Games and Mathematics: Subtle Connections

by David G. Wells

The appeal of games and puzzles is timeless and universal. In this unique book, David Wells explores the fascinating connections between games and mathematics, proving that mathematics is not just about tedious calculation but imagination, insight and intuition. The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. This thought-provoking book is perfect for anyone with a thirst for mathematics and its hidden beauty; a good high school grounding in mathematics is all the background that is required, and the puzzles and games will suit pupils from 14 years.

Genres: Nonfiction, Mathematics

272 pages, Kindle Edition

First published August 31, 2012

About the author

David Wells is a writer on mathematics and puzzles.

Librarian Note: There is more than one author in the Goodreads database with this name.

Reviews

[Behrooz Parhami · Rating 4 out of 5]

This book consists of two parts, “Mathematical Recreations and Abstract Games” (Chs. 1-5) and “Mathematics: Game-Like, Scientific and Perceptual” (Chs. 6-20). A listing of chapter titles provides a good indication of the book’s scope and coverage.

01. Recreations from Euler to Lucas
02. Four abstract games
03. Mathematics and games: mysterious connections
04. Why chess is not mathematics
05. Proving versus checking
06. Game-like mathematics
07. Euclid and the rules of his geometrical game
08. New concepts and new objects
09. Convergent and divergent series
10. Mathematics becomes game-like
11. Maths as science
12. Numbers and sequences
13. Computers and mathematics
14. Mathematics and the sciences
15. Minimum paths from Heron to Feynmann
16. The foundations: perception, imagination and insight
17. Structure
18. Hidden structure, common structure
19. Mathematics and beauty
20. Origins: Formality in the everyday world

One feature of abstract games and traditional puzzles is that, unlike language and literature, they are appreciated across different cultures. Most puzzles and games are quite old, re-emerging in different times and places with minor variations. For example, evidence of dice games has been found in excavations in southeastern Iran, at a site believed to date back to 3000 BCE.

Despite the existence of mathematical games and puzzles, a significant number of games do not arise from math. However, almost all games are eventually tied to and studied using mathematical tools. Insights gained from math can help in the development of games and may even render them trivial. Solving puzzles is a lot like proving theorems in mathematics, which involves finding the right transformations and the order in which they are applied.

Wells has chosen some well-known games & puzzles, and quite a few delightfully original ones, to make his philosophical points. Like other authors dealing with philosophical aspects of mathematics, Wells discusses the notion of mathematical beauty and what it means to be a mathematician. I take pleasure in highly recommending this enlightening book, which offers much more than a mere compilation of thought-provoking games & puzzles.

[Michael Montes · Rating 3 out of 5]

Insight into the history and process of maths

[Mills College Library]

510 W4536 2012