We can say that this book opens the way to mathematics. Danzig explains the basics of mathematics very simply, eloquently speaking about the deep philosophical problems that have arisen along the way. It describes the properties of all types of numbers - integers, primes, irrationals, transcendentals and others; explains the importance of introducing the concept of zero and shows what revolution in arithmetic the appearance of this number caused. The author shows how the invention of symbols for algebraic transformations marked the beginning of a new era in mathematics; how arithmetic and geometry are related and how the concept of infinity is used to model the continuity of space and time.

This book was first published in 1930. More than 50 years later, Joseph Mazur has written a new afterword, notes, and bibliography, and Barry Mazur has written a foreword. This book tells how the most remarkable geniuses in the history of mankind appeared, how the pursuit of knowledge led to the rise and fall of civilizations.