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.
Riemann hypothesis reportadly also solved (Score:5, Interesting)
This particular problem has big implications for online cryptography as it deals with the distribution of prime numbers. Apparantly.
(I'm no mathematics person BTW.)
abstract- not complicated at all! (Score:1, Interesting)
Re:He'd post AC (Score:5, Interesting)
It probably would only take $15K in the US to rent a small apartment in a cheap city and buy food for a year, allowing him to work on his problems. I think the point is that this guy may have been able to make a significant contribution to human knowledge and maybe centuries of notoriety with what it cost to live for a few years. Most of the rest of us would have taken the same amount of money and just dumped it into buying an upscale SUV.
Re:He'd post AC (Score:3, Interesting)
"On the electrodynamics of moving bodies"
is exceedingly boastful.
In computer science, an analogy might be to publish a paper titled:
"On datastructures, in general"
What an oddly broad topic to choose, unless
you are claiming to be saying something
rather profound.
The "reclusive nut's" picture (Score:1, Interesting)
The guy is a bit scary..
Interesting View (Score:2, Interesting)
Perelman and the prize (Score:5, Interesting)
So think about his perspective: he's a complete loner who was ignored by the mathematical community for 10 years! Now that he's going to be a "certified" genius (with the $1M prize) why exactly should he care.
Also, it's worth pointing out that like Wiles (who solved the Fermat Conjecture), Perelman's work develops a theory that has the Poincare conjecture as a corollary which is interesting but not of central importance.
Turning down the money is nothing special (Score:1, Interesting)
Time (Score:3, Interesting)
Russian? Brit? (Score:2, Interesting)
So did the British man or the Russian solve it? April 02 newscientist has the same basic story with the names changed.
Re:Hopefully he has better luck than de Branges (Score:5, Interesting)
Re:Hopefully he has better luck than de Branges (Score:2, Interesting)
As opposed to Perelman, who appears to have actually proved a larger conjecture, of which the Poincaré conjecture is a specific case.
Re:Problems with the Millenium Problems (Score:3, Interesting)
The results of different mathematicians, some big and some small, are put together by the next generations of mathematicians to derive new results. Many people who deal with the practical are content to buil on fairly old results. They can decry all they want, but most likely even they use somee result which was initially a solution waiting for a problem. General relativity is a good example of mathematics that had no application at first. Einstein needed the tools of differential geometry (beyond just surfaces in 3 dimensions) to formulate and express the theory. I might needd to check my math history a bit, but I can't think of any major mathematics which were developed for a specific practical purpose since about Gauss. There have been serveral that have been applied, though.
What new "techniques" were invented to (suposedly) solve this problem?
I don't quite understand the details as I have only taken a single class in differential geometry and I don't think a paper has been released yet, but Perelman gave a lecture on his results at MIT and my unerstanding of it is: By doing something studying the Ricci flow in a new way, spawning some new field that I heard refered to as "Geometrization" or some such, he created a theory which solves a large class of problems. The poincare conjecture is just a special case of his theory.
In general, though, all the really hard problems in mathematics have spawned many theories and techniques as people attempted (and failed) to solve them. While Andrew Wiles proved and important conjecture in the process of proving Fermat's last theorem, 250 years of mathematicians created all sorts of wolderful results along the way. If I told you them, would you appreciate them, or even understand them?
They were the base foundations for the research and development of what we have today
And things like this will be the base foundations for the research and development of what we have tomorrow. But when things like that were being worked on, they had no practical use outside of mathematical puzzles and other bits of mathematics. I believe that Hardy once said that he loved number theory because he knew he was working on something with no applications. You don't know what results will be based upon this work and for you to use hindsight to justify the work that became important while dismissing all work that doesn't have immediately obvious applications is at the very least illogical. You don't know the future, and its pretty clear that you don't know the past. Don't pass judgement on a major achievement before it has hadd a chance to bear fruit.
Re:Perelman and the prize (Score:5, Interesting)
What I find particularly interesting is that this guy was able to devote 10 years of his life to solving a problem so complex that there was no intermediate output. The same happened to Wiles, who took 7 years to get hold properly of the Fermat theorem.
Obviously, in both cases it would have been impossible to reach such great results if the authors had had to keep a steady pace of lesser publications. But this is the rule in the academic world: "publish or perish". You must prove yourself "productive" year by year, otherwise you're out.
I've always thought that applying industrial methods of prouctivity measurement to research is utter madness (I am an academic myself). IMO, Perelman's and Wiles' cases show it clearly.
Old news? (Score:1, Interesting)
Translated for better reading (I use to speak spanish):
Robinson, S., Russian reports he has solved a celebrated math problem, New York Times, 15 April 2003, F3
In November, 2002 appeared a rumor on the Internet saying that the mathematician Russian Grigory Perelman, from the Institute Steklov of the Russian Academy of Sciences in Saint Petersburg, had published in arXiv a preprint presenting a proof of Poincaré's Conjecture.
