Due to the current COVID-19 situation, our customers may experience some delivery delays. We apologise for any inconvenience this may cause.

Making up Numbers: A History of Invention in Mathematics

Making up Numbers: A History of Invention in Mathematics Ekkehard Kopp
Paperback ISBN: 978-1-80064-095-5 £20.95
Hardback ISBN: 978-1-80064-096-2 £30.95
PDF ISBN: 978-1-80064-097-9 £0.00

Click here to read the PDF online for free Click here to read the HTML online for free

Read about the importance of this contribution on our .

This book tells a lively story and is crammed with interesting, and often technical, mathematics, which the author nevertheless makes accessible to a wide readership.
Christopher Hollings, University of Oxford

This book examines the theoretical growth of mathematics from a historical perspective. Kopp (Univ. of Hull) offers a fascinating and enlightening presentation in which basic notions are evolved into advanced mathematical concepts. As shown here, abstraction becomes a natural result of mathematical development. 

D. P. Turner, Faulkner University, CHOICE Connects, June 2021 Vol. 58 No. 10

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
Ekkehard Kopp | October 2020
280 pp. | 6.14" x 9.21" (234 x 156 mm)
ISBN Paperback: 9781800640955
ISBN Hardback: 9781800640962
ISBN Digital (PDF): 9781800640979
DOI: 10.11647/OBP.0236
Subject Codes: BIC: PB (Mathematics), YQM (Educational: Mathematics and numeracy), PBK (Calculus and Mathematical Analysis); BISAC: MAT000000 (MATHEMATICS / General), MAT 015000 (MATHEMATICS / History and Philosophy), MAT027000 (MATHEMATICS / Research); OCLC Number: 1226545401.

You may also be interested in:


Prologue: Naming Numbers Download
Ekkehard Kopp

Chapter 1.: Arithmetic in Antiquity Download
Ekkehard Kopp

Chapter 2.: Writing and Solving Equations Download
Ekkehard Kopp

Chapter 3.: Construction and Calculation Download
Ekkehard Kopp

Chapter 4.: Coordinates and Complex Numbers Download
Ekkehard Kopp

Chapter 5.: Struggles with the Infinite Download
Ekkehard Kopp

Chapter 6.: From Calculus to Analysis Download
Ekkehard Kopp

Chapter 7.: Number Systems Download
Ekkehard Kopp

Chapter 8.: Axioms for number systems Download
Ekkehard Kopp

Chapter 9.: Counting beyond the finite Download
Ekkehard Kopp

Chapter 10.: Solid Foundations? Download
Ekkehard Kopp

Epilogue Download
Ekkehard Kopp


Name Index


Ekkehard Kopp is a Professor Emeritus at the University of Hull, where he lectured in Mathematics for many years. He has published many articles in academic mathematical journals, and has authored and co-authored books on probability, models and mathematics of financial markets, stochastic calculus for finance, and portfolio theory and risk management.
Mathematical Miscellany Download