How Mathematics Happened: The First 50,000 Yearsby Peter S. Rudman
Pub. Date: 02/28/2007
Publisher: Prometheus Books
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… See more details below
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.
- Prometheus Books
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Table of Contents
List of Figures 7
List of Tables 11
Mathematical Darwinism 21
The Replacement Concept 28
Number Systems 38
The Birth of Arithmetic 49
Pattern Recognition Evolves into Counting 49
Counting in Hunter-Gatherer Cultures 53
Pebble Counting Evolves into Written Numbers 67
Herder-Farmer and Urban Cultures in the Valley of the Nile 67
Herder-Farmer and Urban Cultures by the Waters of Babylon 82
In the Jungles of the Maya 114
Mathematics in the Valley of the Nile 131
Egyptian Multiplication 131
Egyptian Fractions 141
Egyptian Algebra 158
Mathematics by the Waters of Babylon 187
Babylonian Multiplication 187
Babylonian Fractions 208
Plimpton 322-The Enigma 215
Babylonian Algebra 231
Babylonian Calculation of Square Root of 2 240
Mathematics Attains Maturity: Rigorous Proof 249
We Learn History to Be Able to Repeat It 263
Teaching Mathematics in Ancient Greece and How We Should but Do Not 263
Answers to Fun Questions 27
Notes and References 295
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This book is very well written and explains ancient mathematics as well as very expensive and rarely read book only found in University Libraries. I do however feel that he occasionally includes folklore which can easily be proved false. For example on page 257 he describes the "well known" story of how Eratosthenes was the first to measure the Circumference of the earth. He almost discovers the truth where he writes that the measurement is easier using the north star. The circumference of the Earth was measured at least 2500 years before Eratosthenes was born. Here is the proof. The distance between alexandria and Syene was said to be 7.2 degrees in latitude. Looking it up on google earth, I cannot disagree therefore the distance is 432 arc minutes. Syene is 150 nautical miles east of Alexandria so the straight line distance would have been about 458 nautical miles. The Egyptian Stadia was 500 reman or 0.101236 nautical miles, the greek stadia was 600 attic feet or 0.09998 nautical miles. if the Egyptian scribes has correctly stated the NORTH- SOUTH distance between the cities as 4320 greek stadia or 4270 Egyptian stadia, Eratosthenes would have instantly known that the measurement had been made at least 2500 years earlier.
MUST READ! "How Mathematics Happened" is exactly how we need to teach children about math. This was a fascinating book that had great math problems ranging from changing base 10 to base 60 to geometric algebra proofs . Rudman spells out exactly how counting and measuring were was created and how the ancient people's mind set led them to form a mathematical system that is founded on different bases, different algorithms for division and multiplication, and different representation. His final chapter is what needs to be read by all in education business. He understands that by having our young children taught by people that do not like (or understand) math causes them once in high school students to hate math too. Rather than force a humanities teacher to change his/her lessons to support Math in Science, maybe we should teach math the ones that want to learn it. Computers/calculators take care of the arithmetic now, so why waste brain power and time on memorizing tables when we could be exploring abstract thought. As I say to many students, "I am a Mathematician, not an Arithmetician." Rudman understands this difference and his book will spells the differnce out very well.
how mathematics happened 50,000 yrs ago is profoundly great.