Trivial to prove / the description must be wrong. (Score:2, Interesting)
Cut a 4 Sphere with a plane right down the center.
The cross section is a 3 sphere. Consider that section to be the section wrapped with your 3 sphere "rubber band".
Now move a short distance perpenducular to the this slice and take another slice. It will be a smaller sphere. You've just slide your "rubber band" down the apple a bit.
If you keep doing this the 3 sphere slices get small and smaller, converging to a point.
Viola, it's simply connected.
How do you get your jollies? (Score:3, Interesting)
If you're a sex fiend, you'll spend your time in the gym, and maybe convincing people to pay you hefty consulting fees to tell them things they already know.
If you're a musician, you'll be in a band, even if you'll never make more thana hundred bucks a gig.
If you want to be the richst man in the world, well, if I knew the answer to that I'd be the richest man in the world.
But if you're a guy who actually does like solving math problems, and someone comes along and offers you $1 million, it's probably pretty useless to you, sine it doesn't help you solve math problems.
(Ok, in reality, that's kinda short-sighted, as you could buy $1 million of computer time, but maybe he doesn't like computers.)
Why aren't proofs verifiable via software? (Score:3, Interesting)
I am not talking about having a computer generate the proof itself, which can be difficult of course, I am just talking about verifing a given proof.
Re:He'd post AC (OT) (Score:3, Interesting)
West Virginia can use a few selected people who are willing to come here. Jobs can be had, but may not be everyones cups of tea. With oil back up, well drilling has started up again, which has taken up most of the slack from the closeier(sp) of several glass making operations due to far eastern imports cutting the market for our higher priced hand-blown products. Basicly, he who is willing to work, can usually find work. It may not be at what one would call the prevailing scale, but then neither is the cost of living here (older places in bad need of some sweat equity can be had for under $20k) other than its almost de-rigor for the first vehicle to be a 4wd. There is one thing we've got planty of, and thats hills. Right up in your face hills.
I seemed to have fit right in when I came here as I am essentially self-educated in electronics and have been making my living making electrons do interesting work since the late 1940's. My highest 'formal' education is the 8th grade. But in local tv broadcasting, I am a very big frog in a quite tiny pond, spending the last 20 years in that office/workshop. With all the perks added in, I was making more than $60k when I retired.
To give you an idea of the climate here for technical jobs, about 10 years ago I gave a 10 explanation of how tv works to a bunch of 8th graders touring the station as an end of the school year perk. I finished up by saying that my job keeping all this working was an interesting job, but that someday I would retire, and I wanted one of them to be nipping at my heels wanting to replace me. 30 some 8th graders laughed their collective asses off, they didn't understand that like shoveling shit out of the cowbarn, somebody has to do it. I'm an old Iowa farm kid, so I know about shoveling shit out of the cowbarn too. So I wrote that possibility off and never mentioned it again to an end of the school year tour group. AFIAC, it was their loss, not mine. I rather enjoyed being the old man on the mountain, the guru if you will, that when things went to hell, got the phone call. Of course, 2.5 years after I retired, I still do. No one knows that 40 year old GE transmitter (locally anyway) like I do. OTOH, I get paid to answer the phone too, which helps in the health insurance dept.
To put something in here thats not OT, I would hope that this russian does take the money, and that he has more sense than to turn into a russian version of Jack Whitaker, who won the lottery here for about 140 mill 2 years ago, and has had nothing but legal problems since. He's also been mugged & left for half dead several times since everyone knows he carries several hundred $K around with him as he frequents the bars. IMO, thats not what winning the lottery should be about.
The russian would be similarly targeted as one to be taken advantage of if he had that kind of money at his disposal. Because of this, he may see it as a less than ideal situation. If he was smart, he'ed open an account here, and have a regular funds transfer to there of maybe 1 or 2 hundred a month setup in perpetuity. That amount would go a long way in raising his standard of living I'm sure. As to how to assure he got it when the russion mafia probably owns the local bank there, I don't know.
Cheers, Gene
Re:He'd post AC (Score:2, Interesting)
So in a sense, that high esteem that he'd earned was his currency, albeit a less fungible one. But it still was value previously earned, stored in some other form.
Re:He'd post AC (Score:4, Interesting)
Let's say that there is a small economy. I am a central bank. Right now, there is no money. Therefore, you take a loan out for $10, and I charge $1 interest. Frank takes out a loan for $10, and I charge him $1 interest. The whole economy has $20 in it, but they owe $22. There's no way this can be paid off. Now, one of you could handle their money better than the other, and get a $1 advantage to pay off their loan, but that would leave only $9 in the economy to pay off a remaining $11 loan. One of you would be fine, but there is no way in this system for everyone to pay back their debts. So, eventually, the banks own nearly everything.
This is why the founders of our country hated central banks, and was one of the primary reasons for the revolutionary war.