Making up Numbers: A History of Invention in Mathematics by Ekkehard Kopp
Making up Numbers: A History of Invention in Mathematics - Table of Contents
PART I: ANTIQUITY & ALGEBRA
- 1. Arithmetic in Antiquity
- 2. Writing and Solving Equations
- 3. Construction and Calculation
- 4. Coordinates and Complex Numbers
PART II: CALCULUS & NUMBER SYSTEMS
- 5. Struggles with the Infinite
- 6. From Calculus to Analysis
- 7. Number Systems and Continuums
PART III: AXIOMS & TRANSFINITE MATH
- 8. Axioms for Number Systems
- 9. Counting Beyond the Finite
- 10. Solid Foundations?
What You Will Learn in Making up Numbers: A History of Invention in Mathematics
Making Up Numbers: A History of Invention in Mathematics by Ekkehard Kopp is an authoritative, open-access historical textbook published by Open Book Publishers that explores how human societies invented, extended, and formalized number concepts over millennia. This comprehensive volume guides readers through ancient Babylonian and Greek arithmetic, geometric construction methods, algebraic equation solving, the introduction of complex numbers, infinitesimal calculus developments, real number completions, Peano axiomatizations, and Cantor's transfinite set theory with exceptional historical perspective and mathematical clarity.
Designed for undergraduate mathematics students, secondary educators, math historians, and general science readers, this foundational text bridges cultural history and formal mathematical concepts. Kopp details step-by-step conceptual shifts from practical counting to abstract number systems, highlighting foundational debates over negative numbers, infinitesimals, irrationals, and set-theoretic paradoxes. Whether you are studying the history of analysis, exploring how number field definitions evolved, or teaching foundational mathematics, this book offers an indispensable roadmap.
Recognized globally as one of the best accessible histories of mathematical invention, it stands as one of the best introductory books on the historical development of number systems and analysis. By unifying historical narrative with rigorous mathematical evolution, it serves as an essential tool for mastering the history and foundations of mathematics with confidence.
Book Details & Specifications
Title:
Making up Numbers: A History of Invention in Mathematics by Ekkehard Kopp
Publisher:
Open Book Publishers
Year:
2020
Pages:
283
Type:
PDF
Language:
English
ISBN-10 #:
1800640951
ISBN-13 #:
978-1800640955
License:
CC BY 4.0
Amazon:
Amazon
About the Author: Ekkehard Kopp
The author Ekkehard Kopp
is Emeritus Professor of Mathematics at the University of Hull, UK, widely celebrated for his extensive contributions to measure theory, stochastic integration, mathematical finance, and the history of mathematics. He has authored multiple successful textbooks designed to make foundational pure mathematics accessible to broad academic audiences.
Through Making Up Numbers: A History of Invention in Mathematics, Kopp delivers a clear, engaging, and historically grounded account of mathematical discovery. His lucid narrative structure, primary source analysis, and focus on foundational evolution make this text a classic reference for the history of number systems valued by students, educators, and historians worldwide.
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