​​Why Do We Use The Letter X to Represent The Unknown in Maths?

Why Do We Use The Letter X to Represent The Unknown in Maths
Why Do We Use The Letter X to Represent The Unknown in Maths

In algebra, we often solve for x; in English, we use the letter x to symbolize unknown X-rays. Even leaders like Malcolm X chose the symbol to express the forgotten name of his African ancestors. Like many of my students, you might think it is a random choice, just a simple convention for an unknown value. However, I discovered that there is a fascinating history behind this enigmatic character.

So, why do we use the letter X to represent the unknown in maths? We use the letter X to represent the unknown in maths because the scholars in the 11th century couldn’t translate the Arabic letter “Shin,” denoting unknowns, to Spanish. In Arabic, Shin (ش‎) is read as /ʃ/, similar to the sound sh; however, there is no Shin sound in Spanish. That is why the Greek letter “Chi” (Χ, χ) was later transliterated to X.

Read on to find out the origins of ‘x’ and uncover its fascinating history and discover the possible reasons behind the use of ‘x’ to symbolize unknown quantities that we’re all familiar with today. You might also enjoy reading: The Impact of Differential Equations in Our Everyday Lives (9 examples!)

Why Do We Use The Letter X to Represent The Unknown in Maths?

Have you ever wondered why we use the letter ‘x’ to represent the unknown in mathematics? Whether working through algebraic equations or complex variables, x almost always represents mystery and some form of complexity.

The Birth of Unknown X in Mathematics

As mathematics evolved over centuries, the concept of unknown quantities emerged as a crucial element. To express unknown quantities, mathematicians from ancient Greece, China, and India developed their notation systems.

The foundation for modern algebra and its systematic approach to representing the unknown can be attributed to the Persian mathematician Al-Khwarizmi. His 9th-century work “Al-Jabr wa Al-Muqabalah” (The Compendious Book on Calculation by Completion and Balancing) introduced algebraic techniques that would transform mathematics forever.

Mathematicians use the letter X to characterize the unknown because the scholars in the 11th century couldn’t translate the Arabic letter “Shin,” denoting unknowns, to Spanish. 

In the Arabic language, Shin (ش‎) is read as /ʃ/, equivalent to the sound sh; however, there is no “Shin” sound in Spanish. Therefore, the Greek letter “Chi” (Χ, χ) was later transliterated to X.

If you are interested in exploring more about why we use the letter X to represent the unknown in maths, I encourage you to watch the video below.

Arabic Origins and the Journey to Europe

Fast forward to the 9th century, Persian mathematician Al-Khwarizmi introduced the concept of algebra, which was later translated into Latin.

The word “algebra” itself comes from the Arabic word “al-jabr,” which means “reunion of broken parts.” Al-Khwarizmi used the Arabic term “shay” or “thing” (in place of our modern ‘x’) to represent the unknown value in his calculations.

When his works were translated into Latin, “shay” became “res,” the Latin word for “thing.” It is here that our mystery letter ‘x’ starts to take shape.

You might also enjoy reading: Algebra vs. Calculus: How do they differ?

The Role of Latin in Transmitting Mathematical Knowledge

Greek, Arabic, and Latin texts heavily influenced European mathematics in the Middle Ages. Translation of these texts not only brought new mathematical ideas but also influenced the use of language in mathematical notation.

Latin became the lingua franca in teaching mathematics, especially in European universities. It played a pivotal role in standardizing the use of specific letters that are now commonly found in mathematical notation.

As the Arab texts were translated into different languages across Europe, different Latin-speaking scholars adopted their own conventions to represent unknown variables using the Latin alphabet.

Italian mathematician Leonardo Fibonacci, for example, utilized the first few letters of the alphabet – a, b, and c – for predetermined values while using the last few letters, such as z, y, and x, for unknowns.

This wasn’t the standard yet, but the ‘x’ was getting closer to its starring role as the symbol of the unknown.

The Story Begins with the Ancient Greeks

The roots of using a symbol to represent an unknown value date back to the ancient Greeks, who employed letters from their alphabets, such as alpha, beta, and gamma, to represent unknown quantities.

Greek mathematician Diophantus wrote a series of books called “Arithmetica” around the 3rd century AD, in which he sought to find numerical solutions to various problems.

Diophantus used symbols to represent unknowns, and though it wasn’t ‘x’ yet, the tradition of using letters was well underway.

Why Do We Use The Letter X to Represent The Unknown in Maths
Why Do We Use The Letter X to Represent The Unknown in Maths

The Final Touch: Descartes and Algebraic Notation

The adoption of ‘x’ to represent the unknown in mathematics can be attributed to several historical developments.

In the 17th century, French philosopher and mathematician René Descartes played a crucial role in establishing our modern algebraic notation, which included using ‘x’ to represent unknowns.

In his groundbreaking work “La Géométrie” (1637), Descartes simplified the representation of unknown quantities by introducing the convention that represents known quantities with the letters a, b, c, and unknown quantities with the letters x, y, z.

As Latin translations of Arabic mathematical texts became widespread, the Latin word “cōsa,” meaning “thing” or “unknown thing,” was often used to indicate the unknown.

Latin vocabulary influenced mathematical notation, and it was with this influence that abbreviations using Latin letters began to emerge as symbols for unknown quantities.

The use of ‘x’ may have been just a matter of alphabetical order, or as some linguistic scholars suggest, it could have been chosen because of its rarity in French language usage.

Descartes’ system of notation remarkably transformed the way mathematics was written and transcribed, making ‘x’ the go-to choice for expressing the unknown.

The Cultural Impact and Universality of ‘x.’

The influence of ‘x’ as the symbol for the unknown has transcended mathematics and interwoven itself into various aspects of popular culture.

We hear phrases like “X marks the spot” or use ‘x’ to represent a secret, a mysterious identity, and even unknown forces in the universe. It has become the symbol of riddles, enigmas, and the unknown both in scientific and everyday contexts.

Descartes’ influential work set the stage for future developments in mathematics, allowing for simplified notation and conceptual abstraction. The convention of using ‘x’ as a symbol for unknown quantities spread throughout Europe and became a cornerstone of modern algebraic notation.

Its influence would eventually extend beyond mathematics as other sciences adopted similar conventions for dealing with variables and unknown quantities.

Breaking the Shackles: Infinite Possibilities Beyond ‘x.’

In contemporary mathematics, the letter ‘x’ remains the most well-known symbol for the unknown, but it is far from the only one!

As math continues to evolve, new notation systems are developed to deal with increasingly diverse and intricate problems.

From matrices and vector spaces to differential equations and probability theory, different areas of mathematics have adopted various notations to express unknowns more effectively.

What to read next:

Wrapping Up

Why do we use the letter X to represent the unknown in maths? The answer is a blend of historical traditions, linguistic translations, and influential mathematicians’ choices. The legacy of ‘x’ represents not just the unknown value in math but also the journey of knowledge transfer across cultures and centuries.

Its origins lie in the Latin language’s influence over European education, the evolution of algebraic notation systems, and the desire for simplicity in mathematical representation.

As we continue to explore new frontiers in mathematics and science, ‘x’ will undoubtedly remain a guiding symbol, reminding us of the ever-present mysteries waiting to be discovered and solved.


I am Altiné. I am the guy behind mathodics.com. When I am not teaching math, you can find me reading, running, biking, or doing anything that allows me to enjoy nature's beauty. I hope you find what you are looking for while visiting mathodics.com.

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