This volume, originally published in China and translated into four other languages, presents a fascinating and unique account of the history of mathematics, divided into eight chronologically organized chapters. Tracing the development of mathematics across disparate regions and peoples, with particular emphasis on the relationship between mathematics and civilization, it examines mathematical sources and inspirations leading from Egypt, Babylon and ancient Greece and expanding to include Chinese, Indian and Arabic mathematics, the European Renaissance and the French revolution up through the Nineteenth and Twentieth Centuries. Each chapter explores connections among mathematics and cultural elements of the time and place treated, accompanying the reader in a varied and exciting journey through human civilizations. The book contemplates the intersections of mathematics with other disciplines, including the relationship between modern mathematics and modern art, and the resulting applications, with the aid of images and photographs, often taken by the author, which further enhance the enjoyment for the reader.
Written for a general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities.
Author(s): Tianxin Cai
Edition: 1
Publisher: Birkhäuser
Year: 2023
Language: English
Commentary: Publisher PDF
Pages: 359
City: Cham
Tags: Indian Mathematics; Chinese Mathematics; Literature; Poetry; Philosophy; Egyptian Mathematics; Pythagoras; Euclid's Elements; Omar Khayyam; The Renaissance; Analytic Geometry; Bernoulli
The book of time
Preface
Contents
About the Author
1 The Middle East, or the Beginning
The Origins of Mathematics
The Beginnings of Counting
Number Bases
Arabic Numerals
Shape and Geometry
Civilization on the Nile River
A Peculiar Terrain
The Rhind Papyrus
Egyptian Fractions
Between the Rivers
Babylonia
The Clay Tablets
Plimpton 322
Conclusion
2 The Sages of Ancient Greece
The Birth of Mathematicians
The Greek Arena
The First Proofs
Pythagoras
The Platonic Academy
Zeno's Tortoise
Plato's Academy
Aristotle
The Alexandrian School
Euclid's Elements
Archimedes
Other Mathematicians
Conclusion
3 The Chinese Middle Ages
Prologue
The Pre-Qin Era
Zhoubi Suanjing
Nine Chapters on the Mathematical Art
From Circle Divisions to the Method of Four Unknowns
Liu Hui's π Algorithm
The Sun Zi-Qin Jiushao Theorem
Other Mathematicians
Conclusion
4 India and Arabia
From the Indus River to the Ganges
The Indo-European Past
The Shulba Sutras and Buddhism
The Number Zero and Hindu Numerals
From North India to South India
Aryabhata
Brahmagupta
Mahāvīra
Bhāskara II
Sacred Land
The Arabian Empire
The House of Wisdom in Baghdad
The Algebra of al-Khwarizmi
The Scholars of Persia
Omar Khayyam
Nasir al-Din al-Tusi
Jamshīd al-Kāshī
Conclusion
5 From the Renaissance to the Birth of Calculus
The Renaissance in Europe
Medieval Europe
Fibonacci's Rabbits
Alberti's Perspective Method
Da Vinci and Dürer
The Invention of Calculus
The Awakening of New Mathematics
Analytic Geometry
The Pioneers of Calculus
Newton and Leibniz
Conclusion
6 The Age of Analysis and the French Revolution
The Age of Analysis
The King of the Amateurs
The Further Development of Calculus
The Influence of Calculus
The Bernoulli Family
The French Revolution
Napoleon Bonaparte
The Lofty Pyramid
The French Newton
The Emperor's Friend
Conclusion
7 Modern Mathematics, Modern Art
The Rebirth of Algebra
Toward a Rigorous Treatment of Analysis
Abel and Galois
The Quaternions of William Rowan Hamilton
A Revolution in Geometry
A Scandal in Elementary Geometry
The Arrival of Non-Euclidean Geometry
Riemannian Geometry
A New Era of Art
Edgar Allan Poe
Baudelaire
From Imitation to Wit
Conclusion
8 Abstraction: Mathematics Since the Twentieth Century
The Road to Abstraction
Set Theory and Axiomatic Systems
The Abstraction of Mathematics
Abstraction in Art
Applications of Mathematics
Theoretical Physics
Biology and Economics
Computers and Chaos Theory
Mathematics and Logic
Russell's Paradox
Wittgenstein
Gödel's Theorems
Conclusion
A A Mathematical Chronology
B The Origin of Some Common Mathematical Symbols
Bibliography
Index
