下面是從教育學術轉載的一個翻譯。裡面有點翻譯的錯誤，我給他做了一點改正。我認為基督徒不能走向另外一個極端：就是反智。這裡有人認為沒有學問就是最屬靈，是很不對的。

斯坦福科學家對龐家萊猜想的公開評論

送交者: nyny 2006年8月01日18:15:29 於 [教育與學術]http://www.bbsland.com


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

數學家也許解決解決了百年難題
NPR 訪談

Scott Simon:
今年8月將在西班牙召開國際數學家大會，屆時很可能宣布一個著名數學難題被解決的消息。這個難題被稱為龐卡萊猜想，但是對於它的解決，現在還有很多爭論。來自斯坦福大學的Keith Devlin，將為大家作一介紹。

Keith Devlin:
龐卡萊猜想是數學中最大的難題之一，也是克雷數學研究所的七道千禧數學難題之一。它是1904年由偉大的法國數學家亨利•龐卡萊提出的。許多大數學家都對這個問題作過研究。他們有的還給出了證明，但不久都發現有錯。

這個問題就是要確定我們所生活的空間的形狀。這是龐卡萊很感興趣的問題。他是一位偉大的數學家，差點比愛因斯坦還要更早地發現了狹義相對論。那麼空間的形狀是指什麼呢？對數學家來說，就是拓撲形狀。在拓撲學中，我們對距離和彎曲程度不感興趣，所以用拓撲學術語來說，一個網球，高爾夫球或者足球都是同樣的東西。而甜麥圈就不同了，因為中間有個洞。所以如果問我們所居住的空間是什麼形狀，困難就在於我們生活在空間的內部。

你能區分球面和甜麥圈(也就是數學家所稱的二維環面)嗎？從外部來看，我們很容易看到它們是不同的，因為環面有一個洞。但是對於生活在曲面上的二維生物來說，它們怎樣來區分球面和環面呢？龐卡萊猜想的挑戰就在於我們要從空間內部來決定空間的形狀。這個問題長期以來進展緩慢。

重要的進展發生在上個世紀80年代，一位美國數學家理查德•哈密爾頓引入了Ricci流的方法，給出了用Ricci流證明龐卡萊猜測的框架。但是他自己沒有完全給出證明。到了2003年，一位受人尊敬的俄國數學家，普萊爾曼在網上公布了三篇文章，聲稱這三篇文章給出了證明龐卡萊猜想的一個描述。世界各地的數學家都很興奮，開始仔細閱讀這些文章，試圖給出普萊爾曼所聲稱的證明。沒有數學家發現普萊爾曼文章中的任何錯誤。但是仍然有一些缺口需要彌補，所以沒人敢說這個證明已經很完整了。於是就出現了這樣的情況，人們經常互相打聽，“（龐卡萊猜想）已經證明了沒有？”

直到最近，兩位中國數學家，其中一位在美國工作。他們寫了一篇300多頁的文章，宣稱補上了普萊爾曼文章中的所有缺口，從而給出了龐卡萊猜測的完整證明。

哈密爾頓等權威人物，也高度評價這兩位中國數學家的工作。

普萊爾曼是一個非常不願拋頭露面的人。他最初公開文章時，曾到美國訪問，給了一系列演講。許多著名數學家參加了他的講座。當他回到俄國以後，人們試圖聯繫他，你的證明我看不懂，能不能解釋一下什麼的，他根本不理，他又開始了類似隱士的生活。他對百萬美元獎金也沒有興趣。他把文章放到網上後就不管了。這令許多西方的數學家都沒招。

Scott Simon:
那麼解決這個問題究竟有什麼好處呢？

Keith Devlin:
數學家思考這個問題已經有很多年了。永遠不要低估其重要性。為了解決這個了不起的問題，已經推動了許多嶄新的數學分支的誕生。我經常想，這種情況就如同山頂發生的雪崩，你並不知道這些雪塊會奔向何方，但是有一點可以肯定。就是雪塊所及之處，都會產生巨大的衝擊。

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.