# Assalamualaikum

Welcome to another edition of English Corner, my name is Rifki Kusmana. This is an article about Al-Qalasadi, a mathematician from Andalusia.

An Indonesian version of this article is available here.

Muslims have also made many contributions to Mathematics. I have written about Al-Khwarizmi from Persia, but today I would like to talk about Al-Qalasadi from Andalusia.

Al-Qalasadi whose full name was Abū al-Hasan ibn ʿAlī al-Qalaṣādī was a Mathematician born in 1412 in Bastah, a Moorish town in Andalusia which is now part of Spain. Andalusia comes from the Arabic name Al-Andalus used by Muslims to refer to the entire region of Spain and Portugal occupied by Muslims from the 8th to the 11th century.

Al-Qalasadi was a Muslim who grew up in Bastah. In his childhood life in Bastah was quite difficult because the Christian Empire often made raids on the city of Bastah. He himself began to get an education in Bastah to study law and the Qur’an. As a teenager he moved south, away from the war zone to Granada where he continued his studies, particularly in philosophy, science and Islamic law.

Al-Qalasadi chose to remain in the Islamic world and he left Granada and began travelling in Islamic countries. In particular he spent much of his time in North Africa. He lived in Islamic countries that gave strong support to Andalusia both politically and with military assistance in resisting Christian attacks.

He spent time in Tlemcen where he studied under the guidance of his teachers to learn arithmetic and its applications. After that he travelled to Egypt where he studied with several prominent scholars. Finally, al-Qalasadi reached Mecca, to perform the pilgrimage and returned to Granada again.

When Al-Qalasadi returned to Granada, the state of the region had worsened. The remaining part of the Muslim territory was under attack by the Christians of Aragon and Castile. However, Al-Qalasadi continued to teach and write some of his major works during this period. But the constant attacks of the Christian armies made it difficult for him to live in Granada. The defeat of all Muslim territories in Granada finally occurred in 1492. The city of Granada fell to the Christians.

Al-Qalasadi wrote several books on arithmetic and a book on algebra. Some of them contained comments on Ibn al-Banna’s work in his book Talkhis amal al-Hisab (Summary of arithmetic operations). Ibn al-Banna himself was a Moroccan scholar who had died more than 100 years before al-Qalasadi wrote his commentary.

Al Qalasadi’s main treatise is al-Tabsira fi’lm al-Hisab (Clarification of the science of arithmetic). This work is a difficult book to learn, perhaps requiring a certain sharpness of mind to study it. His work was influenced by the work of Ibn al-Banna. Although Al-Qalasadi has tried to simplify the level of complexity of al Banna’s work as his predecessor. The book is too difficult to be used as teaching material because it uses dust letters.

Both simpler versions of Al-Qalasadi’s arithmetic works proved popular in teaching arithmetic in North Africa and his works were used for more than 100 years. Now despite many popular maths teaching books, there remains little of Al-Qalasadi’s contribution in mathematics taught today. For example, the sequences Σ n, n2, or n3 had been learnt by al-Samawal and al-Baghdadi, and the method for calculating square roots was known as far back as Babylon.

In fact, many 19th-century historians lacked an understanding of the mathematical contributions of Muslim scientists. Many of them did not know the ancient Muslim mathematicians. This is due to the lack of information and certain records that show the existence of these ancient mathematicians in the Islamic world. But Al-Qalasadi is apparently well known to historians.

19th century writers believed that algebraic symbols were first developed in Islam by the Spanish-Arabic mathematicians Ibn al-Banna and Al-Qalasadi. As it turned out, the algebraic symbols were not the invention of Al-Qalasadi.

The algebraic symbols often used by Al-Qalasadi were invented by other Muslim mathematicians in North Africa 100 years earlier, but Al-Qalasadi had a major contribution in introducing the algebraic symbols to the world. The algebraic symbols had been used in the Eastern Muslim empire, perhaps even earlier than that. The scarcity of mathematical symbols in Italy may be due to Italian scholars such as Leonardo Fibonacci who was very influential in medieval Italy being unaware of the great works of Andalusian mathematicians.

# Citations

O’Connor, John J.; Robertson, Edmund F., “Abu’l Hasan ibn Ali al Qalasadi”, MacTutor History of Mathematics archive, University of St Andrews

Rebstock, Ulrich (1990). “Arabic Mathematical Manuscripts in Mauretania”. Bulletin of the School of Oriental and African Studies. **52** (3): 429–441. doi:10.1017/s0041977x0015133x. JSTOR 618117.

And that’s it for today’s English Corner, I hope you have enjoyed this article and I hope to see you again. Thank you for reading.

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