Making Up Numbers A History Of Invention In Mathematics
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Making Up Numbers
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of 'infinity' and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
Making up Numbers: A History of Invention in Mathematics
Author: Ekkehard Kopp
language: en
Publisher: Open Book Publishers
Release Date: 2020-10-23
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
Numbers and the Making of Us
Author: Caleb Everett
language: en
Publisher: Harvard University Press
Release Date: 2017-03-13
“A fascinating book.” —James Ryerson, New York Times Book Review A Smithsonian Best Science Book of the Year Winner of the PROSE Award for Best Book in Language & Linguistics Carved into our past and woven into our present, numbers shape our perceptions of the world far more than we think. In this sweeping account of how the invention of numbers sparked a revolution in human thought and culture, Caleb Everett draws on new discoveries in psychology, anthropology, and linguistics to reveal the many things made possible by numbers, from the concept of time to writing, agriculture, and commerce. Numbers are a tool, like the wheel, developed and refined over millennia. They allow us to grasp quantities precisely, but recent research confirms that they are not innate—and without numbers, we could not fully grasp quantities greater than three. Everett considers the number systems that have developed in different societies as he shares insights from his fascinating work with indigenous Amazonians. “This is bold, heady stuff... The breadth of research Everett covers is impressive, and allows him to develop a narrative that is both global and compelling... Numbers is eye-opening, even eye-popping.” —New Scientist “A powerful and convincing case for Everett’s main thesis: that numbers are neither natural nor innate to humans.” —Wall Street Journal