英语阅读系列第1篇-数教家黎曼

Category: Science & Society 文本领域: 科学与社会 （本文本仅得当中门生英语阅读进修）

Text: 804 words 正文有804个单词

Title: Before his early death, Riemann freed geometry from Euclidean prejudices

黎曼在英年早逝之前，把多少学从欧几里得的私见中解放出来

The originator of the famous math hypothesis also established the basis for a modern view of spacetime

闻名数学假说的始祖也为当代时空观奠基了底子

Bernhard Riemann 伯恩哈德 黎曼

Bernhard Riemann was a man with a hypothesis.

伯恩哈德 黎曼是一位以料想而有名的人。

He was confident that it was true, probably. But he didn’t prove it. And attempts over the last century and a half by others to prove it have failed.

他确信这（个料想）很大概是真的。 但他没有证明。在已往一个半世纪里，其他人试图证明它的实验都失败了。

A new claim by the esteemed mathematician Michael Atiyah that Riemann’s hypothesis has now been proved may also be exaggerated. But sadly Riemann’s early death was not. He died at age 39. In his short life, though, he left an intellectual legacy that touched many areas of math and science. He was “one of the most profound and imaginative mathematicians of all time,” as the mathematician Hans Freudenthal once wrote. Riemann recast the mathematical world’s view of algebra, geometry and various mathematical subfields — and set the stage for the 20th century’s understanding of space and time. Riemann’s math made Einstein’s general theory of relativity possible.

受人尊重的数学家迈克尔·阿蒂亚 (Michael Atiyah) 提出的黎曼料想现已得到证明的新主见也大概被夸大了。但遗憾的是黎曼的早逝并非云云。他在39岁时去世。不外在他短暂的平生中，他留下了涉及数学和科学很多范畴的知识遗产。正如数学家汉斯·弗洛伊登塔尔 (Hans Freudenthal) 曾经写道的那样，他是“有史以来最深刻、最具想象力的数学家之一”。 黎曼重塑了数学天下对代数、多少和种种数学子范畴的见解—并给20世纪对空间和时间的了解奠基了底子。黎曼的数学使爱因斯坦的广义相对论成为大概。

“It is quite possible,” wrote the mathematician-biographer E.T. Bell, “that had he been granted 20 or 30 more years of life, he would have become the Newton or Einstein of the nineteenth century.”

数学家兼列传作家E.T.贝尔写道“这很有大概”，“假如他能再活20或30年，他就会成为19世纪里像牛顿或爱因斯坦那样巨大的人。”

Riemann’s genius developed despite unpromising circumstances. Born in Bavaria in 1826 the son of a Protestant minister, he was poor and often sick as a child. Bernhard was homeschooled until his teenage years, when he moved to live with a grandmother where he could attend school. Later his mathematical aptitude caught the attention of a teacher who provided Riemann a nearly 900-page-long textbook by the legendary French mathematician Adrien-Marie Legendre to keep the precocious student occupied. Six days later, Riemann returned the book to the teacher, having mastered its contents.

黎曼的天赋是在倒霉的条件下进展起来的。他于1826年诞生于巴伐利亚，是一位新教牧师的儿子，他很穷，小时间每每抱病。伯恩哈德 (Bernhard) 一向在家自学，直到他十几岁才搬到与祖母住在一路，在那边他可以上学。厥后，他的数学天赋引起了一位老师的细致，他为黎曼提供了一本由法国传奇数学家阿德里安-玛丽·勒让德 (Adrien-Marie Legendre) 编写的近900页长的教科书，让这个早熟的门生有事可做。六天后，黎曼把握了书的内容，将书还给了老师。

When he entered the University of Göttingen, Riemann began (at his father’s urging) as a theology student. But Göttingen was the home of the greatest mathematician of the era, Carl Friedrich Gauss. Riemann attended lectures by Gauss and dropped theology for mathematics. More advanced math instruction was available at Berlin, where Riemann studied for two years before returning to Göttingen to finish his math Ph.D.

当黎曼进入哥廷根大学时，他开始（在他父亲的鞭策下）成为一名神学门生。但哥廷根是谁人期间最巨大的数学家卡尔·弗里德里希·高斯的家乡。黎曼到场了高斯的讲座并为了数学放弃了神学。柏林能提供更高级的数学讲授，黎曼在那边进修了两年，然后返回哥廷根完成他的数学博士学位。

Nowadays a Ph.D. is generally considered impressive, but in Germany back then it was only step one toward qualifying for a job. Step two was conducting and reporting advanced work on a specialized topic, to be delivered as a lecture to a university committee. Gauss encouraged Riemann to report on a new approach to geometry. Riemann titled his lecture on the topic, presented in 1854, “On the Hypotheses which Lie at the Foundations of Geometry.”

