Written by the man hailed as the last mathematical universalist and the greatest mathematician since Gauss, this book explores the basic methodology and psychology of scientific discovery, particularly in regard to mathematics and mathematical physics. It explains how scientists analyze and select the facts with which they work and examines the application of experimentation, theory, and the mind in pursuit of organized knowledge. Poincare illustrates his discussion of the germination of ideas with examples from many scientific fields and from his personal experience. This volume contains his famous discussion of his own idea-creating mental processes and use of the unconscious mind. Modern mathematicians and logicians will find his searching examination of the ideas of Whitehead, Hilbert, and Russell especially illuminating.