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 in ninth-century Baghdad. 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 from one language to another. He blended and improved mathematical concepts from ancient Babylonian, Greek, and Hindu scholars, forever changing how we do math.

Al-Khwarizmi studied at a famous library in Baghdad called the House of Wisdom. He was invited there by the ruler of the Abbasid Empire around 820 CE. 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, but his teachings live on through his books. He made important discoveries in geography, astronomy, geometry, and calendar systems. However, his most important contributions were in mathematics.

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

Al-Khwarizmi is best known for his work on 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 fī hisāb al-jabr wal-muqābala (Arabic for The Compendious Book on Calculation by Completion and Balancing) is where we get the word algebra (from the Arabic word al-jabr, which means balancing). This book offered detailed instructions for solving linear and quadratic equations,¹ and earned al-Khwarizmi the title “father of algebra.”

You might not be too excited about algebra, so I understand if you’re not eager to thank al-Khwarizmi. But consider this: algebra can also help you solve some of life’s more complicated problems in a simple way. Basically, 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 offers solutions for people who need to figure out common, everyday problems. For example, his book explains 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 for solving a problem. They’re the basis of computing machines, so that means we wouldn’t have computers or phones without al-Khwarizmi and his work on algorithms. 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 using 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 was 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 100 (or, as you might have learned to think of it, it’s in the hundreds column). 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.

Adding to human knowledge

Al-Khwarizmi’s work in mathematics contributed to many 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.

The House of Wisdom

Called Bayt al-Hikmah in Arabic, the House of Wisdom was the famous institution of learning under the Abbasid caliphate in Baghdad (present-day Iraq). Founded in the eighth or ninth century, the House of Wisdom welcomed scholars from across Afro-Eurasia. Persian, Indian, Central Asian, Chinese, East African, and other scholars all traveled to the House of Wisdom. There, they studied and wrote about mathematics, history, chemistry, astronomy, medicine, and philosophy.

In addition to attracting all those scholars, the House of Wisdom also contained a huge library of ancient texts. One of the biggest contributions of the House of Wisdom scholars was the translation of ancient texts from Greek and other languages into Arabic. This preserved ancient knowledge that might otherwise have been lost after the decline of the Roman Empire. Yet, these scholars did far more than just translate and preserve. They also interpreted, analyzed, and challenged ancient ideas. In the process, they advanced scientific knowledge in many fields.

We know that a lot of important scholarship emerged from the House of Wisdom, but we don’t know much about its founding or its purpose. That’s because in 1258, the army of the great Mongol Empire conquered Baghdad, destroying the city. The House of Wisdom was demolished, along with most of the books it contained. So, we have very little archaeological evidence of its existence. Yet it is a testament to the work of five centuries of scholars in the House of Wisdom that their knowledge was not lost with the destruction of the library. Their works had already spread widely across the Islamic world and beyond. Later, those same works would help launch the Renaissance and Scientific Revolution in Europe.

¹ Explaining—and understanding!—these equations is complicated. Thankfully, this is a history class. All you need to know right now is that linear equations help mathematicians solve problems with a straight line, and quadratic equations, which are more complicated, involve curved lines.