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The History of Mathematical Symbols and Civilization

Behind every mathematical symbol lies a story of civilization. This series explores the origins and evolution of mathematical symbols, revealing how they became some of humanity's most powerful cognitive tools—and how they have continually shaped the development of mathematics, science, and civilization itself.

We use mathematical symbols every day, yet few of us ever stop to ask why they look the way they do.

Why is addition represented by + rather than some other shape? Why does the equals sign consist of two parallel lines? Why is the unknown quantity so often written as x? And why do symbols such as ∞, ∫, ∑, and √ each have their own unique forms?

These symbols were not invented overnight by a single person. They emerged across different civilizations and different eras, shaped by centuries of experimentation, competition, refinement, and eventual standardization. From Ancient Egypt, Babylon, and Greece to India, the Islamic world, and Renaissance Europe, every mathematical symbol carries a story of knowledge transmission, cultural exchange, and the evolution of human thought.

Yet the true significance of mathematical symbols goes far beyond making mathematics easier to write.

Every new mathematical symbol is, fundamentally, a new cognitive tool. It enables us to compress information, organize knowledge, express abstract ideas, and extend the limits of human thought. Many mathematical concepts that seem obvious today only became possible after the symbols capable of expressing them had been invented. In this sense, the progress of mathematics has depended not only on new discoveries and new theorems, but also on new ways of representing ideas.

In this series, we journey back through history to explore the origins of mathematical symbols—from addition, subtraction, multiplication, division, and the equals sign to square roots, integrals, summation, infinity, and many more. Along the way, we discover how these symbols were created, how they evolved, and how they gradually transformed the way humanity understands the world.

As we rediscover these familiar symbols, we uncover more than the history of mathematical notation. We uncover the history of human cognition itself—and, with it, the story of civilization.

Series

Contents

5 contents
  1. 01Video | The Origins of + − × and ÷Journey from ancient Egypt to Leibniz and uncover the remarkable story of the four basic arithmetic symbols that reshaped mathematics.
  2. 02Article | What Is a Unit Fraction? Why Didn't the Ancient Egyptians Use Ordinary Fractions?Why did the ancient Egyptians rarely use the ordinary fractions we take for granted today? Instead, they expressed almost every fraction as a sum of unit fractions—a seemingly cumbersome system that shaped Egyptian mathematics for thousands of years. This article explores what unit fractions are, why they became the foundation of Egyptian mathematics, the way of thinking behind them, and why they were eventually replaced by the modern fraction notation we use today.
  3. 03Article | Why Did Ancient Egyptians Guess the Answer First? — The Idea Behind the Method of False PositionFour thousand years ago, the ancient Egyptians had neither unknowns nor an equals sign, yet they were able to solve problems that would require equations today. They first guessed a number that was easy to work with, then repeatedly adjusted it using proportions. This was the method later known as the Method of False Position. More intriguingly, this idea of gradually approaching an answer from an initial starting point has a connection to modern numerical computation that spans thousands of years. Starting with an ancient Egyptian mathematical problem, this article explores the mathematical thinking behind the Method of False Position, and how humanity gradually moved from working with specific numbers toward studying relationships between quantities—the foundation of modern algebra.
  4. 04Article｜Newton’s Method of Fluxions: What Did Calculus Look Like Before Leibniz’s Notation?Before Leibniz’s dx/dy and integral notation became the standard language of calculus, Newton used a very different way to describe change. This approach, known as the method of fluxions, raises a fascinating question: what did it actually look like? Let’s return to the birth of calculus and see how mathematicians tried to capture change in the world before they had the symbolic language we use today.
  5. 05Article | What Is Modular Arithmetic? Why Can 17 and 5 Be “Equal”?Modular arithmetic is a mathematical system that allows us to understand integers through the idea of “cycles.” Why can 17, which clearly is not equal to 5, be written as 17 ≡ 5 (mod 12)? Starting with clocks and remainders, this article explores congruence, residue classes, and the mathematical ideas behind the symbol “≡”, and shows how a seemingly simple symbol can open the door to a whole new world of modern mathematics.