Few discoveries have had as much impact on our perception of human thought as Gödel’s proof in 1930 that any logical system such as usual rules of arithmetic, must be inevitably incomplete, i.e. , must contain statements which are true but can never be proved. Professor Uspensky’s makes both a precise statement and also a proof of Gödel’s startling theorem understandable to someone without any advanced mathematical training, such as college students or even ambitious high school student. Also, Uspensky introduces a new method of proving the theorem, based on the theory of algorithms which is taking on increasing importance in modern mathematics because of its connection with computers. This book is recommended for students of mathematics, computer science, and philosophy and for scientific layman interested in logical problems of deductive thought.