The Companion Encyclopedia is the first comprehensive work to cover the principal developments and themes in the history and philosophy of mathematics from ancient times up to the 20th century. In 176 articles contributed by authors of 18 nationalities, the work describes and analyzes the variety of theories, proofs, techniques, and cultural and practical applications of mathematics. The work's aim is to recover our mathematical heritage and to demonstrate this discipline's importance in today's world by examining its interactions with the related disciplines of physics, astronomy, engineering and philosophy. The Companion also covers the history of higher education in mathematics and the growth of institutions and organizations connected with the development of the field. Part 1 deals with mathematics in various ancient and non-Western cultures from antiquity up to medieval and Renaissance times. Part 2 treats developments in the main areas of mathematics