Mathematics and Plausible Reasoning

This is a guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. The book as a whole is organized around the central thesis that a good guess is quite as important as a good proof. – Volume I, on Induction and Analogy in Mathematics, covers a wide variety of mathematical problems, revealing the trains of thought that lead to solutions, pointing out false bypaths, discussing techniques of searching for proofs. Problems and examples challenge curiosity, judgment, and power of invention. The function of the first volume in the theory of plausible reasoning is to provide some concrete mathematical raw material. – If the first volume is more the mathematician's volume, the second is the philosopher's. Volume 2, on Patterns of Plausible Inference, is more interested in an abstract philosophical discussion of the patterns that the first volume indicates. M.-M. V.