剑桥雅思11阅读Test3Passage3原文翻译

这篇文章的主旨内容是关于数学思维方式的探讨。作者介绍了数学中的简单发现和推理，同时强调数学在培养分析能力方面的重要性。他希望通过这本书，读者能够欣赏数学的美丽并理解其逻辑。文章讨论了数学在不同领域的应用，例如医学和法律，并引用了医生和律师的证言来支持这种观点。此外，作者还提到了数学与人文科学之间的鸿沟，并展示了通过数学思维方式可以缩小这种鸿沟的可能性。最后，作者希望读者能够感受到解决问题的喜悦和数学的实用性。因此，文章的主旨是鼓励读者体验数学思维方式，并认识到数学对于分析能力的重要性。

A部分

Occasionally, in some difficult musical compositions, there are beautiful, but easy parts – parts so simple a beginner could play them. So it is with mathematics as well. There are some discoveries in advanced mathematics that do not depend on specialized knowledge, not even on algebra, geometry, or trigonometry. Instead they may involve, at most, a little arithmetic, such as ‘the sum of two odd numbers is even’, and common sense. Each of the eight chapters in this book illustrates this phenomenon. Anyone can understand every step in the reasoning.

The thinking in each chapter uses at most only elementary arithmetic, and sometimes not even that. Thus all readers will have the chance to participate in a mathematical experience, to appreciate the beauty of mathematics, and to become familiar with its logical, yet intuitive, style of thinking.

A部分

有时，在一些困难的音乐作品中，会有美丽而简单的部分——部分如此简单，以至于初学者也能演奏。数学也是如此。在高等数学中，有一些发现并不依赖于专业知识，甚至不依赖代数、几何或三角学。它们可能涉及到最多一点算术，比如“两个奇数的和是偶数”，以及常识。本书的八个章节中的每一章都阐明了这种现象。任何人都可以理解推理的每一步。

每一章的思考最多只使用基本的算术，有时甚至连那个都不用。因此，所有读者都有机会参与数学的体验，欣赏数学的美丽，并熟悉它的逻辑，同时又直观的思维方式。

B部分

One of my purposes in writing this book is to give readers who haven’t had the opportunity to see and enjoy real mathematics the chance to appreciate the mathematical way of thinking. I want to reveal not only some of the fascinating discoveries, but, more importantly, the reasoning behind them.

In that respect, this book differs from most books on mathematics written for the general public. Some present the lives of colorful mathematicians. Others describe important applications of mathematics. Yet others go into mathematical procedures, but assume that the reader is adept in using algebra.

B部分

我写这本书的目的之一是让那些没有机会看到和欣赏真正数学的读者有机会欣赏数学的思维方式。我想揭示的不仅是一些迷人的发现，更重要的是它们背后的推理。

在这方面，这本书不同于大多数面向普通读者的数学书籍。有的书介绍了色彩斑斓的数学家的生活。其他一些描述了数学的重要应用。还有一些介绍了数学程序，但假设读者擅长使用代数。

C部分

I hope this book will help bridge that notorious gap that separates the two cultures: the humanities and the sciences, or should I say the right brain (intuitive) and the left brain (analytical, numerical). As the chapters will illustrate, mathematics is not restricted to the analytical and numerical; intuition plays a significant role. The alleged gap can be narrowed or completely overcome by anyone, in part because each of us is far from using the full capacity of either side of the brain. To illustrate our human potential, I cite a structural engineer who is an artist, an electrical engineer who is an opera singer, an opera singer who published mathematical research, and a mathematician who publishes short stories.

