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The Story of Mathematics
192 pages, Paperback
First published September 13, 2001
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Displaying 1 - 3 of 3 reviews
December 29, 2022
It is rare for a popular work written by a natural scientist or mathematician to display much of a sensitivity to cultural context. For this reason alone, Richard Mankiewicz’ The Story of Mathematics (originally published by the Princeton University Press in 2001) deserves approbation. Anyone curious about the meaning of doing mathematics will find much to reflect upon here. Mankiewicz reviews the history of mathematics going back to pre-historic times with an eye to what its practice could have signified to our ancestors under the circumstances of the societies in which they lived and enters into minute historical detail, especially illuminating as to question of why certain cultural practices supported the development of mathematics – e.g., Chinese divination, the proper construction of Hindu altars, the Islamic injunction to pray at specific times of the day. In all such cases, one was not satisfied with a rough approximation, but rather, the religious impulse leads one to seek out the optimal solution attainable and thus serves as a motivational force behind progress in mathematical technique. Nor are the instances already mentioned exhaustive; there are also Chaldaean astrology, Christian computation of the date of Easter and so on. It is safe to say that religion is everywhere the ground of culture and Mankiewicz’ illustrations exemplify how it plays this role in one major aspect of life in a technological civilization.
But Mankiewicz has more than this to purvey, for not only is the historical context set out in more than usual granularity, the mathematical content itself in his treatment surpasses that of most popular expositions. The standard topics receive due attention, of course, but where the author excels is at explaining the procedure behind the solution to ancient problems – e.g., on the Chinese method of extracting square and cube roots [p. 36-37], on how to calculate trigonometric tables [p. 50] etc. After reading Manckiewicz, one appreciates not only what they knew but also how they found it out, often in sufficient detail that one could in principle reproduce their results, if one were so minded. A particularly notable instance of this can be had with his graphic exemplification of the practical value of logarithms:
Navigators, who had to handle sines and cosines, found that a typical task of multiplying two seven-figure numbers was reduced to consulting their logarithms, making one addition and then referring back to the table where the inverse logarithm would give the required answer. Before, when a calculation could take you an hour, your answer would always lag an hour behind your real position. This had now been cut down to a few minutes. [p. 73]
Another facet merits mention. Not only is Mankiewicz’ narrative lavishly illustrated with numerous glossy color plates, the illustrations are more than just ornamental. For instance, reproductions from illuminated manuscripts depict various astronomical instruments in use; Renaissance paintings demonstrate perspective; terrestrial and celestial maps show how people envisioned our world and its place in the universe etc.
The selection of topics conforms for the most part with what a seasoned reader of popular literature might expect, although Mankiewicz allows some scope for individuality when it comes to modern times, with concise treatments of games, the theory of computation, the connection between mathematics and modern art and lastly, chaos and complexity theory. What is impossible to portray in a review, however, is the sheer pleasure of taking in Mankiewicz’ elegant prose and thoughtful cultural commentary which go a long way towards bearing out his thesis that mathematics forms an integral part of human civilization, as he expresses in the first paragraph of his preface:
This book was created because it didn’t exist. I was searching for a way of representing the history of mathematics in an accessible style. Rather than taking the reader through a sequence of ‘great theorems’, I wanted to illustrate how the mathematical sciences were intimately linked to the interests and aspirations of the civilizations in which they flourished. I thought this would be best achieved by combining the visual aspects of mathematics together with sketches of the historical periods in question and key developments in mathematical ideas….[T]his book presents selected highlights of the story that ebbs and flows with the changing fortunes of the some of the world’s great civilizations. [p. 8]
Well executed, four stars. Would make an ideal gift to present to a non-mathematical friend or a curious child of the right age, pre-adolescent to adolescent.
But Mankiewicz has more than this to purvey, for not only is the historical context set out in more than usual granularity, the mathematical content itself in his treatment surpasses that of most popular expositions. The standard topics receive due attention, of course, but where the author excels is at explaining the procedure behind the solution to ancient problems – e.g., on the Chinese method of extracting square and cube roots [p. 36-37], on how to calculate trigonometric tables [p. 50] etc. After reading Manckiewicz, one appreciates not only what they knew but also how they found it out, often in sufficient detail that one could in principle reproduce their results, if one were so minded. A particularly notable instance of this can be had with his graphic exemplification of the practical value of logarithms:
Navigators, who had to handle sines and cosines, found that a typical task of multiplying two seven-figure numbers was reduced to consulting their logarithms, making one addition and then referring back to the table where the inverse logarithm would give the required answer. Before, when a calculation could take you an hour, your answer would always lag an hour behind your real position. This had now been cut down to a few minutes. [p. 73]
Another facet merits mention. Not only is Mankiewicz’ narrative lavishly illustrated with numerous glossy color plates, the illustrations are more than just ornamental. For instance, reproductions from illuminated manuscripts depict various astronomical instruments in use; Renaissance paintings demonstrate perspective; terrestrial and celestial maps show how people envisioned our world and its place in the universe etc.
The selection of topics conforms for the most part with what a seasoned reader of popular literature might expect, although Mankiewicz allows some scope for individuality when it comes to modern times, with concise treatments of games, the theory of computation, the connection between mathematics and modern art and lastly, chaos and complexity theory. What is impossible to portray in a review, however, is the sheer pleasure of taking in Mankiewicz’ elegant prose and thoughtful cultural commentary which go a long way towards bearing out his thesis that mathematics forms an integral part of human civilization, as he expresses in the first paragraph of his preface:
This book was created because it didn’t exist. I was searching for a way of representing the history of mathematics in an accessible style. Rather than taking the reader through a sequence of ‘great theorems’, I wanted to illustrate how the mathematical sciences were intimately linked to the interests and aspirations of the civilizations in which they flourished. I thought this would be best achieved by combining the visual aspects of mathematics together with sketches of the historical periods in question and key developments in mathematical ideas….[T]his book presents selected highlights of the story that ebbs and flows with the changing fortunes of the some of the world’s great civilizations. [p. 8]
Well executed, four stars. Would make an ideal gift to present to a non-mathematical friend or a curious child of the right age, pre-adolescent to adolescent.
October 12, 2013
A great read on, well, the story of mathematics. Entertaining tales of the number 0, arithmetic, algorithms, geometry, and more. If you're just a little interested in numbers and calculation, you should be able to read this as great fun literature.
January 2, 2021
Entretiene y enseña, divulgación pura y dura
Displaying 1 - 3 of 3 reviews