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(More customer reviews)Written by Peter S. Rudman (Professor Physics, Technion-Israel Institute of Technology), How Mathematics Happened is explores the history and prehistory of human mathematical discovery. From the different ways Egyptians and Babylonians expressed fractions so that they would almost never be nonterminating fractions, to the evolution of pattern recognition to finger counting to pebble counting, to the underappreciated Mayan mathematics system, to concepts of abstraction and rigor invented by Greek mathematicians such as Pythagoras, Eratosthenes, and Hippasus. An amazing tour of human discovery, illustrated with black-and-white diagrams and punctuated with "fun questions" (with answers) for the reader to solve as well as references and an index, How Mathematics Happened is an engaging read for students, scholars, and laypeople alike.
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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.
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