A Story of Numbers — Class 8 Mathematics

This is a historical-mathematical chapter tracing how humans learned to count and to write numbers. Counting begins with one-to-one mapping — matching each object to a stick, a sound, or a symbol — leading to the idea of a number system as a standard ordered sequence. Early systems counted in groups (the Gumulgal of Australia counted in twos) and then used landmark numbers, as in the Roman system with . A major breakthrough was the idea of a base: choosing landmark numbers that are powers of a fixed number gives a base- system, of which the Egyptian system (base ) is an example. The next leap was place value, where a symbol’s position fixes which power of the base it represents — seen in the Mesopotamian (base ), Mayan and Chinese systems. The crowning idea was the Hindu number system: a base- place-value system with ten digits including , treated as a number in its own right by Aryabhata and codified by Brahmagupta. Because of , every number can be written unambiguously with finitely many symbols.