How X Became the Unknown: A History of Algebra from Babylon to Descartes

Overview

The video explains how the letter X, a relatively rare English letter, became the universal symbol for the unknown in algebra. It weaves together a timeline from ancient scripts to the birth of modern algebra, showing how unknowns moved from words to symbols and why a single letter persisted. Along the way, it connects mathematical ideas to real world applications and cultural touchstones, illustrating how a symbol can reshape our view of patterns, predictions, and the world itself.

From Babylonian arithmetics to Descartes, the talk links the saga of X to big ideas about placeholders, notation, and the quest for universal rules in math. The result is a concise tour through the history of how we learned to name what we don’t know.

Introduction: Why X Captivates Mathematicians and Curious Minds

The video opens by asking why the letter X is so ubiquitous despite being one of the English language’s least common letters. It traces X’s ascent as the symbol for the unknown in algebra and explains that this symbol’s prominence is a story not just about math, but about how humans conceptualize and communicate unknown quantities. The narrative threads together linguistic history, mathematical theory, and cultural impact to show how a simple character can unlock universal patterns and rules that govern the world.

From Chi to X: The Long Path of a Letter

Ancient Greeks borrowed the Phoenician symbol for unknown sounds and transformed it into chi, a letter that appears in words like christos or chimera. As the symbol traveled through Latin into English, its function in mathematics was not yet defined. The video highlights that X was never a natural mathematical symbol at first; it emerged later as part of a broader shift from written words to symbolic notation. This transition—replacing words with symbols—began to crystallize in the 1500s, when mathematicians started using letters to stand for unknowns, a change that would ultimately standardize across Europe and beyond.

The Unknown Before X: Babylonian, Greek, Indian Traditions

The Babylonians and others posed problems where the unknown was embedded in the question itself, such as calculating the sides of plots or solving quadratic-type problems. While these cultures solved unknown quantities, they did not use X as a symbol. The video emphasizes that the concept of the unknown was already central in ancient math, but the symbol X would only later come to embody it as a universal placeholder.

Algebra’s Rise: The Power of Rules for Unknowns

The middle chapters introduce Al-Khwarizmi, whose algorithms for solving equations gave birth to the word algebra and established the idea that you can understand the relationship between knowns and unknowns through a systematic method. His work showed that algebra could solve a broad class of problems, not just a single instance, and that solving for unknowns could illuminate underlying relationships across many situations.

The Great Shift: Toward Symbols in the 16th–18th Centuries

As word problems became more complex, mathematicians began replacing words with symbols to reveal patterns more clearly. Viet's nineties notation used vowels to indicate unknowns, a stepping stone toward modern algebraic notation. By the late 1700s, inconsistent symbols across regions threatened mutual comprehension, prompting a push toward universal conventions. The video notes that Descartes, in particular, popularized a scheme in which known quantities used early alphabet letters and unknowns used late alphabet letters, a practice that helped cement X as the preferred unknown in later centuries.

Why X? The Theories Behind the Symbol

Multiple theories attempt to explain why X, rather than another letter, became the standard unknown. Some propose a linguistic path through the Spanish translation of Al-Khwarizmi’s work, where the Arabic word she approximated the unknown’s sound and was rendered with chi, which morphed into x through translation. Another theory centers on Descartes himself, who used early alphabet letters for knowns and unknowns in his influential book, with X eventually becoming predominant. A final, tongue-in-cheek idea suggests printers had more spare Xs on hand, so Descartes’s usage might have been a matter of convenience. The video presents these theories as unresolved puzzles that feed the legend surrounding X’s ascent.

Impact: The Unknown as a Driver of Mathematical and Real-World Insight

Beyond pure math, the unknown symbol enabled practitioners to model, predict, and reason about the real world. The video highlights how algebra and the practice of solving for X underpin modern technologies like GPS, Wi-Fi, and even space discoveries conducted on paper before observation. The X symbol helped reveal universal patterns and laws that apply widely, guiding scientists as they explore phenomena from planetary motion to galaxy masses. The narrative also links X to broader culture, noting how the symbol appears in science and technology branding, as well as in notable historical figures such as Malcolm X and in the naming of products like Apple’s Mac OS X and SpaceX.

Conclusion: A Symbol’s Enduring Allure

The video closes by reflecting on X’s enduring appeal as a symbol of unknown frontiers, inviting viewers to stay curious about how notation shapes knowledge. The story of X shows that a single letter can codify a powerful way of thinking about what we do not yet know, opening doors to new discoveries and a better understanding of the world around us.