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## Big History Project

### Unit 8: Lesson 6

8.3—Commerce & Collective Learning

# Thank You for Algebra: Muhammad Ibn Musa al-Khwarizmi

The Muslim mathematician al-Khwarizmi built on ancient ideas and offered new approaches to mathematics that we still rely on today.

## Thank You for Algebra: Muhammad Ibn Musa al-Khwarizmi

By Bennett Sherry
The Muslim mathematician al-Khwarizmi built on ancient ideas and offered new approaches to mathematics that we still rely on today.

## Translating the heavens

Is math the language of science? If it is, then we should thank Muhammad Ibn Musa al-Khwarizmi for translating it for us. Al-Khwarizmi was a scholar at the House of Wisdom in ninth-century Baghdad (see Figure 1). There, he was part of a community of scholars from across the world who translated and studied ancient manuscripts on science, math, medicine, history, philosophy, and more. But like most scholars, al-Khwarizmi did more than simply translate ancient books. He blended and improved mathematical concepts from ancient Babylonian, Greek, and Hindu scholars, revolutionizing how we do math. Al-Khwarizmi was invited to the House of Wisdom by the Abbasid caliph (ruler), al-Ma’mun.
Al-Khwarizmi was a Persian man, probably born somewhere in Central Asia near today’s Uzbekistan. We don’t know a lot about his life. The sands of time have erased many of the details. Yet his teachings live on through his books. He made important contributions in geography, astronomy, geometry, and calendar systems. But his most important contributions were in mathematics.

## Algebra. Wow. Thanks. You shouldn’t have...

Al-Khwarizmi is best known for revolutionizing algebra and arithmetic. He didn’t invent algebra, but he did improve the techniques we use to solve algebraic problems. His book, al-Kitāb al-mukhtasar fīhisāb al-jabr wal-muqābala(Arabic for The Compendious Book on Calculation by Completion and Balancing) is where we get the word “algebra” (from “al-jabr” or “balancing”). This book offered detailed instructions for solving linear and quadratic equationsstart superscript, 1, end superscript, earning him the title “father of algebra.”
Now, you might not be too excited about algebra, so you’re forgiven for not rushing to thank al-Khwarizmi. But consider this: algebra sounds complicated, but it can also help you solve some of life’s more complicated problems in a simple way. At its most basic, algebra allows us to use symbols (like x and y) in equations to find unknown numbers. It could be as simple as the linear equation x + 1 = 2 , where we can quickly figure out that x equals 1. Or it can be as complicated as Einstein’s blockbuster: “E = mc2.” Quadratic equations are essential if you want to do things like fly a plane, plot a course to Mars, or pass Algebra II.
Unlike Einstein, you probably don’t need to solve problems involving the speed of light. Thankfully, al-Khwarizmi’s book also offered solutions for people who needed to figure out common, everyday problems. For example, his book explained how to use equations to split an inheritance, divide a plot of land, and find measurements for canals and buildings. While al-Khwarizmi was not the first person to understand these equations, he was the first to provide algorithms for solving them. Algorithms are sets of rules to solve a problem. They’re the basis of computing machines, so that means we wouldn’t have computers or phones without algorithms—or al-Khwarizmi. In fact, the English word “algorithm” comes from the Latinized spelling of his name, “Algorismi.” Now doesn’t al-Khwarizmi deserve some thanks?
Rather than using numbers and symbols in his book on algebra (algebraic equations tend to look something like this: ax2 + bx + c = 0), al-Khwarizmi explained how to solve equations in words. This is surprising, because his second-most famous book encouraged mathematicians to adopt the Hindu numbering system. Developed in ancient India, these numerals are today called Hindu-Arabic numerals. Al-Khwarizmi popularized the Hindu-Arabic numeral system in the Islamic world, and his book is responsible for their adoption in Europe five centuries later.
This numbering system made math a lot easier because it introduced the number zero and the concept of positional notation, which is basically the idea that the position of numbers determines their value. For example, consider the number 503. The five is in the third place to the left, which means it symbolizes units of a hundred. In this number, we know there are five hundreds and three ones. Why did this make math easier? Well, let’s try an experiment. Add up the cost of a video game, a pizza, and a pair of jeans. But here’s the catch: you can’t use the numbers you’re used to, only Roman numerals (I, V, X, L, C)...and you have to show your work. The cost of the game is LIX dollars, the pizza costs XV dollars, and the jeans are XXXIX dollars. Which adds up to “What the !@XV#%?”
Now, imagine how much time you would have saved if you were adding 59+15+39. A lot faster, right? That’s thanks to al-Khwarizmi and the ancient Hindu numbering system he introduced to the Islamic world.