Catalogue


How mathematics happened : the first 50,000 years /
Peter S. Rudman.
imprint
Amherst, New York : Prometheus Books, 2007.
description
314 pages : illustrations ; 24 cm.
ISBN
1591024773 (alk. paper), 9781591024774
format(s)
Book
Holdings
More Details
imprint
Amherst, New York : Prometheus Books, 2007.
isbn
1591024773 (alk. paper)
9781591024774
catalogue key
6142901
 
Gift to Victoria University Library. Danesi, Marcel. 2018/03/09.
Includes bibliographical references (pages 295-308) and index.
A Look Inside
Full Text Reviews
Appeared in Choice on 2008-01-01:
What a breath of fresh air to read a prehistory of mathematics like Rudman's. Most such books take every even slightly plausible theory on the origin of counting or arithmetic, no matter how scanty the evidence, as clear and established truth. Rudman (retired, solid-state physics, Technion-Israel Institute of Technology), on the other hand, is willing to explain without making definitive conclusions when they are not warranted, and to hedge when hedging is necessary. He presents statements as fact only when there is sufficient evidence to do so. Not only is this a high-quality popular history of arithmetic and mathematics from 50,000 BCE until the beginnings of rigorous proof in Greece, but it is actually historiographically credible as well, in that it considers the many schools of interpretation that have examined and remarked on the same few available pieces of documentation and physical evidence. His project, in his words, is not so much to explain what happened--thank goodness, as we have seen far too much of that--as to explain why it happened as it did. He constructs plausible and interesting explanations, even if (as he admits) they are ultimately unverifiable. Summing Up: Highly recommended. General readers; lower- and upper-division undergraduates. A. B. Riskin Mary Baldwin College
Reviews
This item was reviewed in:
Booklist, October 2006
Choice, January 2008
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Summaries
Main Description
In this fascinating discussion of ancient mathematics, author Peter Rudman does not just chronicle the archeological record of what mathematics was done; he digs deeper into the more important question of why it was done in a particular way. Why did the Egyptians use a bizarre method of expressing fractions? Why did the Babylonians use an awkward number system based on multiples of 60?Rudman answers such intriguing questions, arguing that some mathematical thinking is universal and timeless. The similarity of the Babylonian and Mayan number systems, two cultures widely separated in time and space, illustrates the argument. He then traces the evolution of number systems from finger counting in hunter-gatherer cultures to pebble counting in herder-farmer cultures of the Nile and Tigris-Euphrates valleys, which defined the number systems that continued to be used even after the invention of writing.With separate chapters devoted to the remarkable Egyptian and Babylonian mathematics of the era from about 3500 to 2000 BCE, when all of the basic arithmetic operations and even quadratic algebra became doable, Rudman concludes his interpretation of the archeological record.Since some of the mathematics formerly credited to the Greeks is now known to be a prior Babylonian invention, Rudman adds a chapter that discusses the math used by Pythagoras, Eratosthenes, and Hippasus, which has Babylonian roots, illustrating the watershed difference in abstraction and rigor that the Greeks introduced. He also suggests that we might improve present-day teaching by taking note of how the Greeks taught math.Complete with sidebars offering recreational math brainteasers, this engrossing discussion of the evolution of mathematics will appeal to both scholars and lay readers with an interest in mathematics and its history.Peter S. Rudman (Haifa, Israel) is professor (ret.) of solid-state physics at the Technion-Israel Institute of Technology and the author of more than 100 articles in physics.
Main Description
Complete with sidebars offering recreational math brainteasers, this engrossing discussion of the evolution of mathematics will appeal to both scholars and lay readers with an interest in mathematics and its history.
Main Description
In this fascinating discussion of ancient mathematics, author Peter Rudman does not just chronicle the archaeological record of what mathematics was done; he digs deeper into the more important question of why it was done in a particular way. Why did the Egyptians use a bizarre method of expressing fractions? Why did the Babylonians use an awkward number system based on multiples of 60? Rudman answers such intriguing questions, arguing that some mathematical thinking is universal and timeless. The similarity of the Babylonian and Mayan number systems, two cultures widely separated in time and space, illustrates the argument. He then traces the evolution of number systems from finger counting in hunter-gatherer cultures to pebble counting in herder-farmer cultures of the Nile and Tigris-Euphrates valleys, which defined the number systems that continued to be used even after the invention of writing. With separate chapters devoted to the remarkable Egyptian and Babylonian mathematics of the era from about 3500 to 2000 BCE, when all of the basic arithmetic operations and even quadratic algebra became doable, Rudman concludes his interpretation of the archaeological record. Since some of the mathematics formerly credited to the Greeks is now known to be a prior Babylonian invention, Rudman adds a chapter that discusses the math used by Pythagoras, Eratosthenes, and Hippasus, which has Babylonian roots, illustrating the watershed difference in abstraction and rigor that the Greeks introduced. He also suggests that we might improve present-day teaching by taking note of how the Greeks taught math. Complete with sidebars offering recreational math brainteasers, this engrossing discussion of the evolution of mathematics will appeal to both scholars and lay readers with an interest in mathematics and its history.
Table of Contents
List of Figuresp. 7
List of Tablesp. 11
Prefacep. 15
Introductionp. 21
Mathematical Darwinismp. 21
The Replacement Conceptp. 28
Number Systemsp. 38
The Birth of Arithmeticp. 49
Pattern Recognition Evolves into Countingp. 49
Counting in Hunter-Gatherer Culturesp. 53
Pebble Counting Evolves into Written Numbersp. 67
Herder-Farmer and Urban Cultures in the Valley of the Nilep. 67
Herder-Farmer and Urban Cultures by the Waters of Babylonp. 82
In the Jungles of the Mayap. 114
Mathematics in the Valley of the Nilep. 131
Egyptian Multiplicationp. 131
Egyptian Fractionsp. 141
Egyptian Algebrap. 158
Pyramidiotsp. 175
Mathematics by the Waters of Babylonp. 187
Babylonian Multiplicationp. 187
Babylonian Fractionsp. 208
Plimpton 322-The Enigmap. 215
Babylonian Algebrap. 231
Babylonian Calculation of Square Root of 2p. 240
Mathematics Attains Maturity: Rigorous Proofp. 249
Pythagorasp. 249
Eratosthenesp. 254
Hippasusp. 258
We Learn History to Be Able to Repeat Itp. 263
Teaching Mathematics in Ancient Greece and How We Should but Do Notp. 263
Answers to Fun Questionsp. 27
Notes and Referencesp. 295
Indexp. 309
Table of Contents provided by Ingram. All Rights Reserved.

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