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Travelling Mathematics - The Fate of Diophantos' Arithmetic

  • Book
  • © 2010

Overview

Authors:
  1. Ad Meskens

    1. , Department Bedrijfskunde, ..., Artesis Hogeschool Antwerpen, Antwerpen, Belgium

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  • The first comprehensive study on Diophantos and the Arithmetika in nearly 100 years
  • The first study to include the Nachleben of the Arithmetika during the Middle Ages and the Renaissance
  • Provides an in depth study of the mathematics of the Arithmetika
  • Provides teachers examples of how the development of mathematics is not always rectilinear
  • Includes supplementary material: sn.pub/extras

Part of the book series: Science Networks. Historical Studies (SNHS, volume 41)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Arithmetic and the beginnings of algebra

    • Ad Meskens
    Pages 1-26

  3. Alexandria ad Aegyptum

    • Ad Meskens
    Pages 27-41

  4. Diophantos and the Arithmetika

    • Ad Meskens
    Pages 43-102

  5. Sleeping beauty in the Dark Ages

    • Ad Meskens
    Pages 103-122

  6. New vistas

    • Ad Meskens
    Pages 123-132

  7. Humanism

    • Ad Meskens
    Pages 133-138

  8. Renaissance or the rebirth of Diophantos

    • Ad Meskens
    Pages 139-153

  9. Fair stood the wind for France

    • Ad Meskens
    Pages 155-169

  10. Coda: Hilbert’s tenth problem

    • Ad Meskens
    Pages 171-172

  11. Stemma

    • Ad Meskens
    Pages 173-175

  12. Back Matter

    Pages 177-208
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Keywords

About this book

In this book the author presents a comprehensive study of Diophantos’ monumental work known as Arithmetika, a highly acclaimed and unique set of books within the known Greek mathematical corpus. Its author, Diophantos, is an enigmatic figure of whom we know virtually nothing. Starting with Egyptian, Babylonian and early Greek mathematics the author paints a picture of the sources the Arithmetika may have had. Life in Alexandria, where Diophantos lived, is described and, on the basis of the limited available evidence, his biography is outlined. Of Arithmetika’s 13 books only 6 survive in Greek. It was not until 1971 that these were complemented by the discovery of 4 other books in an Arab translation. This allows the author to describe the structure, the contents and the mathematics of the Arithmetika in detail. Furthermore it is shown that Diophantos had a remarkable skill to solve higher degree equations. In the second part, the author draws our attention to the survival of Diophantos’ work in both Arab and European mathematical cultures. Once Xylander’s critical 1575 edition reached its European public, the fame of the Arithmetika grew. It was studied, translated and modified by such authors as Bombelli, Stevin and Viète. It reached its pinnacle of fame in 1621 with the publication of Bachet’s translation into Latin. The marginal notes by Fermat in his copy of Diophantos, including his famous “Last Theorem”, were the starting point of a whole new research subject: the theory of numbers.

Reviews

From the reviews:

“The chapters are really surveys of the existing literature. … The book begins with an outline of early arithmetic and algebra … . Travelling Mathematics provides a wonderful overview of the Arithmetic and a valuable account of its influence. Anyone interested in Greek mathematics and in the history of algebra and number theory will want to read Meskens’ book and follow the many references provided.” (Fernando Q. Gouvêa, The Mathematical Association of America, January, 2011)

“This book is a very good introduction to the literature available on Diophantus and the interpretations of his work, and provides the reader with solid information on the various editions, their history and their background. … a must-read for anyone studying the number theoretic contributions by mathematicians from Bachet and Fermat to Euler and beyond.” (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1204, 2011)

Authors and Affiliations

  • , Department Bedrijfskunde, ..., Artesis Hogeschool Antwerpen, Antwerpen, Belgium

    Ad Meskens

Bibliographic Information

  • Book Title: Travelling Mathematics - The Fate of Diophantos' Arithmetic

  • Authors: Ad Meskens

  • Series Title: Science Networks. Historical Studies

  • DOI: https://doi.org/10.1007/978-3-0346-0643-1

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Basel AG 2010

  • Hardcover ISBN: 978-3-0346-0642-4Published: 27 September 2010

  • Softcover ISBN: 978-3-0348-0314-4Published: 06 November 2012

  • eBook ISBN: 978-3-0346-0643-1Published: 24 September 2010

  • Series ISSN: 1421-6329

  • Series E-ISSN: 2296-6080

  • Edition Number: 1

  • Number of Pages: X, 210

  • Topics: History of Mathematical Sciences

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