
Re:He'd post AC (Score:2, Insightful)
Exceedinly boastful? The title is an accurate description of the content - it was a new model for the electrodynamics of moving bodies. There is no indication of merit or pride in the title, it's you who ascribes those attributes. You then attempt to denigrate Einstein for describing what he has done, apparently purely on the basis that his ideas were novel and better than those which went before.
Perhaps if you ever achieve something noteworthy you'll realise that stating what you have done in an appropriate forum is not boasting. Saying something profound is not boasting. If you think it is the problem lies with your self-esteem.
You may have a tiny penis, but that doesn't mean those of us with a monster dick should hide the fact.
Re:He'd post AC (Score:3, Insightful)
This means you can do it on welfare from your trailer park home, or from a cardboard box under a bridge if that's your thing. Significant mathmatical breakthroughs have, in the past, been made by incredibly poor persons with little schooling to speak of. Admittedly this is rare, but not unheard of.
You really just need access to a library of some sort and that rarest of commodities, an inquiring mind of your very own...
Re:He'd post AC (Score:2, Insightful)
"On the data distribution in the p2p networks", or
"Stability of the Internet networks".
And these are the _real_ titles of the modern CS papers.
Computer Time (Score:3, Insightful)
Computer time will only help with P problems, or P elements of NP problems. Great mathematicians seem to be NP-solving machines. A hundred years of computing time on the best computer might releive some of their tedium but would actually have an insignificant impact on their ability to solve problems.
The rest of us lesser beings might consider spending out time building a super-high resolution MRI machine. We'd want to be able to image every atom in a person's brain and record a year's worth of data at something like 100k samples per second. The MRI should be light and comfortable so our test subject could wear it comfortably for that year.
Once the suerp-MRI machine is ready, we manufacture it into a comfortable yet stylish (to the eyes of mathematicians) hat, and invite a prize-winning mathematician to wear it for a year.
At the end of the year, we need to locate some prize-winning neuroscientists to help us decode our brain scans and prize-winning computer scientists to help us build it.
some terminology (Score:5, Insightful)
The n-sphere (which mathematicians generally denote by S^n) can be thought of as `all points in (n+1)-dimensional space which are at unit distance from the origin'. So S^2 is the surface of a solid 3-dimensional ball. This sometimes surprises people, who expect this to be S^3 but the key observation here is that the 2 refers to the intrinsic dimension of the object, rather than the extrinsic dimension of any space you might happen to put (`embed') the object in. The fact that we often think of the 2-sphere as being embedded in 3-dimensional space doesn't change the fact that it's inherently a 2-dimensional object. An ant wandering around on it still only has two degrees of freedom.
The 3-sphere (S^3) locally looks like ordinary, flat, Euclidean 3-space, but on a larger scale it kind of doubles back on itself - if you keep walking (or floating) in a `straight line' (well, actually the 3-dimensional analogue of a `great circle', but never mind) in any direction, then you'll eventually get back to where you started.
The Poincaré Conjecture says
This, by itself, isn't particularly enlightening to the non-topologist, but what it actually boils down to is:
What does this mean?
Well, an `n-manifold' is a space which locally looks like ordinary, flat, Euclidean n-dimensional space. So a 3-manifold is a space (like S^3) which locally looks like ordinary 3-space (but which might twist back on itself in a peculiar way on a larger scale).
`Closed' means that the 3-manifold doesn't have a boundary - no matter how far you walk, you're not going to run into a brick wall, or fall off the end. `Compact' is a bit more technical, but in this context essentially means you don't get odd shooting-off-to-infinity stuff you have to deal with.
And `simply-connected' means that the first homotopy group (the `fundamental group' of the space) is trivial. What that means is that any closed loop (of string, if you like), in the manifold, can be continuously shrunk down to a point. Here `continuous' means that you're not allowed to cut or glue the string while you're doing it.
To use a 2-dimensional analogy, the 2-sphere (the surface of the 3-dimensional ball, remember, or alternatively a British doughnut) is simply-connected, because given any closed loop in the surface, you can shrink it down to a point without it getting snagged on anything. Whereas the 2-torus (the surface of an American doughnut) isn't, because you can't shrink all closed loops down to a point - one which goes all the way round the central hole, for example, can't be shrunk.
Finally, `homeomorphic' is basically a technical word for `topologically equivalent' - we allow continuous deformations (stretching, twisting, etc, but not cutting or pasting), rotations, reflections, or any combination of these.
So, the (classical) Poincaré Conjecture is essentially a technical way of saying ``If it looks like a 3-sphere then, basically, it is''. (For certain definitions of `is', and `looks like'.)
The analogous conjecture in n-dimensional space is known to be true for n=1 (trivial), 2 (pretty simple), and 5 and above (the 5-dimensional case was proved by Zeeman, who is my PhD grandsupervisor - my supervisor was one of his students). The 4-dimensional case is weird, and there are three different forms to consider - the `piecewise linear' and `topological' cases have been proved, but the `smooth' case is still unproven.
As I understand it, what Perelman claims to have done is prove Thurston's Geometrisation Conjecture, which implies the Poincaré Conjecture as a special case - rather lik
Re:He'd post AC (Score:2, Insightful)
Re:Problems with the Millenium Problems (Score:1, Insightful)
Re:Hopefully he has better luck than de Branges (Score:3, Insightful)
It's not a court, Branges doesn't need to do anything - someone needs to prove it one way or another for the science to progress.
Except... (Score:3, Insightful)
Re:Hopefully he has better luck than de Branges (Score:3, Insightful)
Yeah, I skimmed his paper, and noticed that as well. Apparently, "apology" in this context means a proof that has not yet been subjected to peer review, but which the author is deeply convinced is correct. Pasting some output from a dict apology, it seems:
Clearly, de Branges is using the term in this sense.
It doesn't really matter though, because if you actually read his paper [purdue.edu], the first third is all incomprehensible background nonsense about the nature of the problem, while the last third is all incomprehensible arrogant nonsense about what he wants to do with his prize money. The actual meat of the paper is buried somewhere in the middle, but it's like that's all just an afterthought to the guy's mad ravings about his place in history and his imminent wealth.
He couldn't be more different than the person that seems to have solved the Poincare conjecture. Where Perelman is silent behind a paper that seems to concretely prove not just the problem at hand, but a whole broader class of problems, de Branges has this ridiculous paper that goes on and on about what a big shot he is, while stomping around his university like a little tinpot Napoleon. I'm no math whiz, but hot air isn't always hard to recognize...
Re:Hopefully he has better luck than de Branges (Score:2, Insightful)
Just like Perelman, de Branges can just sit and wait. Hopefully, someone will eventually read the proof thouroughly and see whether there are any significant errors. And then everyone will benefit from knowning whether the proof exists and if yes, what it is and that the conjecture is true.