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Poincare Conjecture Proof Completed
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!"
What kind of strange rabbits have these topologists seen? The rabbits I've seen have a hole from end to end through them called the digestive tract.
AccountKiller
Most of the freaky genius mathematicians who can do the really wierd stuff are usually (but not always) high MIPS, low I/O types anyway. Spend a week coming up with a partial proof of one percent of a subproof for a much larger problem, no problem. Contemplate going out of the house for bread and milk. See if you can get it delivered, or maybe get someone else to do it (you know, someone you know, someone you won't have to talk to very long...)
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.
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"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.
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!
Soylent Green is peoplicious!
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 sense and in the practical sense. The fruits of that labor wouldn't have come out without placing such emphasis on the problem. Hilbert's lecture at the beginning of the 20th century was similar. Here was (one of the best minds at the time propising a framework in which to work, goals to look towards. Not even close to all of them have been resolved, but they are smart problems that have led to all sorts of applications and results. It's a goal to work towards. The Clay prize does the same thing. Is the Navier Stokes problem that important? Yes, that's why we have this great initiative for a derivation of classic and not weak solutions, or at least existence. The quest for the solution to the problems and those like it have created real progress. Without this kind of framework, we'd possibly not have the amazing work in PDEs and weak solutions that let us do great composite designs and image processing (to name two areas).
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?
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 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.
Don't you hate meta-sigs?
The USA, instead, is not subject to problems of abuse of the legal system, as the case of Dmitry Sklyarov demonstrated.
You know...I think you're trying to be sarcastic, but you shouldn't because you're actually correct.
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...
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?
(And BTW mods, how the f*ck is that "insightful" in any way?)
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
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.
"Indeed, it is wise never to consider any form of electronic data as final." --Arnold Robbins
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.
All hope abandon ye who enter here.
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.
Life is too short to proofread.