The basic notions of number and magnitude can be seen in markings on cave walls and primitive tools. However, it took many thousands of years for the first use of quantities to evolve into the abstract concept of numbers as we use them today.

The cultures of the Mesopotamian region had developed the use of written numbers by about 1800 B.C. The Babylonians, in particular, developed a sophisticated number system, estimated π with some accuracy, used fractions, and solved complex quadratic equations. Mesopotamian mathematics was spread far and wide by the many conquerors of the region. Their ideas influenced other cultures from Europe to China.

Chinese mathematics also developed at an early date. The earliest surviving works, dating from about 300 B.C., contain detailed astronomical calculations, as well as surveying, agricultural, and other practical math problems. The...