Mathematics, Queen and Servant of Science: Queen and Servant of Science

One of the most thorough surveys of mathematics I have read. Tends to concentrate on algebras. Too little on probability and statistics. Also somewhat dated for anything near cutting edge. Nothing on computer science or computational theory, for example. For a newer survey, esp more on philosophical and applications, though less on how it is done, you might try Davis & Hersh, The Mathematical Experience.

If I was to ever teach a course in expository writing in mathematics, decide to write a popular book in mathematics, or be asked to advise someone who was going to do either one, this book would be my first and highest recommendation as a resource. There is no one better than Bell at wrapping an engaging story around mathematics. It is hardly surprising that he was also successful as a writer of science fiction. In less than 450 pages he manages to explain why mathematics is important, give a reasonably complete history of the subject and show how well both can be done. This book should be required reading for all mathematics majors and minors.

I will keep this very brief. I am an electrical engineer and computer scientist, and, after a couple of decades in the "commercial world" , am always amazed at the "unreal effectiveness" of mathematics when applied to this and the real world. Bell's book captures this essence in a timeless tome that must be required reading and regular re-reading for all aspiring. and indeed, practising, mathematicians, engineers and scientists. It is a source of both inspiration and "bringing back to earth" to those that read it. No serious practitioners library should be without it.