A History of Mathematics: From Mesopotamia to Modernity

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OUP Oxford, Jun 2, 2005 - Mathematics - 296 pages
A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwarizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader.

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Contents

Introduction
1
Babylonian mathematics
14
Greeks and origins
33
Greeks practical and theoretical
57
Chinese mathematics
78
Islam neglect and discovery
101
Understanding the scientific revolution
133
The calculus
161
Geometries and space
189
Modernity and its anxieties
213
A chaotic end?
235
Conclusion
260
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Page 240 - Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
Page 260 - Yesterday all the past. The language of size Spreading to China along the trade-routes; the diffusion Of the counting-frame and the cromlech; Yesterday the shadow-reckoning in the sunny climates. Yesterday the assessment of insurance by cards, The divination of water; yesterday the invention Of cartwheels and clocks, the taming of Horses.
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Page 42 - This king [Sesostris, ca. 1300 BC] moreover (so they said) divided the country among all the Egyptians by giving each an equal square parcel of land, and made this his source of revenue, appointing the payment of a yearly tax. And any man who was robbed by the river of a part of his land would come to Sesostris and declare what had befallen him; then the king would send men to look into it and measure the space by which the land was diminished, so that thereafter it should pay the appointed tax in...
Page 217 - This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call : There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus.
Page 60 - Archimedes possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge, that though these inventions had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can...

References to this book

The Theft of History
Jack Goody
Limited preview - 2007

About the author (2005)

Luke Hodgkin is a Senior Lecturer in the Department of Mathematics at King's College London.

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