READ: Thank You for Algebra — Muhammad Ibn Musa al-Khwarizmi

By Bennett Sherry

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.

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 equations${}^1$‍, 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.

Al-Khwarizmi’s work in mathematics revolutionized or made possible other fields, including finance, optics, engineering, chemistry, astronomy, geography, and computing. Al-Khwarizmi made some of these innovations himself. He improved on Ptolemy’s famous world map, recording the latitudes and longitudes of thousands of cities. He produced new calendar and calculation systems for tracking the movement of the planets, Sun, and Moon. In 1202 CE—four hundred years after al-Khwarizmi wrote his books—the Italian mathematician Fibonacci introduced the Hindu numbering system to Italy. Within two centuries, these numerals were the standard across Europe.

Isaac Newton claimed that he saw far because he stood on the shoulders of giants. But we often forget that he was only able to stand on those shoulders because he could read their words. The great Islamic scholars who lived during the Golden Age of Islam are the people that Newton had to thank for translating and improving the ancient works of Greek, Hindu, Babylonian, and Roman scholars. Their works circulated throughout the Islamic world, emerging from centers of learning like Baghdad, Cairo, Cordoba, Fez, and Basra. Carried by scholars from across Afro-Eurasia, these works were passed from student to teacher and translated into new languages. The early Islamic caliphs brought scholars from as far away as China and West Africa to Baghdad, where new ideas swirled together and added to our collective learning.

Bennett Sherry holds a PhD in history from the University of Pittsburgh and has undergraduate teaching experience in world history, human rights, and the Middle East. Bennett writes about refugees and international organizations in the twentieth century. He is one of the historians working on the OER Project courses.