Photo from freepik
If you want to learn math today, you might buy a college algebra textbook for learning from. These books are full of problems with x and y.
But math was not always this way.
The story of algebra is the story of a slow and brilliant discovery. It is the tale of zeroing in on the idea of the unknown.
For centuries, smart people have focused intently on solving puzzles, directing their attention to the unknown. They were slowly narrowing their focus on the empty spaces in their math, engaging the mind in the mental effort required to find the missing numbers they knew must be there but could not yet see.
Photo from freepik
The Ancient Puzzle Solvers
Long ago, people did math for practical reasons. They needed to split land, figure out supplies for armies, and build giant structures. They were solving equations, but they did not use symbols.
Instead, they wrote everything out in words.
They were pinpointing the answer through slow, step-by-step methods. Sometimes, they also needed to find the difference between quantities to solve such problems.
These early mathematicians were clever. They had recipes for solving specific problems, often breaking them into factors, and these recipes often relied on geometric or verbal means to arrive at a solution.
But each type of problem needed its own special recipe. There was no single rule that could solve them all. They were working in the dark, feeling their way toward answers without a general map.
They knew how to find a number, but they had not yet grasped the power of representing the number before they found it.
The Dawn of New Methods
Long before algebra became a global language, mathematicians in the Indian subcontinent were quietly creating new ways to work with numbers and equations.
Indian mathematicians explored advanced number systems, laying the groundwork for how we understand and use numbers today.
Their work on linear and quadratic equations, including early studies of polynomial equations, was not just important for their time—it helped shape the very systems that support modern algebra.
The origins of the word “algebra” may trace back to Arabic, but the methods and ideas that predominantly defined the subject were adopted and enriched by Indian mathematicians, whose innovations were supported by a tradition of rigorous scholarship and have continued to influence the field up to the present day.
Al-Khwarizmi and the Arabic Golden Age
The big leap forward for algebra happened in the 800s in Baghdad. A brilliant mathematician named Muhammad ibn Musa al-Khwarizmi wrote a book that changed everything. Its title gave us the word “algebra.” He called it The Compendious Book on Calculation by Completion and Balancing.
Al-Khwarizmi’s great breakthrough was honing in on a standard way to solve equations involving unknown quantities. He started to classify problems into different types, organizing equations into categories based on their properties or solutions. More importantly, his method of “completion and balancing” is exactly what we do today when we solve an equation.
The Slow Birth of the Symbol
For hundreds of years after al-Khwarizmi, algebra was still done mostly with words. It was like reading a long, complicated paragraph to solve a single math problem.
Then, in Europe, during the Renaissance, mathematicians began concentrating on and developing a new idea: symbolism.
This shift allowed algebra to become freer and flexible, as mathematicians replaced words with symbols, making algebraic operations more general and accessible.
This was a revolution. By letting a symbol represent the unknown, mathematicians could now see the problem in a new way.
The accumulation of mathematical information, such as the foundational work of Euclid and the study of conic sections, played a crucial role in shaping the development of algebraic symbolism. They could write down relationships between numbers they didn’t yet know. They could manipulate the symbols according to rules, almost like moving pieces on a chessboard, to find the answer.
Algebra Crosses New Frontiers
As the Renaissance swept across Europe, algebra entered a new era of creativity and discovery.
Mathematicians worked to transform algebra from a collection of methods into a distinct branch of mathematics. Several figures authored key mathematical treatises that introduced symbols for unknowns, making it possible to write and solve equations in a way that was both efficient and powerful. One particular mathematician authored works that established the use of coordinates and graphs, creating a bridge between algebra and geometry that would change the course of mathematics forever.
This period was a turning point not just for algebra, but for the sciences as a whole. The work of these mathematicians helped to share and establish algebra as a foundational tool for physics, engineering, and beyond.
The Renaissance was a time when the boundaries of knowledge were being redrawn, and the distinct identity of algebra was firmly established, shaping the way we use mathematics in New York, across the world, and throughout time.
Zeroing In on the Missing Number Systems
The most important “unknown” that mathematicians finally zeroed in on was the number zero itself. It seems obvious to us now, but the concept of “nothing” as a number was a deeply strange idea for a long time. Early number systems, like the one used by the Romans, had no zero. Try writing the year 2024 in Roman numerals (MMXXIV). It’s clear they had no symbol for the tens and hundreds places that are empty—these places were simply left without a symbol.
The acceptance of zero was a game-changer for algebra. It allowed for a proper place-value system (like units, tens, hundreds). This made calculating much easier.
Photo from freepik
But it also did something more profound for algebra: it gave mathematicians a tool to represent “nothing.”
The concept of zero revived mathematical thinking, opening up new ways to approach equations and problems. This was a powerful new way of thinking.
This was the final piece in narrowing focus on the complete picture of numbers, from positive to negative to zero.
Algebra Today: The Language of Patterns
Today, algebra is the grammar of the modern world. It is no longer just about finding a missing number. It is the language of science, engineering, computer programming, and economics.
Ready to decode algebra yourself? Check out College Algebra in the Digital Age and master the math that built our world!
