The Wild and Contentious History of Mathematical Symbols

A mathematician has uncovered the stories behind the symbols used in math.

Introduction

History classes often focus on great battles and wars, but one lesser-known conflict was waged over a symbol—the equals sign "=". In the mid-1500s, European mathematicians fiercely debated how to best represent equality. This intriguing controversy is only one part of the rich narrative explored in Raúl Rojas’s book, The Language of Mathematics: The Stories behind the Symbols. Rojas reveals how cultural needs, philosophical debates, and even personal rivalries shaped the symbols we now take for granted.

The Evolution of Mathematical Notation

Mathematical symbols have not always been as standardized as they are today. Over centuries, various cultures and regions developed their own notations to express mathematical ideas.

The Equals Sign Debate

Originally, equality was conveyed through words rather than symbols. Over time, attempts were made to capture the idea visually. For instance, in France, René Descartes experimented with a rotated Taurus symbol (∝), while in Germany, Gottfried Wilhelm Leibniz favored a wedge-like mark. It was Robert Recorde from the United Kingdom who eventually introduced the elongated "=" that became popular. The debate even extended to operational symbols, with contests over whether to use signs like “+” and “–” or alternatives such as “p” and “m,” until the former emerged as the universal standard.

The Enigmatic History of Zero

Another enduring mystery is the origin of the numeral “0.” The Babylonians, who used a base-60 system, often left a blank space to represent nothingness. This practice evolved as the idea of zero spread to Greece and later to India, where early Hindu mathematicians are credited with developing a specific symbol for it. New archaeological discoveries continue to push back the known origins of zero, illustrating that this everyday symbol has a history spanning thousands of years.

An Interview with Raúl Rojas

Scientific American sat down with Raúl Rojas to delve into the human stories behind mathematical notation and to explore how these symbols evolved over time.

What Sparked Your Interest in the History of Mathematical Symbols?
Rojas:
I began teaching in 1977 and quickly noticed that students were fascinated by the origins of mathematical ideas. When I started sharing the backstories of concepts in linear algebra or calculus, even those who typically lost interest in class became engaged. Revealing the human side behind abstract symbols makes mathematics much more relatable and vibrant.

How Did Certain Notations Become Standard?

Rojas:
In earlier centuries, different regions—Italy, Germany, the U.K., and France—all developed their own mathematical symbols. With the rise of the printing press, there was an explosion of new ideas, leading to heated debates among prominent mathematicians. Through these “popularity contests,” symbols like “=” and the universally recognized “+” and “–” eventually prevailed, but not without decades of discussion and contention.

The Story Behind the “For All” Symbol (∀)
Rojas:
One symbol that particularly fascinates me is the “for all” sign, ∀. I’ve described it as “a cubist tear flowing from an eye that Picasso could have painted.” Gerhard Gentzen, the mathematician behind this symbol, led a tragic life. Despite his brilliance, his career was overshadowed by his moral compromises during the Nazi era. His story reminds us that even a simple symbol can carry an incredibly complex and poignant history.

The Human Side of Mathematics
Mathematics is not merely a collection of abstract formulas; it is a vibrant, evolving discipline built on centuries of human experience and debate. Understanding the origins of the symbols—from “0” to “=”—offers insight into the creativity and conflicts that have shaped modern mathematics.

Final Thoughts

Every time you encounter a mathematical symbol, remember that it is the culmination of countless years of human thought, rivalry, and innovation. These symbols, far from being arbitrary, are a testament to the enduring, dynamic nature of mathematical progress.