Qalasadi: The uncrowned king of Algebraic symbols

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Algebraic symbols

Initiation of Algebraic symbols 

Who can imagine algebra today without algebraic symbols? Yet how many of us today would even remotely recognize the name Abu’l Hasan ib Ali al-Qalasadi? Yet, historically one is inseparable from the other. J J O’Connor and E F Robertson, School of Mathematics and Statistics, University of St. Andrews, Scotland, in an article, describe him as “a Spanish Islamic mathematician who took the first steps toward the introduction of algebraic symbolism by using letters in place of numbers”. Qalasadi was a Muslim mathematician of the 15th century from al-Andalus, a region which is today part of Spain.

Life and times of Qalasadi 

Qalasādi was born in 1412 in Baza, a small outpost of the Emirate of Granada. Before becoming one of the first scholars to introduce algebraic symbols, he studied Islamic disciplines in Baza. At age of 24, he left for a tour across North Africa, and over the next 15 years, he spent learning from African scholars. The most famous among such scholars as Ibn Hajar al-Asqalānī, of Egypt, who taught Qalasādi the Hadith. He then returned to Spain, and settled down in Granada, and wrote a number tomes on mathematics, which is where he initiated algebraic symbols. He also wrote books on law and philosophy. When Christian forces of Ferdinand and Isabella started attacking Grenada in the 1480s, Qalasadi was forced to leave for Tunisia. He died in 1486 in Beja, a town about 100 Km from Tunisia’s capital Tunis.

Works and contribution of Qalasadi to Algebra and other fields 

Qalasādi wrote at least eleven books on mathematics, in one of which he introduced algebraic symbols. This magnum opus was titled Tafsir fi’l-‘Ilm al-Hisab (Commentary on the Science of Arithmetic). In it, he progressed far ahead of simple notations that Greek mathematician Diophantus and Indian scholar Brahmagupta had established.

Qalasadi used a symbol, which looked like ‘∫’ to denote an equal sign (similar to the manner in which we use =). He turned the Arabic equivalent of m (mal) into a symbol for squared values and the Arabic equivalent alphabet of k (ka’b) for cubed values. Not only these, but Qalasadi also standardized the use of the Arabic terms “wa” for addition, “illā” for subtraction, “fī” for multiplication, and “‘alā” for the division. These algebraic symbols obviously gave mathematicians to take a quantum leap in complicated calculations.

However, not only a mathematician Qalasadi was a versatile genius, and penned momentous treatises on poetry, grammar, and language. For example, he wrote a book, which explains how the rules of algebra could be applied to writing great poems. Qalasadi wrote eleven major books on Maliki jurisprudence and commentaries on the Hadith. He wrote over two and a half scores of books on astronomy and nine on grammar and language.

Sadly, following the Christian ‘reconquista’ of al-Andalus 15th centuries onwards, raiding armies burnt down many of Qalasadi’s treatises, along with those of many other scholars. However, much of it has thankfully survived, which has enabled historians to recognize Qalasadi as the father of algebraic symbols.


(Written by Author and Translator Nilanjan Hajra)