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A mathematical odyssey. Journey from the real to the complex. (English) Zbl 1300.00008

New York, NY: Springer (ISBN 978-1-4614-8938-2/hbk; 978-1-4614-8939-9/ebook). xvi, 382 p. (2014).
Although on first glance one of many popular mathematical books, this exceptional, beautifully illustrated book is quite atypical in its category. In contrast to most other popular mathematical books, it focuses on modern mathematics – mathematics that is, contrary to popular believe, alive and developing. The fourteen self-sufficient chapters cover different topics, from better known (like the four-color theorem) to less generally known (like primality testing). The chapters cover both history as well as descriptions, applications and examples. Even the topics which appear frequently in popular mathematical literature, like Fermat’s last theorem, are given a new angle.
Most of the book requires no more than standard mathematical education and thus this book should be a must-read (opinion of reviewer) for any well-educated person, but can be also of much help for mathematicians working in education or popularization for finding new ideas or even themselves learning some not so well-known recent developments, and also it should be interesting for anybody curious what mathematics is about. In any case, after reading the book the reader will quite certainly be left with two new (or deepened) insights: (a) mathematics is far from being a closed up set of rules – it is creative and evolving; (b) mathematics is both beautiful and useful.

MSC:

00A09 Popularization of mathematics
00A05 Mathematics in general
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