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History of Mathematics: Highways and Byways (Spectrum)

2 customer reviews
ISBN-13: 978-0883855621
ISBN-10: 0883855623
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Editorial Reviews


In this translation from the 1986 French work, Dahan-Dalmedico and Peiffer (both, CNRS, French National Center for Scientific Research) provide a concise yet relatively detailed history of mathematics from antiquity to the beginning of the 20th century. The organization of the book is topical rather than strictly chronological, with an emphasis on describing the particular mathematical ideas of individuals and how they relate to one another. The authors provide considerable discussion of the early Arab contribution, particularly to algebra, and how, from 400 to 200, Arab scholars managed to retain and augment the tradition of ancient Greek mathematics. Also noteworthy is the treatment of the early development of analysis, particularly notions of limits. However, the authors do not pretend to give a comprehensive history; there are no accounts of either topology or probability theory (or much applied mathematics, for that matter). The only references appear in a brief bibliography of general texts in English, provided by the translator. Nonetheless, this is a serious, mathematics-driven account, suitable for academic students. Summing up: Recommended. Academic libraries serving lower-division undergraduates through graduate students. --S.J. Colley, Oberlin College, CHOICE Magazine

As the title suggest the book traces developments in the history of mathematics from its beginnings, although not always following the most obvious paths. Within eight chapters, the authors interweave many interesting and less well known snippets of mathematical history following a historical time line from the Babylonians through to a discussion on present day Algebraic Structures.

The history of mathematics is vast and it is difficult to capture it all in one book. However, the authors highlight some of the main highways and then takes time to journey down some lesser known side streets; I feel this works well. ...

Throughout the book there are illustrations of mathematics to give concrete examples of the sort of work that was going on at that time. In Chapter 6, The Concept of Function and the Development of Analysis, the authors start in Babylonian mathematics with the construction of sexagesimal for reciprocals, squares, square roots, and many more, then journey through to Lebesgue-Integrable Functions. Along the way they discuss Galioleo's formula of 1623 from the book II Saggiatore: 'The great book of the written in mathematical language." We are told that linked to Galileo's need to experiment, is the astronomers wish to calculate, resulting in the development by Napier and others of Logarithmic tables. As we journey through the development of functions in this chapter we gain a greater understanding of Euler's part in this and also the work of others, such as Fourier...

The book gives a sense of flow to mathematics over the years; it will be of interest to those mathematicians who wish to gain an understanding of how events in mathematical history have interplayed to create the whole picture. I enjoyed the links made to other developments and the ideas of how the body of knowledge grew over collective generations. --Steve Humble, Mathematics Today

Book Description

This book is arranged to show the development of the different branches of mathematics over time and contains many illustrations to support the text. In all, a short, innovative and easy-to-read history of mathematics.

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Product Details

  • Series: Spectrum
  • Hardcover: 330 pages
  • Publisher: Mathematical Association of America (December 8, 2009)
  • Language: English
  • ISBN-10: 0883855623
  • ISBN-13: 978-0883855621
  • Product Dimensions: 6 x 0.9 x 9 inches
  • Shipping Weight: 1 pounds (View shipping rates and policies)
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #1,743,199 in Books (See Top 100 in Books)

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3 of 4 people found the following review helpful By Viktor Blasjo on June 24, 2010
Format: Hardcover
This is an unexceptional and awkwardly translated history of mathematics.

Among the many common myths unthinkingly propagated by the authors is the nonsense that the development of "the concept of function" is somehow enlightening and important. An entire chapter is devoted to this meaningless study, in which we read such bogus as:

"Descartes' idea of restricting the notion of function only to algebraic expressions was an iron collar" (p. 233) (Incidentally, this sentence illustrates the poor quality of the translation. Of course what is meant here is that Descartes restricted the notion of function to algebraic expressions alone, i.e. that he restricted too much, not that he "only" restricted the notion to some extent but not enough, as the translation clumsily suggests. Awkward expressions like this occur on virtually every page.)

No evidence is ever provided for claims such as these, of course, since they are mere prejudices without any basis in historical fact. One might as well claim that the 17th century conception of "vehicle" as necessarily animal-powered was an "iron collar" impeding the development of cars. People held this conception not because they were dense or unimaginative but because a more general conception would have served no purpose whatsoever at the time. So also with functions, which makes the study of history through this anachronistic lens a complete waste of time.

Another flaw of the book is that is that it is full of casually scattered statements that are neither explained nor supported and very often too brief and vague for anyone to gain anything from them or even to understand what they mean.
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Format: Hardcover
This history of mathematics book is all history, unlike most books written as texts in the subject, there are no pictures of the referenced mathematicians and no asides giving interesting facts about their life and times. The focus is almost exclusively on western mathematics plus the Arab contribution when European mathematics went dark; there is no real mention of what was done in other areas of the globe.
Although there is a brief mention of early mathematics, the detailed explanations begin with the sudden development of abstract mathematics in ancient Greece. The concept of formal proof and logical reasoning was a revolutionary and necessary concept, without it mathematics can be little more than measuring and computing. Advancements in mathematics are tracked from there through the abstract algebra concepts of Galois and the rise of group theory.
In the spectrum of books on the history of mathematics, this one is at the higher end of content and rigor. The authors are all business; there is nothing in the way of fluff or tangential development.

Published in Journal of Recreational Mathematics, reprinted with permission
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History of Mathematics: Highways and Byways (Spectrum)
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