Chinese Mathematicians Prove Poincare Conjecture 288
Joe Lau writes to mention a story running on the Xinhua News Agency site, reporting a proof for the Poincare Conjecture in an upcoming edition of the Asian Journal of Mathematics. From the article: "A Columbia professor Richard Hamilton and a Russian mathematician Grigori Perelman have laid foundation on the latest endeavors made by the two Chinese. Prof. Hamilton completed the majority of the program and the geometrization conjecture. Yang, member of the Chinese Academy of Sciences, said in an interview with Xinhua, 'All the American, Russian and Chinese mathematicians have made indispensable contribution to the complete proof.'"
This is... (Score:5, Interesting)
Ok, in plain english (Score:3, Interesting)
Bonus points if you can explain some consequences of it being proven true.
more info (Score:3, Interesting)
Two very good reasons (Score:5, Interesting)
Math isn't dead (Score:5, Interesting)
I was just having a conversation about this yesterday with my math teacher.
Lots of people think that high level math is just advanced adding and subtracting.
This is good stuff. Props to Zhu Xiping and Cao Huaidong- this shows people that a career in studying mathematics is actually an interesting and rewarding career.
Re:Dear God (Score:2, Interesting)
Hopefully enough folks complain to get the runner up and a few others added. It's easy to provide the choice.
... not yet. But it may die soon. (Score:4, Interesting)
Re:Two very good reasons (Score:2, Interesting)
If you think in cartesian terms the the unreal axis is at 90 degrees to the real axis. This maps very neatly to where entities work at 90 degrees to each other, as in electric currents running through a wire in a magnetic field. Additionally, although I can't remember the details as it was thirty five years ago when I studied this, the shape of an aerofoil can be described using i, and if you do so the maths relating to the airflow becomes much simpler.
As I said, I studied engineering thirty five years ago and I'm very rusty, I'm sure that other /.ers could provide plenty of examples
Re:wouldn't trust it yet (Score:4, Interesting)
Unfortunately, automated proof tools are not sophisticated enough to handle the kind of maths seen in solving the Really Big Problems. Not yet, anyway.
Re:It's all a conjecture (Score:2, Interesting)
Re:Joe Public goes (Score:3, Interesting)
There's a whole slew of mathematical theorems, conjectures, hypotheses, et. al. that sound like Robert Ludlum novels [everything2.com]:
Re:Chinese == Good at Math (Score:5, Interesting)
The Chinese school system (and in ancient times, the scholar system, which stratified society into a "scholar class" and the "masses") is completely and utterly innovation stifling. It emphasises testing and memorization above all else, and curiosity and individuality are systematically beaten out of students. No snide comments about communism, please, it has nothing to do with that (any mathematician will tell you that the Soviet Union produced a metric tonne of talented mathematicians, my advisor was one). Chinese students memorize everything. Because I speak Chinese and love math, I have tutored quite a number of high school and university undergraduate students in math and the simple reason that they suck at it is they basically cannot wrap their head around proofs.
Proofs are difficult for most people at first, but you have to understand that the way a typical mainland Chinese kid approaches math is by memorizing every formula in his math textbook and then trying as best he can to choose the one that "works" with the problem he is presented. He does not do this because he stupid: he does this because the Chinese standardized testing system reinforces the behaviour. The exam problems are expressly designed so that various formulas are the "keys" to the problem, that is, answering the (usually multiple choice) question correctly relies on your ability to quickly recall one formula (perhaps two) and plug the numbers in effectively. So many problems are presented and so little time is given that no time for derivation or logic is really provided. Because of this, essentially every Chinese kid can recite from memory a whole host of trigonometric identities without having the faintest idea why they work or how to derive them, even when the derivation is relatively simple.
Because there's so much anti-Chinese sentiment in the west these days and on Slashdot in particular, I want to reiterate for a moment and say that this is not an inherent failure in the Chinese kids themselves -- they are not stupid -- but they are completely crippled by their education system. From day one they memorize everything. They memorize entire passages written in old Chinese and are asked to reproduced them from memory at exam time -- I've been told by several kids here in Beijing that writing even one character wrong is essentially equivalent to forfeiting the entire problem. These are not 3 line passages folks: we're talking two or three pages of old Chinese. Imagine being told at 17 to memorize 3 pages of Beowulf. That's what we're talking about.
The thing is (as any drama major will tell you) memorization, like all things, gets easier with practice. And from day one (when I first arrived in China I moonlighted as a Kindergarten teacher, so I have some first hand experience here) kids are memorizing stuff, from poems to proverbs to Chinese characters. It becomes easy for them, and over the years they depend on it more and more. The worst part is, high school and lower division level mathematics (if it can be called that) presents problems (like doing integrals or calculating derivatives) that lend themselves well to the "memorize a formula" method. And so Chinese kids tend to do exceptionally well in these courses, and then mistakenly assume they are good at math. This is in fact not