如今一个博士学位会被广泛以为令人印象深刻。但在其时的德国，这只是得到事情资格的第一步。第二步是开展和陈诉关于一个专业主题的事情希望，以讲座的情势向大学委员会颁发。高斯鼓舞黎曼陈诉一种新的多少学要领。黎曼将他在1854年颁发的关于这个主题的演讲定名为“关于奠基多少学底子的料想”。

In that lecture, Riemann cut to the core of Euclidean geometry, pointing out that its foundation consisted of presuppositions about points, lines and space that lacked any logical basis. As those presuppositions are based on experience, and “within the limits of observation,” the probability of their correctness seems high. But it is necessary, Riemann asserted, to “inquire about the justice of their extension beyond the limits of observation, on the side both of the infinitely great and of the infinitely small.” Investigating the nature of the world, he said, should not be “hindered by too narrow views,” and progress should not be obstructed by “traditional prejudices.”

在那次演讲中，黎曼切入欧几里得多少的焦点，指出其底子由关于点、线和空间的预设构成，缺乏任何规律底子。因为这些预设是基于履历的，而且“在观看范畴内”，是以它们精确的大概性彷佛很高。但是，黎曼断言，有须要“在无穷大和无穷小方面扣问它们凌驾观看范畴的扩展的公理性”。他说，探究天下的素质不该该被“过于局促的看法所拦阻”，也不该该被“传统私见”所拦阻。

Freed from Euclid’s preconditions, Riemann derived an entirely different (non-Euclidean) geometry. It was this geometry that provided the foundation for general relativity — Einstein’s theory of gravity — six decades later.

开脱了欧几里得的先决条件，黎曼推导出了一种完全差别的（非欧几里得）多少。正是这种多少学为广义相对论 - 爱因斯坦的引力理论——奠基了底子。

Riemann’s insights stemmed from his belief that in math, it was important to grasp the ideas behind the calculations, not merely accept the rules and follow standard procedures. Euclidean geometry seemed sensible at distance scales commonly experienced, but could differ under conditions not yet investigated (which is just what Einstein eventually showed).

黎曼的看法源于他的信心，即在数学中，把握盘算背后的头脑很紧张，而不但仅是担当规章并遵照尺度步伐。欧几里得多少在通常履历过的间隔标准上彷佛是公道的，但在尚未研究的条件下大概有所差别（这正是爱因斯坦终极展示的）。

Riemann’s geometrical conceptions extended to the possible existence of dimensions of space beyond the three commonly noticed. By developing the math describing such multidimensional spaces, Riemann provided an essential tool for physicists exploring the possibility of extra dimensions today.

黎曼的多少观点扩展到大概存在的空间维度凌驾了通常细致到的三个维度。通过进展形貌这种多维空间的数学，黎曼为当今探究多维度大概性的物理学家提供了一个必不行少的东西。

He made many other contributions to a wide range of technical mathematical issues. And he took great interest in the philosophy of mathematics (as Freudenthal said, had he lived longer, Riemann might eventually have become known as a philosopher). Among his most famous technical ideas was a conjecture concerning the “zeta function,” a complicated mathematical expression with important implications related to the properties of prime numbers. Riemann’s hypothesis about the zeta function, if true, would validate vast numbers of additional mathematical propositions that have been derived from it.

他对遍及的技能数学题目做出了很多其他奉献。他对数学哲学非常感兴趣（正如弗洛伊登塔尔所说，假如他活得更久，黎曼终极大概会以哲学家的身份着名）。他最闻名的技能头脑之一是关于“zeta函数”的料想，这是一个庞大的数学表达式，对证数的性子具有紧张意义。黎曼关于zeta函数的假设假如为真，将验证从中导出的大量其他数学命题。

Riemann performed many calculations leading him to believe in his hypothesis, but did not find a mathematical proof before his early death. In fact, he spent much of the last four years of his life under the duress of tuberculosis, seeking relief by long stays in the more comfortable climate of Italy. He died there on July 20, 1866, two months before he would have turned 40.

黎曼举行了很多盘算，使他信赖他的料想，但在他早逝之前没有找到数学证明。究竟上，他生掷中最终四年的大部门时间都在肺结核的胁迫下度过，通过在意大利更安宁的天气中恒久停留来追求摆脱。他于1866年7月20日，在他马上满40岁的两个月前，在那边去世，。

Had he lived as long as Michael Atiyah (age 89), maybe Riemann would have proved his hypothesis himself.

假如他活得和Michael Atiyah（89岁）一样长，或许黎曼会亲身证明他的料想。

（存眷杨老师STEAM教诲，进修更多的英语科技类文章）