Travelling Mathematics - The Fate of Diophantos' Arithmetic

ISBN-13: 9783034803144 / Angielski / Miękka / 2012 / 210 str.

Ad Meskens

Opis

This book offers a comprehensive study of Diophantos' Arithmetika, a unique book within the known Greek mathematical corpus whose author, Diophantos, is an enigmatic figure. It details the structure, contents and mathematics of the Arithmetika.

Recenzje

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)

Spis treści

Arithmetic and the beginnings of algebra.- Alexandria ad Aegyptum.- Diophantos and the Arithmetika.- Sleeping beauty in the Dark Ages.- New vistas.- Humanism.- Renaissance or the rebirth of Diophantos.- Fair stood the wind for France.- Coda: Hilbert’s tenth problem.- Stemma.

Blurb

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.