C部分

我希望这本书能帮助弥合那个臭名昭著的分隔两种文化的鸿沟：人文科学和自然科学，或者我应该说右脑（直觉）和左脑（分析，数值）。正如这些章节将阐明的那样，数学不仅限于分析和数值；直觉也起着重要作用。任何人都可以在一定程度上缩小或完全克服所谓的鸿沟，部分原因是我们每个人远未充分利用大脑的任何一侧。为了说明我们的人类潜力，我引用了一个同时是艺术家的结构工程师、一个同时是歌剧演唱家的电气工程师、一个发表数学研究的歌剧演唱家，以及一个发表短篇小说的数学家。

D部分

Other scientists have written books to explain their fields to non-scientists, but have necessarily had to omit the mathematics, although it provides the foundation of their theories. The reader must remain a tantalized spectator rather than an involved participant, since the appropriate language for describing the details in much of science is mathematics, whether the subject is expanding universe, subatomic particles, or chromosomes. Though the broad outline of a scientific theory can be sketched intuitively, when a part of the physical universe is finally understood, its description often looks like a page in a mathematics text.

D部分

其他科学家写过向非科学家解释他们领域的书籍，但他们必须剔除数学，尽管它为他们的理论提供了基础。读者必须始终保持一种令人心痒难耐的旁观者状态，而不是参与者，因为描述科学细节的合适语言通常是数学，无论是扩张的宇宙、亚原子粒子还是染色体。尽管科学理论的大纲可以用直觉概括，但当对物理宇宙的某个部分最终理解时，其描述通常看起来像数学教科书上的一页。

E部分

Still, the non-mathematical reader can go far in understanding mathematical reasoning. This book presents the details that illustrate the mathematical style of thinking, which involves sustained, step-by-step analysis, experiments, and insights. You will turn these pages much more slowly than when reading a novel or a newspaper. It may help to have a pencil and paper ready to check claims and carry out experiments.

E部分

然而，非数学读者在理解数学推理方面可以走得很远。这本书呈现了细节，说明了数学的思维方式，其中包括持续的、一步一步的分析、实验和洞察。您会比阅读小说或报纸时翻阅这些页面慢得多。准备一支铅笔和纸可能有助于核对主张并进行实验。

F部分

As I wrote, I kept in mind two types of readers: those who enjoyed mathematics until they were turned off by an unpleasant episode, usually around fifth grade, and mathematics aficionados, who will find much that is new throughout the book.

This book also serves readers who simply want to sharpen their analytical skills. Many careers, such as law and medicine, require extended, precise analysis. Each chapter offers practice in following a sustained and closely argued line of thought. That mathematics can develop this skill is shown by these two testimonials.

F部分：

在撰写本书时，我考虑了两种读者类型：那些在五年级左右有过不愉快经历，从而对数学产生了厌恶感的人，以及对数学热衷的人，他们将在本书中发现很多新的东西。

本书还适用于那些只是想提高自己分析能力的读者。许多职业，如法律和医学，需要进行精确和深入的分析。每一章都提供了实践，让读者能够跟随并仔细分析思维线索的发展。这些两个证言显示了数学如何培养这种技能。

G部分

A physician wrote, ‘The discipline of analytical thought processes [in mathematics] prepared me extremely well for medical school. In medicine one is faced with a problem which must be thoroughly analyzed before a solution can be found. The process is similar to doing mathematics.’

A lawyer made the same point, ‘Although I had no background in law – not even one political science course – I did well at one of the best law schools. I attribute much of my success there to having learned, through the study of mathematics, and, in particular, theorems, how to analyze complicated principles. Lawyers who have studied mathematics can master the legal principles in a way that most others cannot.’

I hope you will share my delight in watching as simple, even na?ve, questions lead to remarkable solutions and purely theoretical discoveries find unanticipated applications.

G部分：

一位医生写道：“[数学中的]分析思维过程的训练使我在医学院准备得非常好。在医学中，我们面临的问题必须经过彻底的分析才能找到解决方案。这个过程类似于做数学题。”

一位律师也提出了同样的观点：“虽然我没有法律背景 – 甚至没有修过一门政治学课程 – 但我在一所顶级法学院表现出色。我把我的成功归功于通过学习数学，特别是定理学，学会了如何分析复杂原则。那些学过数学的律师能够以其他大多数人所不能的方式掌握法律原则。”

我希望你能分享我对于简单甚至天真问题引导出了卓越解决方案的喜悦，以及纯粹理论发现找到了意想不到的应用的喜悦