Mathematics and the Imagination
| Industry | Publishing |
|---|---|
| Headquarters | United States |
| Products | Books |
Mathematics and the Imagination is a 1940 work authored by Edward Kasner and James R. Newman, published through Simon & Schuster. Featuring 169 illustrations by Rufus Isaacs, the book rapidly gained best-seller status and widespread recognition. It is distinguished for coining the terms googol (10100) and googolplex (10googol). The volume spans 380 pages, containing nine chapters, a detailed bibliography listing 45 works, and an index.
Reviews
I. Bernard Cohen commended the book as "the finest exposition of modern mathematics" available, noting its lucid and captivating narrative. T. A. Ryan appreciated the text’s substantial content for a popular science publication, especially its careful explanation of googol and the common errors involving the term infinite when applied to very large but finite quantities. By 1941, G. Waldo Dunnington acknowledged it as a popular success that effectively conveyed the imaginative pleasure inherent in mathematical problem-solving to a broad audience.
Contents
The introduction presents mathematics as a consistent and enduring discipline amidst social transformations, aiming to reveal its daring and inventive nature as both an artistic and scientific endeavor.
Chapter 1, titled "New names for old," discusses the rationale behind using straightforward words for intricate mathematical ideas, clarifying concepts such as functions, rings, and the Jordan curve theorem. It also addresses historical notions like radicals and the Abel–Ruffini theorem, which concerns the impossibility of solving fifth-degree equations by radicals.
Chapter 2, "Beyond Googol," delves into infinite sets, differentiating between countable sets and uncountable sets. It introduces Aleph numbers and illustrates how infinite sets can be placed in one-to-one correspondence with their proper subsets, revealing distinctive characteristics of infinity.
Chapter 3, "Pie (, i, e) Transcendental and Imaginary," connects the constant e to financial principles such as compound interest and continuous growth, underlining its fundamental role in modeling natural growth processes. The chapter covers the exponential function, the Gauss plane, multiplication by i as a rotation operation, culminating in a discussion of Euler's identity. It ends on an optimistic note about science’s role in guiding society.
Chapter 4, "Assorted Geometries, Plane and Fancy," explores Non-Euclidean geometry and concepts of four-dimensional space, reflecting on profound yet complex ideas about spatial and temporal reality.
In conclusion, the authors consider "What is mathematics?" recognizing its intricacies while affirming it as a universal language—both logical and creative—built upon simple principles that can evolve to meet new challenges.
References
- I. Bernard Cohen (1942), Review, Isis 33(6):723–5.
- G. Waldo Dunnington (1941), Review, Mathematics Magazine 15(4):212–3.
- T.A. Ryan (1940), Review, American Mathematical Monthly 47(10):700–1.