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346:. "n mathematics we have a universal language, valid, useful, intelligible everywhere in place and time ..." Finally, "Austere and imperious as logic, it is still sufficiently sensitive and flexible to meet each new need. Yet this vast edifice rests on the simplest and most primitive foundations, is wrought by imagination and logic out of a handful of childish rules." (p 358)
175:, "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
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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
258:. Further, the characteristic property of infinite sets is given: an infinite class may be in 1:1 correspondence with a proper subset (p 57), so that "an infinite class is no greater than some of its parts" (p 43). In addition to introducing
295:, is more closely connected with human affairs" (p 86). " has played an integral part in helping mathematicians describe and predict what is for man the most important of all natural phenomena – that of growth." The
239:, 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) (
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called it "absolutely paradoxical". A note of idealism is then expressed: "When there is so much humility and so much vision everywhere, society will be governed by science and not its clever people." (pp 103,4)
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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."
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In the final pages the authors approach the question, "What is mathematics?" They say it is a "sad fact that it is easier to be clever than clear." The answer is not as easy as defining
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are discussed. The authors say (p 112) "Among our most cherished convictions, none is more precious than our beliefs about space and time, yet is more difficult to explain."
187:. "Apparently it has succeeded in communicating to the layman something of the pleasure experienced by the creative mathematician in difficult problem solving."
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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
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for 10. The book includes nine chapters, an annotated bibliography of 45 titles, and an index in its 380 pages.
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when applied to large and finite numbers." By 1941 G. Waldo
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In chapter one, "New names for old", they explain why mathematics is
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equal to the function itself." (p 87) The authors define the
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hunting. They say "The infinite may be boojum too." (p 61)
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Chapter 4 is "Assorted
Geometries, Plane and Fancy". Both
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probably expresses the most important idea in the whole
268:, where instructions are given to avoid boojums when
279:, i, e) Transcendental and Imaginary". To motivate
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201:the science that uses easy words for hard ideas
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287:and then
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191:Contents
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61:Language
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