Over the centuries, people have thought of mathematics, and have defined it, in many different ways. Mathematics is constantly developing, and yet the mathematics of 2,000 years ago in Greece and of 4,000 years ago in Babylonia would look familiar to a student of the twenty-first century.

Mathematics, says the mathematician Asgar Aaboe, is characterized by its permanence and its universality and by its independence of time and cultural setting. Try to think, for a moment, of another field of knowledge that is thus characterized. "In most sciences one generation tears down what another has built and what one has established another undoes. In Mathematics alone each generation builds a new story to the old structure," noted Hermann Henkel in 1884.

From Truth to Application

The mathematician and philosopher Bertrand Russell said that math is "the subject in which we never know what we are talking about...