下面是从教育学术转载的一个翻译。里面有点翻译的错误，我给他做了一点改正。我认为基督徒不能走向另外一个极端：就是反智。这里有人认为没有学问就是最属灵，是很不对的。

斯坦福科学家对庞家莱猜想的公开评论

送交者: nyny 2006年8月01日18:15:29 于 [教育与学术]http://www.bbsland.com


http://www.npr.org/templates/story/story.php?storyId=5591652

数学家也许解决解决了百年难题
NPR 访谈

Scott Simon:
今年8月将在西班牙召开国际数学家大会，届时很可能宣布一个著名数学难题被解决的消息。这个难题被称为庞卡莱猜想，但是对于它的解决，现在还有很多争论。来自斯坦福大学的Keith Devlin，将为大家作一介绍。

Keith Devlin:
庞卡莱猜想是数学中最大的难题之一，也是克雷数学研究所的七道千禧数学难题之一。它是1904年由伟大的法国数学家亨利•庞卡莱提出的。许多大数学家都对这个问题作过研究。他们有的还给出了证明，但不久都发现有错。

这个问题就是要确定我们所生活的空间的形状。这是庞卡莱很感兴趣的问题。他是一位伟大的数学家，差点比爱因斯坦还要更早地发现了狭义相对论。那么空间的形状是指什么呢？对数学家来说，就是拓扑形状。在拓扑学中，我们对距离和弯曲程度不感兴趣，所以用拓扑学术语来说，一个网球，高尔夫球或者足球都是同样的东西。而甜麦圈就不同了，因为中间有个洞。所以如果问我们所居住的空间是什么形状，困难就在于我们生活在空间的内部。

你能区分球面和甜麦圈(也就是数学家所称的二维环面)吗？从外部来看，我们很容易看到它们是不同的，因为环面有一个洞。但是对于生活在曲面上的二维生物来说，它们怎样来区分球面和环面呢？庞卡莱猜想的挑战就在于我们要从空间内部来决定空间的形状。这个问题长期以来进展缓慢。

重要的进展发生在上个世纪80年代，一位美国数学家理查德•哈密尔顿引入了Ricci流的方法，给出了用Ricci流证明庞卡莱猜测的框架。但是他自己没有完全给出证明。到了2003年，一位受人尊敬的俄国数学家，普莱尔曼在网上公布了三篇文章，声称这三篇文章给出了证明庞卡莱猜想的一个描述。世界各地的数学家都很兴奋，开始仔细阅读这些文章，试图给出普莱尔曼所声称的证明。没有数学家发现普莱尔曼文章中的任何错误。但是仍然有一些缺口需要弥补，所以没人敢说这个证明已经很完整了。于是就出现了这样的情况，人们经常互相打听，“（庞卡莱猜想）已经证明了没有？”

直到最近，两位中国数学家，其中一位在美国工作。他们写了一篇300多页的文章，宣称补上了普莱尔曼文章中的所有缺口，从而给出了庞卡莱猜测的完整证明。

哈密尔顿等权威人物，也高度评价这两位中国数学家的工作。

普莱尔曼是一个非常不愿抛头露面的人。他最初公开文章时，曾到美国访问，给了一系列演讲。许多著名数学家参加了他的讲座。当他回到俄国以后，人们试图联系他，你的证明我看不懂，能不能解释一下什么的，他根本不理，他又开始了类似隐士的生活。他对百万美元奖金也没有兴趣。他把文章放到网上后就不管了。这令许多西方的数学家都没招。

Scott Simon:
那么解决这个问题究竟有什么好处呢？

Keith Devlin:
数学家思考这个问题已经有很多年了。永远不要低估其重要性。为了解决这个了不起的问题，已经推动了许多崭新的数学分支的诞生。我经常想，这种情况就如同山顶发生的雪崩，你并不知道这些雪块会奔向何方，但是有一点可以肯定。就是雪块所及之处，都会产生巨大的冲击。

Mathematician May Have Solved 100-Year-Old Problem
NPR (National Public Radio) Programm

Scott Simon:
The international congress of mathematicians on August will announce that a famous high complicated math problem has been solved. It’s called Poincare conjecture, but there is much to debate about how and whether it was ever solved. Keith Devlin, a math guy from Stanford university. Thank you for being with us.

Keith Devlin:
The biggest unsolved problem in mathematics, is one of the seven-million dollar millennium prize problems. It was posted in 1904 by one of the most famous mathematicians of all Frenchman, Henri Poincare. Many great mathematicians are have worked on it. They proved it and found their proofs shut down in a few weeks later.

It was determing the shape of the space that we lived in. This was Poincare interested in. He almost invented Relativity before Einstein. The question is what is the shape of the space we are living in? by shape, we mean what a mathematician call a topological shape. We don’t worry about the distance and how much things curve exactly, so in topological terms, a tennis ball, a golf ball, a football, a soccer ball, all are same. But the donut will be a little different, there it got a hole in the middle. So the question is, what is the topological shape of the space we live in. What makes us difficult to answer for physicist is trying to answer from the inside. It has a three dimensional analogue, it’s like a sphere or more like a donut shape.

Can you distinguish a surface, like a surface of the sphere from a surface of a donut, which mathematicians call a torus. From the outside, we can see that they are different, because the torus has a hole in the middle. But the two dimensional creature living on the surface, a creature for what the whole surface is the world. How could that creature determine whether it actually live on the surface of the sphere or the surface of the donut. Poincare’s challenge was to find what clues nature offered in order to determine the shape from inside. People make progress, but no one seems to come close to proving it.

Significant progress made in 1980’s was an American mathematician called Richard Hamilton, who took up ideas about fluid flows essentially and showed how you could use his ideas to prove the Poincare conjecture, but he couldn’t push it through. Then in 2003, a very respected Russsian mathematician, Grigori Perelman, put up three papers on the internet, claiming that those threee papers outlined a proof of Poincare conjecture. Mathematicians around the world were very excited and started to look at these preprints on the web and try to figure out what the proof was Perelman claims behind. No mathematician has found any mistakes or any major errors in what Perelman was doing. And yet there was still some gaps and nobody was prepared to say for certain this proof is correct. So we got this bizarre situation where there were thoughts of “is it a proof?”, “isn’t it a proof?”.

Then very recently, two Chinese mathematicians, one of them based in United States, wrote a paper, a three hundred paper. In that paper, they claim to have actually filled in all the gaps in Perelman’s proof, corrected everything, provided the missing steps and have now nailed a complete proof.

People like Richard Hamilton, one of the grandad in the field have started to say that these guys have got it.

Perelman is a very reclusive guy. When he first posted his papers, he did visite United States, give a series of lectures. Many famous mathematicians attended the lectures. When he come back to Russia, when people try to contact him and say that there is a step on this paper I don’t understand, can you explain out. He didn’t respond, he just went into reclusive life in Russia. He has no interest in the million dollar prize. He just put the paper on the internet and then it has nothing to do with it. It’s very frustrating for western mathematicians of course.

Scott Simon:
Besides the intellectural satisfaction of finally resolving this problem, what will happen for resolving this problem? What the importance for the world?

Keith Devlin:
Mathematicians have asked themselves for many years “what will be the case?”, “if the Poincare conjecture is true?”. You can’t overestimate just how much could flow from new mathematics that has brought into solving this magnitude problem. I often think this kind of steps as to starting an avalanche on the top of the mountain, you are not quite sure which direction these snow are going to flow, but one thing you do know is, a lot of snow is going to flow in a lot of different directions that engender a huge impact below.