Arithmetic

Arithmetic developed slowly over the course of human history, primarily evolving from the operation of counting. Prior to 4000 B.C., few civilizations were even able to count up to ten. Over time however, people learned to associate objects with numbers. They also learned to think about numbers as abstract ideas. They recognized that four trees and four cows had a common quantity called four. The best evidence suggests that the ancient Sumerians of Mesopotamia were the first civilization to develop a respectable method of dealing with numbers. By far the most mathematically advanced of these ancient civilizations were the Egyptians, Babylonians, Indians, and Chinese. Each of these civilizations possessed whole numbers, fractions, and basic rules of arithmetic. They used arithmetic to solve specific problems in areas such as trade and commerce. As impressive as the knowledge that these civilizations developed was, they still did not develop a theoretical system of arithmetic.

The first significant advances in the subject of arithmetic were made by the ancient Greeks during the third century B.C. Most importantly, they realized that a sequence of numbers could be extended infinitely. They also learned to develop theorems which could be generally applied to all numbers. At this time, arithmetic was transformed from a tool of commerce to a general theory of numbers.