A Brief History of Numbers

Mathematics is often called the language of science because, at its foundation, science is the quantization of reality — of the Universe and of Nature — into fundamental laws that describe numerical quantities and relationships of the behavior and phenomena that we witness.

If mathematics is the language of science, then the concepts and formula of mathematics represent the grammar of that language, using numbers as what are essentially the words of maths.

The Invention of Numbers

The earliest use of numbers — or the first intimation for the invention of numbers — takes place around 10,000 years ago in Mesopotamia (an ancient name for a region within what we know today as the Fertile Crescent, the Near East and the Middle East).

The descendants of the world’s first farmers, herdsman, and merchants of this region — who were the first humans to transition to a sedentary village and town lifestyle and, in the millennia to come, would build the first cities, invent writing, and record their traditions which would become Judaism, Christianity, and Islam — would begin to use numbers in increasingly sophisticated, symbolic, and practical functions within society.

These early agriculturalists and pastoralists used tokens — clay pieces, stones, or small objects — to indicate quantities of grain, livestock, cloth and other materials. This shift became necessary with the advent of agriculture and village-based ways of life, as these societal transitions resulted in larger populations living together, requiring greater social organization and planning both to maintain order in their societies and to ensure their survival.

Grain and other food had to be stored and recorded to ensure there would be enough food for everyone, especially given the unpredictability of changing environmental conditions year by year. Another consequence of developing urban lifeways was an increase in trade. As trade increased, numerical communication only increased in importance. Quantities of goods had to be numerically represented and recorded, to ensure fair trade, but also to prevent thievery. (This can be seen in the Bullae system of Prehistoric Mesopotamia.)

Historical Evolutions

After the Dawn of History In Sumer around 3000 BCE (the Sumerians building the first cities in the world, the first schools, writing, law codes, and a staggering number of other first) the nearby Ancient Egyptians — who were ethnically and culturally part of this Near Eastern sphere of civilization — were the first to invent fractions between 2000–1000 BC. [1]

Initially the Egyptians used them to show reciprocals, but eventually they used them to represent equal divisions of a whole quantity — dividing a quantity like a plot of land into quarters ($1/4$), thirds ($1/3$), halfs ($1/4$) and so on.

Developments Through The Millennia

Amazingly, the concept of the number zero as a ‘base state’ or a ‘null condition’ was not invented until the fifth century CE. [1] This revolution is the work of the mathematical savants of Medieval India right at the beginning of the Medieval Period (of World History) and were the first to use zero as a number in calculations, including it in their numerical system.

Negative numbers followed about 200 years later. In surviving texts from this period of Indian History, negative numbers were used to represent a deficit or a loss (such as a debt to be paid) and were the last to be expressed numerically.

Negative numbers were another contribution of Indian scholars to science and mathematics, the first to use the negative numbers in their equations during the seventh century CE to express quantities like financial debt. [1]

To The Modern Day

Our modern number system evolved over some 10,000 years to the system that we see today. From the instinctive whole numbers used for counting, to reciprocals and fractions contributed by Babylonian and Egyptian scholars, which developed further in the great minds of Ancient Greece.

Zeros and negatives emerged in ancient India, which ultimately led to the mathematical and numerical sophistication required for the staggering European developments that gave birth to modern science found in the work of greats like Galileo, Kepler, and Newton.

Notes

Resources

1. Algebra and Trigonometry I. Openstax.

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