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保罗.爱多士  

2009-06-15 18:32:38|  分类: 默认分类 |  标签: |举报 |字号 订阅

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邹老师: 这篇关于数学家Paul Erdös的小文章是恒甫在武汉大学IAS搞学习竞赛必须考试的项目(英译汉). 大家好好地看看伟大的人格.世界上如果缺少了这样的人格,我们活着又有什么意义?! 

                                                     Paul Erdös

                                           保罗.爱多士

                                                        慕光居【译】

If the Martians had made contact with earth during the lifetime of Paul Erdös he would have made a good choice as this planet's ambassador. The aliens would have appreciated his unearthly intelligence. He spoke the universe's common tongue, the theory of numbers, with fluency and wit. Importantly, Mr Erdös would never have missed the trappings of this world. He had no children, no wife, no house, no credit card, no job, no change of shoes, indeed nothing but a suitcase containing a few clothes and some notebooks. Neither was he fussy about food, as long as he had coffee. A mathematician, he said, 'is a machine for converting coffee into theorems.' Mr Erdös's life was streamlined for mathematics.

如果火星人在爱多士有生之年与地球接触,去做这个行星的大使对他而言是个不错的选择。外星球的人会激赏于他超绝尘世的智能。他操持着宇宙间的通用语言,数论,流利而且机智。重要的是,爱多士决不会留恋一切凡尘俗事,他没有孩子,没有妻子,没有信用卡,没有工作,没有备穿的鞋子,事实上,除了一个装着一些衣裳和笔记本的手提箱以外,他一无所有。只要有咖啡,他也从不为吃而担忧。数学家,他说,“就是将咖啡转化成定理的机器”。爱多士的生命为数学而设。

Mathematics? For many it is the most baffling of the sciences. Most people with a bit of education can follow an explanation of say, the Big Bang or genetics, but limit their interest in mathematics to sorting out the intricacies of their bank statement. To mathematicians, though, their science is the purest creation of the human mind, and for many Mr Erdös was its supreme exponent this century.

数学?对多数人而言这是科学门类中最令人困扰的。大多数受过一点教育的人对诸如大爆炸或遗传学这类论题的解释都可以跟进,但是对数学的兴趣则仅止于读懂他们的银行对账单。然而对于数学家们来说,数学是人类心灵最纯粹的创造,并且他们中的许多人都认为爱多士是本世纪数学领域的最高典范。

Typically, he would arrive in a city where he was to lecture, ring up a fellow mathematician, and announce, 'My brain is in town.' He sounds like a guest from hell, but to his hosts this brain was a shared treasure and their collective responsibility. They would lodge him, feed him, launder his clothing.

通常的情形是,将到达一个他要做演讲的城市时,打电话给一个数学家同伴,宣告说,“我的大脑进城了。” 他听起来像一个来之地狱的客人,但对他的主人们而言,这颗大脑是一个共享的宝库也是他们集体的责任。他们要给他安排住宿,照料饮食,还要洗衣服。

Paul Erdös was a constantly wandering Jew. For much of his life Hungary, his homeland, was run by dictators. Many members of his family were murdered by the Germans during the Hitler period. In return for the comfort of friends who took care of his perfunctory needs, Mr Erdös would cut gems of elegance from numbers, graphs and logic. His problems were often simple to pose, yet offered room for creativity and surprise. Suppose an infinite number of dots are painted on an infinite canvas in such a way that the distance in inches between any two dots is a whole number. What would the painting look like? Mr Erdös's brow would furrow as he showed that the result could only be a straight row of dots. But don't ask for an explanation of his elegant proof unless you are interested in conic sections.

保罗.爱多士是一个永远流浪的犹太人。他一生中的许多时间,他的家乡匈牙利都被独裁者所统治。***统治时期,他的许多家庭成员都被德国人杀害了。作为对朋友们照料他那马马虎虎的生活需求的回报,爱多士从数论,图论和逻辑中摘取着精美的宝石。他的问题往往很容易陈述,但是却不乏创造力与惊奇。假设在一块无穷大的帆布上画上无穷个点,使得任两个点之间的距离以英寸为单位都为整数,这副画将是什么样子的?爱多士的额头会皱起来,当他说明结果只能是一直排的点时。但是不要要求对他的优雅证明的解释,除非你对圆锥截面感兴趣。

In his prime

在他的素数中

Paul Erdös's parents were maths teachers, so they presumably looked at him fondly when, at four, he said he had discovered negative numbers. While in his late teens he made discoveries about prime numbers. A number is 'prime' if it cannot be divided by any smaller number except one. Examples of prime numbers are 1913, the year in which Mr Erdös was born, and 83, his age when he died of a heart attack at a mathematics conference in Warsaw. Mr Erdös helped to recast a theory about prime numbers made by an earlier mathematician, using a more elegant approach. This, it was said, was analogous to creating the Panama Canal for shipping that previously went around South America.

