Mathematics and the Imagination
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First edition
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| Author | Edward Kasner, James R. Newman |
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| Illustrator | Rufus Isaacs |
| Country | United States |
| Language | English |
| Subject | Mathematics |
| Publisher | Simon & Schuster |
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Publication date
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1940 |
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| Pages | 380 pp. |
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Mathematics and the Imagination is a book published in New York by Simon & Schuster in 1940. The authors are Edward Kasner and James R. Newman. The illustrator Rufus Isaacs provided 169 figures. It rapidly became a best-seller and received several glowing reviews. Special publicity has been awarded it since it introduced the term googol for 10100, and googolplex for 10googol. The book includes nine chapters, an annotated bibliography of 45 titles, and an index in its 380 pages.
According to I. Bernard Cohen, "it is the best account of modern mathematics that we have", and is "written in a graceful style, combining clarity of exposition with good humor". According to T. A. Ryan’s review, the book "is not as superficial as one might expect a book at the popular level to be. For instance, the description of the invention of the term googol ... is a very serious attempt to show how misused is the term infinite when applied to large and finite numbers." By 1941 G. Waldo Dunnington could note the book had become a best-seller. "Apparently it has succeeded in communicating to the layman something of the pleasure experienced by the creative mathematician in difficult problem solving."
The introduction notes (p xiii) "Science, particularly mathematics, ... appears to be building the one permanent and stable edifice in an age where all others are either crumbling or being blown to bits." The authors affirm (p xiv) "It has been our aim, ... to show by its very diversity something of the character of mathematics, of its bold, untrammelled spirit, of how, both as an art and science, it has continued to lead the creative faculties beyond even imagination and intuition."
In chapter one, "New names for old", they explain why mathematics is the science that uses easy words for hard ideas. They note (p 5) "many amusing ambiguities arise. For instance, the word function probably expresses the most important idea in the whole history of mathematics. Also, the theory of rings is much more recent than the theory of groups. It is found in most of the new books on algebra, and has nothing to do with either matrimony or bells. Page 7 introduces the Jordan curve theorem. In discussing the Problem of Apollonius, they mention that Edmond Laguerre's solution considered circles with orientation.(p 13) In presenting radicals, they say "The symbol for radical is not the hammer and sickle, but a sign three or four centuries old, and the idea of a mathematical radical is even older than that."(p 16) "Ruffini and Abel showed that equations of the fifth degree could not be solved by radicals."(p 17) (Abel-Ruffini theorem)
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