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Qalasādi: The Master Behind Algebraic Symbols

posted on: Jul 21, 2021

Illustration of Qalasadi
Photo: Tirto Id

By: Meral Abu-Jaser /Arab America Contributing Writer

Ever since the early ages, Arabs have always been associated with mathematical discovery. There are many mathematicians who lived during the Islamic Golden Age. For example, many of us know about the father of algebra, Muḥammad ibn Mūsā al-Khwārizmī, but have you ever heard of the Qalasadi? His full name is Abu’l Hasan ibn Ali al Qalasadi and he is the master who invented algebraic symbols. Today, we shall explore Qalasadi life as a mathematician, his discovery of algebraic symbols, and his other contributions to both mathematics and other topics.

An Introduction to Qalasadi’s Education

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Illustration of the Golden Age
Photo: About History

A long time ago, there was a time when algebra equations did not involve symbols. Today we can’t really imagine algebra that doesn’t involve symbolic notations. Therefore, there was a time when bringing these algebraic symbols into the world of mathematics was a major breakthrough. Hence, this brings us to our subject for today: Abu’l Hasan ibn Ali al Qalasadi, an Andalusian Muslim mathematician who took a step forward in algebraic symbols.

Qalasadi was born in 1412 in Bastah, a Moorish city in Al-Andalus which is part of modern-day Spain, during the Islamic golden age. During that time, Islamic scholars, philosophers, and scientists were at the edge of discovery. However, when Qalasadi grew older, it was a difficult time for him since Spain was no longer occupied by the Moors. Thus, it was harder to obtain an education. Nevertheless, that did not stop Qalasadi from continuing his education in Bastah. He ended up entering law school where he studied both the Quran and science along with his law degree. After he finished law school and during the time of war, Qalasadi moved to Granada. He went on by continuing his studies where he became more interested in philosophy, science, and Muslim law.

Qalasadi’s Work on Algebraic Symbols

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Different Algebraic Symbols Used in Modern Mathematics

Once Qalasadi graduated from higher education, he started traveling throughout the Islamic world. He traveled across North Africa for 15 years to study and discuss various subjects with many scholars. Eventually, while traveling Qalasadi became more interested in sciencetic topics, specifically mathematics. He wrote at least 11 major books about mathematics in which he mostly focused on algebraic symbols. The most well-known book is Tafsīr fi’l-‘Ilm al-Hisāb (Commentary on the Science of Arithmetic). In the book, Qalasadi moved beyond the simple notations that earlier Greek mathematicians established.

Qalasadi used Arabic equivalents of symbols we know. For example, he used “m” for squared values and the Arabic equivalent of “k” for cubed values. He also standardized the use of the Arabic terms “wa” for addition, “illā” for subtraction, “fī” for multiplication, and “‘alā” for division. Qalasadi has also been credited for being the first to separate the numerator and denominator of a fraction with a line and to distinguish between fractions of relationship.

What Else is Qalasadi Known for?

Qalasādi, a Great Andalusi Mathematician - FUNCI - Fundación de Cultura  Islámica
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Nevertheless, Qalasadi did not stop here. He also highlighted the importance of the successive approximation method. Today, this method of successive approximation is an essential tool in calculus, and solves problems that we otherwise wouldn’t be able to solve. Qalasādi also took an extra step to demonstrated the importance of this method by using it to obtain the roots of an imperfect square. In one of his books, he discusses extensively about fixed shares.

In addition, there was an artistic side to Qalasadi. While he was very passionate about mathematics, he also admired art. He demonstrates this in one of his books where he explains the algebraic rules of poetry. He managed to publish 26 books, which are most well-known in North Africa, as that is where he spent most of his time after the war in Spain. Out of the 26 books, nine are about grammar and language, and 11 on Mālikī jurisprudence and the traditions and hadīth of Prophet Muhammad. Furthermore, some of his books covered astronomy and mathematics.

The Legacy of Qalasadi

Sadly, Qalasādi’s story ends off on a sad note. Qalasādi was the last Arab Muslim mathematician who passed away in 1486. 6 years after his death in 1492, Granada, the last Muslim city left in Spain, fell to the Christian forces of Ferdinand and Isabella. In this devastating year, Archbishop Cisneros ordered the forced conversion of Muslims and Jews to Christianity. They also demanded to have all their valued manuscripts, including writings such as those of Qalasādi, to be burnt. This is probably why few people know Qalasādi.

However, Qalasādi’s work and ideas survived and continued to be used for centuries in North Africa. One Moroccan scholar stated in his autobiography that in the 1920s, his father would teach him math from “the book of al-Qalasādi”. Eventually, Qalasādi’s work also made its way to Europe. His studies played an important role in the European Renaissance.

With that, we come to an end from our historic journey through the life of the last Arab Muslim mathematician, Abu’l Hasan ibn Ali al Qalasādi. If you enjoyed this story, you can check out Arab America’s blog here for more interesting remarks about the Arab world.