The Nature of Mathematics

The history of mathematics consists of a sequence of discoveries, some of which enhance what has come before, others that clarify and still others completely revolutionize how mathematics is practiced. In this book, one of the best philosophers of mathematics describes some of the primary events and their consequences. The style of presentation is more in a casual style rather than an academic one. The topics are: *) The earliest principles of mathematics as developed in ancient times. *) The development of the abstract symbolism of algebra and the revolution in thought processes and notation needed to practice it. *) The development of analytic geometry and how it enabled mathematics to be applied to motion and figures. *) The application of mathematics to the natural sciences. *) The development of infinitesimals and the expanding role of calculus. *) The modern concept of limits and how it was applied to complete the real number line. *) The philosophy of certainty in mathematics and what it means. All too brief, this book is an excellent primer on the history of mathematics and the historical context within which each of the developments occurred. His life and work were short, but neither are lacking in mathematical quality.