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In the study of ideas, it is necessary to remember that insistence on hard-headed clarity issues from sentimental feeling, as it were a mist, cloaking the perplexities of fact. Insistence on clarity at all costs is based on sheer superstition as to the mode in which human intelligence functions. Our reasonings grasp at straws for premises and float on gossamers for deductions.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
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Review of The Man of Numbers: Fibonacci's Arithmetic Revolution
The Man of Numbers: Fibonacci’s Arithmetic Revolution. Keith Devlin, 2011. 183 pp. Illustrations, bibliography, and index. $25 hardcover, ISBN: 978-0-8027-7812-3. Walker Publishing Company, New York. www.walkerbooks.com
Recently I found myself updating the bibliography of an article on Fibonacci (King, 1963). I was pleased to note the translations of Fibonacci’s major works made since that time and now available to a general reading public (Hughes, 2008; Sigler, 1987, 2002), but still disappointed that a more detailed account of Fibonacci and his work had not been undertaken. Mathematics history books tell us that Fibonacci published Liber abbaci in 1202 and initiated an interesting problem concerning the reproduction of rabbits, but the principal importance of his work to the development of mathematics in Europe has remained vague. His accomplishments certainly deserve a closer examination. Therefore, I was delighted to learn of Keith Devlin’s new book, The Man of Numbers, which builds upon the now available English language translations of Fibonacci’s major works and, in great part, supplies more relevant information on this merchant-turned-mathematician’s impact on the medieval European mathematical scene.
History actually provides little information on the life of Fibonacci. It is known that he was a Pisan merchant, worked in Africa where he came in contact with Arabic mathematical sources, and in his works transferred new mathematical symbols and techniques to a waiting European audience. From the scope and quality of Fibonacci’s existing writings, it is obvious that he was also, in his own right, a talented mathematician. Devlin works from this basis to provide a more informative retrospection of Fibonacci’s accomplishments and his times. Most importantly, he clearly identifies the role of merchants and commercial mathematics in advancing the climate of European mathematics in general. Fibonacci’s work, in its form and content, established a new genre for a series of ongoing European abbaci manuscripts. It was this venue that helped establish the eventual adoption of the Hindu-Arabic numerals and their algorithmic computational schemes into the European mathematics scene.
The information provided in The Man of Numbers is well-organized. Its author takes us from an examination of the status and importance of numbers in early medieval Europe through the tempo of increased European trade, which saw its merchants travelling to foreign lands and acquiring new information and customs. Fibonacci is identified as taking such a journey and being exposed to various Arabic mathematical practices. The major result of this experience was his publication of the Liber abbaci, whose contents and format is examined in good detail. Then, the resulting impact of Fibonacci’s contributions to the European intellectual and mathematical scene is discussed. Along the way, the reader is introduced to many interesting facts: I learned about the personality and power of Fibonacci’s patron, Frederick II, Holy Roman Emperor, and also about the saga of a nineteenth-century statue erected in the mathematician’s honor in Pisa.
In a few instances, however, some facts are misleading. For example, on page 35, in discussing a rising wool industry, the author notes that in Leonardo’s time wool was starting to replace leather for clothing, leaving the reader with the impression that leather clothing was popular in the Middle Ages. This is not exactly correct, as the common people mainly wore clothing woven of flax as well as wool and other animal fibers. On pages 67-69, Devlin discusses a problem involving an indeterminate situation from Chapter 11 of the Liber Abbaci. He refers to it as the problem “well known to mathematicians” as “Fibonacci’s Problem of the Birds.” Although I am familiar with historical problems of note, I have never before heard this expression, but I recognize the problem as a variant of the “Hundred Fowls Problem” from 5th-century China, a mathematical problem that traveled from its Chinese place of origin to Europe via Hindu and Islamic sources.
On page 160, the note for Chapter 2 indicates that much information was gained from “the pamphlet Gies and Gies 1969,” but no further information is given on this pamphlet other than “it is long since out of print.” Frances and Joseph Gies are respected medievalists and authors who have written two books directly reflecting on Fibonacci and his mathematical impact, Leonardo of Pisa and the New Mathematics of the Middle Ages (1969) and Merchants and Moneymen: the Commercial Revolution, 1000-1500 (1972). The first of these works is listed in the bibliography but not cited anywhere in the text. It was republished by New Classics Library in 1983 and is still available. The second of the Gies and Gies books is not mentioned. Despite such occasional inconsistencies, The Man of Numbers is a good source of information and an enjoyable read. I recommend it for personal reference and general library acquisition. It would certainly be a nice addition to secondary school libraries.
Reviewer Frank J. Swetz is Professor Emeritus of The Pennsylvania State University and a founding editor of MAA Convergence.
Gies, Joseph and Frances Gies. Leonardo of Pisa and the New Mathematics of the Middle Ages. New York: Thomas Crowell, 1969. Reprinted 1983, Gainesville, Georgia: New Classics Library.
Gies, Joseph and Frances Gies. Merchants and Moneymen: The Commercial Revolution 1000-1500. New York: Thomas Crowell, 1972.
Hughes, Barnabas (ed). Fibonacci’s De Practica Geometrie. New York: Springer, 2008.
King, Charles. “Leonardo Fibonacci.” Fibonacci Quarterly 1 (Dec. 1963): 15-19.
Sigler, Laurence (trans.). The Book of Squares by Leonardo Pisano: An Annotated Translation into Modern English. Boston: Academic Press, 1987.
Sigler, Laurence (trans.). Fibonacci’s Liber Abaci – A Translation into Modern English of Leonardo Pisano’s Book of Calculation. New York: Springer, 2002.
Swetz, Frank J., "Review of The Man of Numbers: Fibonacci's Arithmetic Revolution," Loci (February 2012), DOI: 10.4169/loci003858