The Mathematical Traveler
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Summary
This is an exploration of number and a history filled with wonder and marvels. From observing humanity's earliest counting to directly experiencing the chaos rooted in number, the theory of numbers—natural numbers, negative numbers, decimals, complex numbers, irrational numbers, transcendental numbers, transfinite numbers, zero, infinity—has been continuously developed and refined in the minds of mathematicians, while the culture of number has evolved and matured in human society. In this book, you will come to understand the importance to humanity of mathematical concepts such as numeral systems, the golden ratio, pi, and irrational numbers, and you will see how numbers and mathematics drive the progress of science and technology and play a vital role in our daily lives. To understand number is to understand the development of human civilization and to see the true face of all things in the universe.
Editor's review
In the editor's view, the book's core value lies in its attempt to "lower the threshold without lowering the depth." It does not evade the concepts themselves but reconstructs them through plain language and apt metaphors, allowing readers once intimidated by symbols to glimpse the inner harmony and beauty of mathematics. The author's background as a mathematics educator gives him a deep understanding of how to build cognitive stepping stones. For readers with some foundation, the book's tracing of the historical context of classic problems and comparison of different proof approaches can also offer new perspectives. Its charm lies not in providing ultimate answers but in revealing the exploratory essence of mathematics as a human intellectual activity—ceaselessly posing questions and enjoying the pursuit of answers.
Who it's for
A good fit for
- Readers interested in mathematical culture and historical stories who wish to understand the humanistic color behind concepts
- Enthusiasts with a middle-school mathematics background who want an accessible introduction to number theory, a core branch of mathematics
- Learners seeking an interdisciplinary perspective, curious about how mathematical thought influences philosophy, art, and even cryptography
- Parents and educators looking for reading material that can ignite an interest in mathematics in children or students
Not a good fit for
- Mathematics majors seeking rigorous, systematic number theory textbooks or exam preparation materials
- Seasoned mathematics researchers expecting large numbers of challenging exercises or cutting-edge research developments
Reading tips
- Read with a 'traveler's' mindset; there is no need to grasp every proof detail at once—follow the author's narrative to appreciate the flow of ideas first
- Keep pen and paper handy; jot down concepts of interest (such as the Goldbach conjecture) and look them up later, using the book as a starting point for exploration
- The historical figures and stories interspersed throughout are highly engaging; read them alongside the mathematical concepts to appreciate how intellectual exploration intertwines with the spirit of the times
About the publisher
Hainan Publishing House is a comprehensive publisher known for literary and intellectual works, covering foreign literature, philosophy, classics, world-famous works, classical poetry and prose miscellanies. Its catalog includes foreign literary classics such as Leo Tolstoy's Anna Karenina and Romain Rolland's Jean-Christophe, philosophical works such as Jean-Jacques Rousseau's The Social Contract: Expert Companion Edition, and Chinese classics and poetic studies such as Lu Xun's essays and prose collections and Wang Guowei's Renjian Cihua, as well as illustrated popular-science works like Fabre's Insects. The involvement of translators such as Zhong Shufeng, Fu Lei and Chen Xiaoqing reflects the publisher's emphasis on translation quality and expert guidance. Public information is limited, and the above is based mainly on the books in the catalog.
Contents
- 版权信息
- 致谢
- 引言
- 第一章 我们是如何计数的
- 词汇
- 自然数
- 计数的特征
- 大脑是如何计数的
- 我们是如何学会计数的
- 第二章 早期的计数
- 我们的远祖
- 手指和身体计数
- 数词计数
- 作为修饰语的数
- 农耕时代之前的数
- 小结
- 第三章 其他物种的计数行为
- 它们究竟有多聪明
- 特殊案例
- 直接感知理解
- 它们能否学会计数
- 第四章 古代的数字
- 农业的诞生
- 苏美尔人发明文字
- 苏美尔人的数学
- 杰出的古巴比伦人
- 古埃及人
- 数、计算和问题
- 我们已走了多远
- 第五章 中国与新大陆的数
- 古代中国
- 中国的数系
- 中国数学
- 新大陆的数学
- 玛雅文明
- 印加帝国
- 独立的发现
- 第六章 天堂的问题
- 早期希腊文明
- 古希腊数系
- 哲学、科学和数学的诞生
- 伟大的毕达哥拉斯
- 毕达哥拉斯学派关于数的概念
- 毕达哥拉斯学派的贡献
- 不可通约
- 亚历山大时期
- 第七章 负数
- 数线
- 古印度的数
- 外部影响
- 印度-阿拉伯数系
- 数系向欧洲进发
- 回到数线
- 第八章 直面无穷
- 不同类型的无穷
- 无穷大量
- 关于无穷大的见解
- 无限可分性
- 将无穷大变成无穷小
- 陷入泥潭
- 穷竭法与限制
- 第九章 狄德金分割
- 无理数
- 欧多克索斯的比例
- 美妙的狄德金分割
- 小数系统的趣味
- 第十章 π的故事：超越数
- 其他种类的方程式
- 定义难以捉摸的
- 审视π和е
- 究竟有多少超越数
- 才华卓绝的格奥尔格·康托尔
- 代数数可数吗
- 有多少超越数
- 第二个证明
- א0与א1之间还存在什么
- 第十一章 王国的扩展：复数
- 解析几何的诞生
- 高斯定位复数
- 有多少复数
- 哈密尔顿的四元数
- 第十二章 超乎想象的大数：超限数
- 定义超限数
- 一些超乎想象的大数
- 康托尔为超限数而做的努力
- 第十三章 天才计算家
- 普通人中的计算家
- 质数与合数
- 约翰和迈克尔的案例
- 这些究竟意味着什么
- 未来的计算
- 第十四章 数到底意味着什么
- 明确问题的实质
- 历史的进程
- 我们所说的存在究竟是何含义
- 进化的角度
- 第十五章 数的过去、现在和未来
- 进入20世纪
- 悖论
- 跨越20世纪
- 机器数学
- 凝视上帝的眼睛
- 费马大定理
- 我们还能走多远
- 注释
- 参考文献
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About the author
Calvin C. Clauson is a Chinese-language book author about whom relatively little public information is available; his nationality, dates of birth and death, and educational background are not clearly recorded, and only one of his works is held in the collection. Based on the existing information, Clauson's name is associated with popular science writing. His representative work, The Mathematical Traveler, is classified under popular science, suggesting that he writes for general readers and seeks to present mathematical content in an accessible way. Judging from the title and category, the book may use a travel-like narrative thread to connect mathematical concepts, ideas, or history, allowing readers to gain knowledge and interest as they read. Because information on the author's life and writing background is lacking, it is difficult to assess the full range of his style or his specific influence in popular science. Readers may regard him as a popular science author who approaches mathematics through popularization and may come to know his manner of expression and choice of topics through this work.
Yang Liru is a Chinese author known mainly for writing popular science. Publicly available information about him is limited, and no clear record of his life, nationality, or educational background has been found. Judging from the three works included in the library—The Magic Number Zero, The Mathematical Traveler, and How Strange Is the Universe We Live In?—his interests center on basic sciences such as mathematics and cosmology. He often takes numbers, travel, and cosmic puzzles as entry points, turning abstract concepts into everyday topics accessible to readers. These works are classified as popular science, reflecting an aim to spread scientific knowledge to general readers: the topics appeal to ordinary curiosity, the writing emphasizes readability, and specific phenomena are used to open up broader scientific vistas. Although the available material is not enough to outline his full writing career, these three books already show a style that connects mathematics with astronomy and balances entertainment with knowledge, suited to readers who wish to enter the world of science with ease.
