英语阅读系列第1篇-数学家黎曼

Category: Science & Society 文本范畴: 科学与社会 （本文本仅适合中学生英语阅读学习）

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，把几何学从欧几里得的偏见中解放出来

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

著名数学假说的鼻祖也为现代时空观奠定了基础

Bernhard Riemann 伯恩哈德 黎曼

Bernhard Riemann was a man with a hypothesis.

伯恩哈德 黎曼是一位以猜想而闻名的人。

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（个猜想）很可能是真的。 但他没有证明。在过去一个半世纪里，其他人试图证明它的尝试都失败了。

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.

受人尊敬的数学家迈克尔·阿蒂亚 (Michael Atiyah) 提出的黎曼猜想现已得到证明的新主张也可能被夸大了。但遗憾的是黎曼的早逝并非如此。他在39岁时去世。不过在他短暂的一生中，他留下了涉及数学和科学许多领域的知识遗产。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”。 黎曼重塑了数学世界对代数、几何和各种数学子领域的看法—并给20世纪对空间和时间的理解奠定了基础。黎曼的数学使爱因斯坦的广义相对论成为可能。

“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.”

数学家兼传记作家E.T.贝尔写道“这很有可能”，“如果他能再活20或30年，他就会成为19世纪里像牛顿或爱因斯坦那样伟大的人。”

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.

黎曼的天赋是在不利的条件下发展起来的。他于1826年出生于巴伐利亚，是一位新教牧师的儿子，他很穷，小时候经常生病。伯恩哈德 (Bernhard) 一直在家自学，直到他十几岁才搬到与祖母住在一起，在那里他可以上学。后来，他的数学天赋引起了一位老师的注意，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，让这个早熟的学生有事可做。六天后，黎曼掌握了书的内容，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（在他父亲的敦促下）成为一名神学学生。但哥廷根是那个时代最伟大的数学家卡尔·弗里德里希·高斯的故乡。黎曼参加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教学，黎曼在那里学习了两年，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.”

现在一个博士学位会被普遍认为令人印象深刻。但在当时的德国，这只是获得工作资格的第一步。第二步是开展和报告关于一个专业主题的工作进展，以讲座的形式向大学委员会发表。高斯鼓励黎曼报告一种新的几何学方法。黎曼将他在1854年发表的关于这个主题的演讲命名为“关于奠定几何学基础的猜想”。

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，黎曼切入欧几里得几何的核心，指出其基础由关于点、线和空间的预设组成，缺乏任何逻辑基础。由于这些预设是基于经验的，并且“在观察范围内”，因此它们正确的可能性似乎很高。但是，黎曼断言，有必要“在无限大和无限小方面询问它们超出观察范围的扩展的正义性”。他说，探索世界的本质不应该被“过于狭隘的观点所阻碍”，也不应该被“传统偏见”所阻碍。

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.

摆脱了欧几里得的先决条件，黎曼推导出了一种完全不同的（非欧几里得）几何。正是这种几何学为广义相对论 - 爱因斯坦的引力理论——奠定了基础。

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).

黎曼的见解源于他的信念，即在数学中，掌握计算背后的思想很重要，而不仅仅是接受规则并遵循标准程序。欧几里得几何在通常经历过的距离尺度上似乎是合理的，但在尚未研究的条件下可能有所不同（这正是爱因斯坦最终展示的）。

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.

黎曼的几何概念扩展到可能存在的空间维度超出了通常注意到的三个维度。通过发展描述这种多维空间的数学，黎曼为当今探索多维度可能性的物理学家提供了一个必不可少的工具。

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.

他对广泛的技术数学问题做出了许多其他贡献。他对数学哲学非常感兴趣（正如弗洛伊登塔尔所说，如果他活得更久，黎曼最终可能会以哲学家的身份出名）。他最著名的技术思想之一是关于“zeta函数”的猜想，这是一个复杂的数学表达式，对质数的性质具有重要意义。黎曼关于zeta函数的假设如果为真，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.

黎曼进行了许多计算，使他相信他的猜想，但在他早逝之前没有找到数学证明。事实上，他生命中最后四年的大部分时间都在肺结核的胁迫下度过，通过在意大利更舒适的气候中长期逗留来寻求解脱。他于1866年7月20日，在他即将满40岁的两个月前，在那里去世，。

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

如果他活得和Michael Atiyah（89岁）一样长，也许黎曼会亲自证明他的猜想。

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