The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be?
In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the mathematics of the 18th to the early 20th century.
Focusing on both foundational debates and practical use numbers, and showing how the story of numbers is intimately linked to that of the idea of equation, this book provides a valuable insight to numbers for undergraduate students, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics.
Corry has compiled a readable account of the history of mathematics focusing on numbers, although for most of the period in question, arithmetic and geometry are not easily separable. The required level of sophistication of the reader is not great, it is certainly at the level of a first-year undergraduate, or a keen sixth-former who is studying mathematics. Even as an experienced university mathematician, the reviewer learnt many interesting things, and has some
misconceptions remedied, on reading Corry's Brief History. * Robin Chapman, LMS Newsletter *
This fine book gives what its title promises ... a well-written treatment of the subject. * Underwood Dudley, MAA Reviews *
It is a highly recommended and pleasant read, not pedantic, but not casual either ... The book is written with great care ... * Adhemar Bultheel, European Mathematical Society *
A Brief History of Numbers is a meticulously researched and carefully crafted look at how mathematicians have explored the concept of number. Corry's prose is clear and engaging, and the mathematical content is uniformly accessible to his audience. ... I highly recommend A Brief History of Numbers to mathematics teachers who wish to know more about how our current edifice of natural, rational, real, complex, and infinite numbers came to be built. * James V. Rauff, Mathematics Teacher *
1: The System of Numbers: An Overview
2: Writing Numbers: Now and Back Then
3: Numbers and Magnitudes in the Greek Mathematical Tradition
4: Construction Problems and Numerical Problems in the Greek Mathematical Tradition
5: Numbers in the Tradition of Medieval Islam
6: Numbers in Europe from the 12th to the 16th Centuries
7: Number and Equations at the Beginning of the Scientific Revolution
8: Number and Equations in theWorks of Descartes, Newton, and their Contemporaries
9: New Definitions of Complex Numbers in the Early 19th Century
10: "What are numbers and what should they be?" Understanding Numbers in the Late 19th Century
11: Exact Definitions for the Natural Numbers: Dedekind, Peano and Frege
12: Numbers, Sets and Infinity. A Conceptual Breakthrough at the Turn of the Twentieth Century
13: Epilogue: Numbers in Historical Perspective