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# Delving into “Math Through the Ages”: An Insightful Look at Mathematical History
In a recent exchange linked to Thony Christie’s commentary on books about the history of mathematics, historian Fernando Q. Gouvêa brought attention to the collaboration he undertook with William P. Berlinghoff — _Math Through the Ages: A Gentle History for Teachers and Others_. Captivated by this suggestion, Christie opted to evaluate whether this book warranted the acclaim it garnered, particularly from noted historian Glen Van Brummelen, who referred to it as “a treasure” and lauded its equilibrium between complexity and understandability.
Christie’s thorough examination of _Math Through the Ages_ presents essential observations regarding both the merits and occasional factual inaccuracies of this endeavor to render the history of mathematics approachable for novices. In this article, we will encapsulate Christie’s evaluation and provide an outline of what readers may anticipate from the book.
## Structure and Methodology
In contrast to numerous singular histories that struggle through a unified chronological account, _Math Through the Ages_ is divided into two separate segments:
1. **A Large Nutshell**: A brief 58-page historical synopsis, charting the progress of mathematics from ancient Mesopotamia to contemporary Europe.
2. **Thirty Sketches**: Self-contained, pedagogically oriented essays on specific subjects, covering topics from the invention of zero and the development of negative numbers to the history of computing and statistical methods.
This adaptable framework, paired with a comprehensive cross-referenced bibliography, invites readers to delve into subjects independently while providing avenues for more in-depth exploration. Christie aptly underscores the strength of this format in enhancing the text’s accessibility for beginners and educators.
## The Positive: Comprehensive and Captivating Entry Points
Christie notes that the majority of the sketches are well-crafted and effectively written, offering concise insights into significant mathematical ideas and their evolution. Notable highlights include:
– A balanced account of the metric system’s introduction during the French Revolution in “By Ten and Tenths.”
– A fairly thorough exploration of the evolution of trigonometry in “Half is Better.”
– An equitable and engaging portrayal of the Pythagorean Theorem’s cultural journey in “A Cheerful Fact.”
– An easy-to-understand introduction to projective geometry and non-Euclidean geometries.
– A surprisingly rich and captivating narrative on the origins of probability theory in the section “What’s in a Game?”
For individuals new to the history of mathematics, this book acts as an excellent introductory guide, providing clear narratives, relatable illustrations, and useful bibliographical references at the conclusion of each sketch to facilitate further inquiry.
## The Negative: Historical Errors and Simplifications
Nonetheless, Christie is not reluctant to highlight shortcomings, particularly regarding accuracy:
– **Factual Mistakes**: Numerous sketches contain inaccuracies. For example, the book inaccurately claims that Leibniz’s Stepped Reckoner utilized binary arithmetic — it did not; it functioned as a decimal machine. Similarly, the statement that Charles Babbage was “cranking out” tables with his Difference Engine is exaggerated since only a small demonstration model was ever finalized.
– **Overgeneralization of Key Figures**: The sections discussing Ada Lovelace perpetuate prevalent myths, attributing accomplishments to her that were largely collaborative and overstating her role as an assistant to Babbage. Alan Turing’s contributions at Bletchley Park are also presented too simplistically, suggesting he directly designed multiple machines, while credit should also be extended to individuals like Gordon Welchman and Tommy Flowers.
– **Missed Details**: Occasionally, important subtleties are overlooked. For instance, John Wilkins’ considerable impact on early metric system ideas is not mentioned, and there is no acknowledgment of William Stanley Jevons’ foundational work in Boolean algebra — a significant omission since Jevons was instrumental in shaping Boolean logic for practical application in modern computing.
– **Uncritical Suggestions**: The “What to Read Next” section endorses some questionable works. Notably, it lists E.T. Bell’s _Men of Mathematics_, notorious for its inaccuracies and embellishments, and Dava Sobel’s _Longitude_, which presents a heavily mythical account of the longitude narrative.
## American Inclination and Educational Focus
As Christie observes, the book displays a slight American inclination, which is understandable given its audience of American students. Nevertheless, the international origins of mathematics — encompassing Ancient Mesopotamia, Egypt, India, China, and the Islamic Golden Age — are generally acknowledged, although occasionally condensed.
The educational focus is clear throughout the work. By prioritizing the clarity and specificity of topics, the authors have crafted an inviting resource well-suited for secondary educators, undergraduates, and those just beginning to engage with the subject.
## Final Thoughts
In spite of its shortcomings, Christie ultimately endorses _Math Through the Ages_ as a cost-effective and largely dependable introduction to the history of mathematics. In comparison to earlier efforts at popularization such as E.