Professor Stewart is a prolific, clear and enthusiastic mathematician and he is also a great promoter of mathematics itself. G.H Hardy once said:
It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds. - A Mathematician's ApologyG.H Hardy was, no doubt, a brilliant mathematician but he has misplaced his belief in thinking that popularizing or promoting mathematics or fields of science is an act of folly. It is an act which requires the clearest of explanatory powers and solidity of understanding. It is also a necessity to promote science and mathematics in order for the numbers of its members to increase and to stimulate a prosperous and intelligent economy. Ian Stewart's book, which is a collection of small adventures into puzzles, history, mathematical concepts and observations is an exemplar of promoting the field without over-simplifying it.
Stewart perfects the art of 'lighting the curious readers fire' by jumping to and fro between varying stimulating mathematics and doing so without waffling. Also Stewart doesn't just reveal an observation he delves into the fundamental reason to why such an observation occurs. This is how pure mathematics is really done: one explores an area of interest which has yet to be explored and finds interesting observations, the mathematician will then clearly describe this observation and formulate either a conjecture or a theorem. The aim of the game is to explain and relate to other realms of mathematics.
What Stewart and Hardy do share is a belief in the artistic pleasure of mathematics, how it should be done purely on the basis of curiosity and of beauty.
This is a must read as it is a book to dip into here and there and one which will provide your brain with enough material to grow!
"Put that in your pipe and smoke it" (Picture of Hardy)
Here is a link to G.H Hardy's- A Mathematician's Apology http://www.math.ualberta.ca/~mss/misc/A%20Mathematician's%20Apology.pdf