Mathematics is one of the most basic - and most ancient - types of knowledge, yet the details of its historical development remain obscure to all but a few specialists. The two-volume Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences aims to recover this mathematical heritage, and brings together many of the world's leading historians of mathematics to examine the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times to the 20th century. In 176 concise articles divided into 12 parts, contributors describe and analyze the variety of problems, theories, proofs and techniques in all areas of pure and applied mathematics, including probability and statistics. The reference demonstrates the continuing importance of mathematics and its use in physics, astronomy, engineering, computer science, philosophy and the social sciences. Also addressed is the history of higher education in mathematics. Carefully illustrated, with annotated bibliographies of sources for each article, the companion should serve as a research tool for students and teachers in all branches of mathematics.