A BRIEF HISTORY OF MATHEMATICAL THOUGHT: KEY CONCEPTS AND WHERE THEY COME FROM
Book ID/图书代码： 07980014B76607
English Summary/英文概要： Mathematics is a product of human culture which has developed along with our attempts to comprehend the world around us. In A Brief History of Mathematical Thought, Luke Heaton explores how the language of mathematics has evolved over time, enabling new technologies and shaping the way people think. From stone-age rituals to algebra, calculus, and the concept of computation, Heaton shows the enormous influence of mathematics on science, philosophy and the broader human story.
The book traces the fascinating history of mathematical practice, focusing on the impact of key conceptual innovations. Its structure of thirteen chapters split between four sections is dictated by a combination of historical and thematic considerations.
In the first section, Heaton illuminates the fundamental concept of number. He begins with a speculative and rhetorical account of prehistoric rituals, before describing the practice of mathematics in Ancient Egypt, Babylon and Greece. He then examines the relationship between counting and the continuum of measurement, and explains how the rise of algebra has dramatically transformed our world. In the second section, he explores the origins of calculus and the conceptual shift that accompanied the birth of non-Euclidean geometries. In the third section, he examines the concept of the infinite and the fundamentals of formal logic. Finally, in section four, he considers the limits of formal proof, and the critical role of mathematics in our ongoing attempts to comprehend the world around us.
The story of mathematics is fascinating in its own right, but Heaton does more than simply outline a history of mathematical ideas. More importantly, he shows clearly how the history and philosophy of maths provides an invaluable perspective on human nature.
Chinese Summary/中文概要： 数学是在人类尝试认知世界的过程中发展起来的人类文化的产物。在《数学思想简史》中，Luke Heaton 探讨了数学语言随时间的演变过程，以及数学语言如何促成新技术的发明和改变人类的思考模式。Heaton 从石器时代的宗教仪式讲到代数、微积分以及计算的概念，来展示数学对科学、哲学和更广义的人类历史所产生的巨大影响。
该书探寻了令人着迷的数学史，重点讲述主要概念创新的影响。该书共十三个章节，分为四大部分，结合了史学及专题分析。
第一部分，Heaton 阐明了数的基本概念。他首先用华丽的语言推测性地描述了史前宗教仪式，接着讲到古埃及、古巴比伦以及古希腊的数学应用。然后他考究了计数与统一度量衡之间的关系，并解释了代数的兴起给我们的世界带来的剧烈变化。第二部分作者探讨了微积分的起源以及随着非欧几里得几何学的萌芽而产生的概念转变。第三部分作者分析了形式论证的局限性以及数学在我们不断尝试认识世界的过程中所扮演的重要角色。
数学的故事本身就是令人着迷的，但是Heaton不仅仅简单列出了数学思想史的要点，更重要的是他清楚地展示了数学史及数学思想如何为我们考察人性提供宝贵的视角。(LNL)
Awards/获奖情况：Fascinating book, written in a charming style. The author does a great job explaining mathematical concepts without getting bogged down in technical details, and I thought the chapter on logic was particularly strong. Highly recommended for anyone interested in the history and philosophy of maths.
About the Author/作者介绍： Luke Heaton 以一等荣誉毕业于爱丁堡大学数学专业，接着在牛津大学攻读数学与计算科学的逻辑基础理学硕士学位。他在花了一年的时间创造数学艺术后，又攻读了西敏斯特大学建筑学学士学位，之后在One20 做建筑助手。后来他又回到牛津大学，攻读了数学生物学的博士学位。现为牛津大学植物科学系研究生研究助理。他主要研究数学与生物学现象的数学建模、数学史及数学思想、形态学和生物模式形成以及高效运输网络的统计特点。他已经在真菌网络的培养和运输生物物理学方面发表了数篇论文。
Dr Luke Heaton graduated with first class honours in Mathematics at the University of Edinburgh before going on to take an MSc in Mathematics and the Logical Foundations of Computer Science at the University of Oxford. After spending a year making mathematically inspired art, he gained a BA in Architecture at the University of Westminster, before working as an architectural assistant at One20. He then returned to Oxford, completing a DPhil in Mathematical Biology. He is currently employed by the University of Oxford as a postgraduate research assistant in the Department of Plant Sciences. Luke’s research interests lie in mathematics and the mathematical modelling of biological phenomena, the history and philosophy of mathematics, morphogenesis and biological pattern formation, network theory, biophysics, and the statistical properties of efficient transport networks. He has published several papers on the biophysics of growth and transport in fungal networks
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