保罗.爱多士的父母都是数学教师,所以可以猜想,当四岁的爱多士说他发现了负数的时候,他们会多么喜爱的看着他。年未弱冠,他就对素数作出了一些发现。一个数如果不能被一以外任何更小的数整除,就被称为素数。素数的例子有,1913,爱多士出生的年份,还有83,在华沙的一次数学会议上死于心脏病时他的岁数。爱多士用一个更为简洁的方法,重铸了一个早先的数学家做出的关于素数的理论。据说,这类似于开凿了一条巴拿马运河以运送那些本来要绕过南美洲的船只。

Elegant indeed, but were Mr Erdös's l,000 or more published papers of any practical value? He made no claim for their practicality. It was enough, he said, that a proof was 'very nice'. Yet mathematics, however pure, has a way of turning up in useful places. 'Combinatorics', a branch of maths explored by Mr Erdös, can be used to calculate the number of tiles needed to pave an irregular space. His work on graphs has been applied to the design of communications networks.

爱多士所发表的1000篇或者更多的论文确实精致,但是它们有没有任何实用的价值呢?他对它们的实用性没有任何要求。他说,证明“非常漂亮”,这就足够了。但是数学,无论多么纯粹,都能找到应用的途径。“组合学”,由爱多士开辟的一个数学分支,可被应用于计算铺满一块不规则的空地所需要的瓷砖数量。他在图论方面的工作已经被应用在通信网络的设计上。

The extraordinary left side of his brain was put at the service of numerous young mathematicians at the start of their careers. To him a mathematician of promise was an epsilon, the Greek letter used by mathematicians to describe a small quantity. To an epsilon he was 'Uncle Paul'. He set them problems, paying them rewards of a few hundred dollars if they came up with solutions, giving away much of his modest income from lectures and prizes (among them the Wolf Prize, an Israel-based sort of Nobel prize). A colleague likened Mr Erdös to a honeybee: an industrious creature who buzzed about the world and pollinated the fields of mathematics.

他将他非凡的左脑用在为无数处于事业开始阶段的年轻数学家服务上了。对他而言,一个有前途的数学家就是一个ε,数学家用来描述一个微小量的希腊字母。对每个ε而言,他是保罗叔叔。他给他们提出问题,如果他们解决了问题,则发给数百美金的奖金,他要送掉他不多的收入当中的很大一部分,这些收入来自于他的演讲和所获的奖金(包括沃尔夫奖-以色列的诺贝尔奖),一个同事把他比作蜜蜂:一个全世界飞来飞去,在数学的园地里授粉的辛勤的生物。

He was compared to Leonhard Euler (1707-83), an awesome Swiss regarded as the most prolific mathematician who ever lived. It is hard to exaggerate Mr Erdös's passion. For 19 hours a day, seven days a week, stimulated by coffee, and later by amphetamines, he worked on mathematics. He might start a game of chess, but would probably doze off until the conversation returned to maths. To find another life this century as intensely devoted to abstraction, one must reach back to Ludwig Wittgenstein (1889-1951), who stripped his life bare for philosophy. But whereas Wittgenstein discarded his family fortune as a form of self-torture, Mr Erdös gave away most of the money he earned because he simply did not need it. 'Private property is a nuisance,' he would say. And where Wittgenstein was driven by near suicidal compulsions, Mr Erdös simply constructed his life to extract from his magnificent obsession the maximum amount of happiness.

人们将他与欧拉(170783)相提并论,后者是一个令人敬畏的瑞士人,被认为是曾经活过的数学家中最多产的人。要想夸大爱多士的激情是非常困难的。在咖啡的刺激下,后期则是安非他明,一天十九个小时,每周七天,他都在做着他的数学工作。他可能会跟别人下棋,但是也许会打起瞌睡直到谈话又回到数学上来。在本世纪要找另一个如此热情的投入抽象理论研究的生命,人们只能回到维特根斯坦(18891951),他献身给了哲学。但是尽管维特根斯坦放弃了家产以作为一种苦修的形式,爱多士送掉他的大部分的收入却仅仅是因为他并不需要它们。“私产是件麻烦事”,他会这样说。在维特根斯坦被近在咫尺的自杀冲动所驱策之处,爱多士只是构造他的生命以从自己高尚的迷恋中汲取最大量的幸福。

 

 

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