Every prospective teacher should read it. In particular, graduate students will find it invaluable. The traditional mathematics professor who reads a paper before one of the Mathematical Societies might also learn something from the book: 'He writes a, he says b, he means c; but it should be d.' --E. T. Bell, Mathematical Monthly [This] elementary textbook on heuristic reasoning, shows anew how keen its author is on questions of method and the formulation of methodological principles. Exposition and illustrative material are of a disarmingly elementary character, but very carefully thought out and selected.--Herman Weyl, Mathematical Review I recommend it highly to any person who is seriously interested in finding out methods of solving problems, and who does not object to being entertained while he does it.--Scientific Monthly Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher's art.--A. C. Schaeffer, American Journal of Psychology Every mathematics student should experience and live this book--Mathematics Magazine In an age that all solutions should be provided with the least possible effort, this book brings a very important message: mathematics and problem solving in general needs a lot of practice and experience obtained by challenging creative thinking, and certainly not by copying predefined recipes provided by others. Let's hope this classic will remain a source of inspiration for several generations to come.--A. Bultheel, European Mathematical Society