Mathematical Recreations and Essays

W. W. Rouse Ball‘s “Mathematical Recreations and Essays” contains an odd but decidedly interesting collection of essays about a range of different subjects. The 4th edition dating from 1905 was recently posted to Project Gutenberg. Far from being interesting to mathematicians only, this book has something for everybody who’s interested in puzzles and number games or in the history of science.

The book is divided into two parts of quite different character. The first part, titled “Mathematical Recreations,” ranges from simple number games of the “guess the number” kind to magical squares and mazes, discussing topics such as mathematical and geometrical fallacies, the “Eight Queens” problem on a chessboard, map colourings and many more. The problems presented are not exactly new or original and don’t pretend to be, but I like the systematic treatment given to many of them.

Part II of the book, titled “Miscellaneous Essays and Problems,” contains a wealth of historical information about mathematics-related topics made even more fascinating by the fact that it was written more than a century ago. It starts with a description of the development of the Mathematical Tripos at Cambridge, giving a very interesting glimpse into the history of mathematics education at one of Britain’s most prestigious universities. The next chapters give a history of classical geometrical problems, the quadrature of the circle the most prominent of them, followed by an introduction to Mersenne’s numbers. After that comes a short description of the “scientific” aspect of astrology, which the author himself wasn’t too sure whether to include. There’s a chapter introducing early cryptography, one on hyper-space, including space with more than three dimensions as well as non-Euclidean geometry, and one on time measurements.

But my absolute favourite is the last chapter on matter and ether theories. At the time this book was written, the internal workings of atoms were not yet known and the subject of the wildest speculations. The author gives an account of the different theories proposed and how they explain the way atoms interact with each other. Rather than reporting scientific developments from a historical standpoint, this chapter provides some valuable insights into science in action, which makes it really fun to read.

Tucked away behind the index are advertisements for the W. W. Rouse Ball’s other works, together with blurbs from probably every review that was ever printed. Let me cite from one of the reviews for this book, which I have to heartily agree with:

… A great deal of the information is hardly accessible in any English books; and Mr. Ball would deserve the gratitude of mathematicians for having merely collected the facts. But he has presented them with such lucidity and vivacity of style that there is not a dull page in the book; and he has added minute and full bibliographical references which greatly enhance the value of his work.–The Cambridge Review.

I thoroughly enjoyed reading this book and would really like to see the other works by this author on PG: they are surely worth a closer look.

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