A History of Mathematics: From Mesopotamia to ModernityA 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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Page v
... texts which we have , and to relate them to our own ideas . Such constructions are often controversial , and always provisional ; but that is the nature of history . The original impulse to write came from David Robinson , my ...
... texts which we have , and to relate them to our own ideas . Such constructions are often controversial , and always provisional ; but that is the nature of history . The original impulse to write came from David Robinson , my ...
Page vii
... texts , and on history Examples Historicism and ' presentism ' Revolutions , paradigms , and all that External versus internal Eurocentrism 1. Babylonian mathematics 1. On beginnings 2. Sources and selections 3. Discussion of the ...
... texts , and on history Examples Historicism and ' presentism ' Revolutions , paradigms , and all that External versus internal Eurocentrism 1. Babylonian mathematics 1. On beginnings 2. Sources and selections 3. Discussion of the ...
Page viii
... texts 4. The golden age 5. Algebra - the origins 57 57 60 63 66 69 71 73 75 76 78 78 80 80 82 85 88 90 95 98 99 101 101 103 106 108 110 6. Algebra - the next steps 115 7. Al - Samaw'al and al - Kashi 117 8. The uses of religion 123 ...
... texts 4. The golden age 5. Algebra - the origins 57 57 60 63 66 69 71 73 75 76 78 78 80 80 82 85 88 90 95 98 99 101 101 103 106 108 110 6. Algebra - the next steps 115 7. Al - Samaw'al and al - Kashi 117 8. The uses of religion 123 ...
Page 2
... texts , and on history Insofar as it stands in the service of life , history stands in the service of an unhistorical power , and , thus subordinate , it can and should never become a pure science such as , for instance , mathematics is ...
... texts , and on history Insofar as it stands in the service of life , history stands in the service of an unhistorical power , and , thus subordinate , it can and should never become a pure science such as , for instance , mathematics is ...
Page 3
... texts which the student is more likely to see do not . The works of Fowler ( 1999 ) and Knorr ( 1975 ) on the Greeks , of Youschkevitch ( 1976 ) , Rashed ( 1994 ) , and Berggren ( 1986 ) on Islam , the collections of essays by Jens ...
... texts which the student is more likely to see do not . The works of Fowler ( 1999 ) and Knorr ( 1975 ) on the Greeks , of Youschkevitch ( 1976 ) , Rashed ( 1994 ) , and Berggren ( 1986 ) on Islam , the collections of essays by Jens ...
Contents
1 | |
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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Common terms and phrases
al-Kashi al-Khwarizmi al-Samaw'al al-Uqlidisi algebra ancient answer Appendix Arabic Archimedes argument axioms Babylonian Babylonian mathematics calculation called century Chinese mathematics circle classical consider construction counting rods cube curve decimal defined Descartes diagram discovery equal equation Euclid Euclidean Euclidean geometry example Exercise fact Fauvel and Gray follows formula fractions give given Greek mathematics Hilbert historians history of mathematics idea important infinitely small Islamic mathematics language later Leibniz machine mathematicians means method modern multiply Newton Nine Chapters non-Euclidean geometry notation particular period postulate practical problem proof proposition Ptolemy Qin Jiushao quadratic question radius ratio reader real numbers rectangle Reidemeister moves result revolution right angles rules scientific seems sexagesimals side solution solve square root straight line subtract suppose tangent textbook texts theorem theory tradition translation triangle writing مال مرتبة
Popular passages
Page 260 - Only an alert and knowledgeable citizenry can compel the proper meshing of the huge industrial and military machinery of defense with our peaceful methods and goals, so that security and liberty may prosper together.
Page 36 - twas the 47 El. libri I. He read the Proposition. By G — , sayd he (he would now and then sweare an emphaticall Oath by way of emphasis) this is impossible! So he reads the Demonstration of it, which referred him back to such a Proposition; which proposition he read. That referred him back to another, which he also read. El sic deinceps [and so on] that at last he was demonstratively convinced of that trueth. This made him in love with Geometry.
Page 49 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
Page 71 - In the bloom of beauty, and in the maturity of wisdom, the modest maid refused her lovers and instructed her disciples; the persons most illustrious for their rank or merit were impatient to visit the female philosopher; and Cyril beheld with a jealous eye the gorgeous train of horses and slaves who crowded the door of her academy.
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.
Page 260 - The prospect of domination of the nation's scholars by Federal employment, project allocations, and the power of money is ever present — and is gravely to be regarded. Yet, in holding scientific research and discovery in respect, as we should, we must also be alert to the equal and opposite danger that public policy could itself become the captive of a scientifictechnological elite.
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...