The life and works of a west African mathematician in the diaspora: Muhammad al-Kashnāwī in 18th century Egypt (Patreon)

Scientific manuscripts make up a significant proportion of Africa's intellectual heritage preserved in various libraries across the continent from Senegal to Kenya, particularly those relating to the field of Astronomy and Medicine, as well as works on Geography and Mathematics.

Many of these scientific manuscripts were written by African scholars and were intended not just for a local audience in Timbuktu, Harar, or Lamu, but also for an international audience extending to Cairo and Medina, where many African scholars from across the continent became prominent teachers and were active participants in linking the scholarly communities spread across the continent.

Among the most prolific West African scientists was the 18th-century mathematician Muhammad al-Kashnāwī from Katsina in what is today Northern Nigeria, who was considered a remarkably influential teacher whose students included many prominent scholars of Egypt. A monument erected for him in Cairo by one of his students, Hasan al-Jabarti, described him as described as "sagacious, charitable and versed in the sciences" which he acquired "in his own country".

This article outlines the biography of Muhammad al-Kashnāwī, including his education in west Africa, his career in Egypt, and his 18th-century mathematical treatise.

 Folios from a copy of Muhammad al-Kashnāwī's mathematical treatise, titled 'Bahjat al- āfāq', completed on 29th, January 1733. now at the Bibliothèque nationale de France .

Early life and education of Muhammad al-Kashnāwī

Muhammad al-Kashnāwī was born in the town of Dan Ranko, one of the dependencies of the Hausa city-state of Katsina in what is today northern Nigeria. Much of his biography is taken from his eight surviving works, two of which include a travelogue of his pilgrimage to Mecca and a compendium of authorities. The latter two works are now lost but were cited by the historian Abd Rahman al-Jabartī (d. 1825) of Ottoman-Egypt and the Sokoto ruler Muhammad Bello (d. 1837), with the former reproducing them in greater detail.

(ALOA, Vol2, pg 37-38)

At the time of his birth in the early 18th century, Katsina was the most powerful of the Hausa city-states, and it was one of the major centers of trade and learning in west Africa, attracting scholars from across the region. Like most of his peers, al-Kashnāwī began his studies with the basic curriculum of Muslim schools in west Africa, before moving on to more advanced subjects including law, logic, arithmetic, and the 'esoteric sciences' such as astrology, astronomy, and geomancy.

(Islamic scholarship in Africa pg 41-42)

Katsina in the late 18th century

Katsina, Sultan's palace and mosque ca. 1918, Bristol archives.

According to al-Jabartī’s account, al-Kashnāwī "studied in his homeland [Katsina] with Muḥammad al-Nawālī al-Birnāwī, Muḥammad al-Bindū, Shāykh Hāshim, and  Muḥammad Fūdū, and Muḥammad Krʿk." According to al-Kashnāwī own account, his teacher, Muḥammad Fūdū, was “the first from whom I attained understanding. I studied most of the books of literature with him and accompanied him, both in residence and in travel, for about four years.”

Scholars argue that Muḥammad Fūdū was the father of Usman dan Fodio (d. 1817) who founded the Sokoto state. As for his other teachers, he writes that Muḥammad al-Bindū taught him "the art of magic squares, arithmetic, and chronology in the style of the Maghribī path (of Sufism), mastering esoteric disciplines of all kinds, literal and numerological, as well as mathematical and calendrical devices". He adds that Muḥammad Krʿk of ‘Kāgh Birn’ [Kāgḫu of Bornu], taught him “many aspects of the secret sciences and geomancy and some books on arithmetic.” Lastly was Muḥammad al-Nawālī, who was a respected authority in Bornu and Baghirmi on matters of theology and grammar.

(Al-Azhar and the Orders of Knowledge, pg 258-263, Islamic scholarship in Africa pg 43-44)

the 18th-century manuscript, Shurb al-zulal' written by Kanuri scholar Harjami (d. 1746). This manuscript eventually found its way to Egypt where it was used by the rector of the Al-Azhar college. at least one of Al-Kashnāwī's teachers, Shāykh Hāshim, was part of the intellectual school that included the author of this didactic work. 

 Muhammad al-Kashnāwī's travel to the Hejaz and career in Cairo.

After his studies, Al-Kashnāwī left Katsina sometime before the year 1730 to make the pilgrimage to Mecca and Medina. Al-Kashnāwī passed through several countries and met with their rulers and learned men, taking the central Sudan route through Bornu to the Fezzan to Cairo.

According to his travelogue titled 'Al-Durr al-manzūm', he writes that "I first entered Mecca al-Musharrafah upon my arrival from Medina, whence my visit preceded my pilgrimage. And this is because I came by way of Egypt and from there I continued to Suez, a port for Egyptian vessels and boarded a boat to Yanbuʿ another port through which the residents of al-Medina receive the grain and provisions that come to them from Egypt"

He notes "my visit [to Medina] preceded my pilgrimage and I sojourned there - blessed and having a good time for a little less than three months. From there, I headed in the visitors caravan of fame in those Meccan lands, the happiest of trails for one hoping to attain the pleasure of his Lord in his life and religion"

(Al-Azhar and the Orders of Knowledge, pg 252-253)

After spending some time in Medina's scholarly community, al-Kashnāwī settled in Cairo, where he composed several major works, taught many students, and including Hasan al-Jabartī (d. 1774). The latter received instruction from the Katsina scholar in a variety of subjects, which included numerology and astrology, and entered the circle of scientists and astrologers Hasan al-Jabartī had gathered at his house. al-Kashnāwī Later died in 1741 and bequeathed his library to Hasan al-Jabartī, who arranged for a monument to be inscribed with the name of the deceased, and the date of his death.

(The Arabic Literature of Nigeria pg 135)

 Muhammad al-Kashnāwī's works

While only eight of his works survived, there were likely many more works that didn't.  Hasan al-Jabrti's son Abd al-Rahman al-Jabartī notes that al-Kashnāwī "possessed great energy and a genuine desire to acquire the knowledge on which the understanding of books depends. He used to say about himself, “One of the ways in which God bestowed favor upon me was that I never read anything in a loaned book. The least I did when I wanted to read a book which I did not own was to copy its text, leaving space between the lines to write whatever comment I wanted, or for the remarks of my shāykh when he was teaching it. When I was more ambitious, I would copy out the commentary and gloss also"

(Al-Azhar Orders of Knowledge, pg 263)

During al-Kashnāwī’s period in Egypt he composed several works, including;

1)

Rihla (Travels) about his pilgrimage to Mecca and Medina

2)

Bulūgh al-arab min kalām al-ʿarab, a work on Arabic grammar dated 1736.

3)

Bughyat al-mawālī fī tarjamat Muḥammad al-Wālī, the biography of Muḥmmad al-Wālī that includes the aforementioned compendium of authorities.

4 & 5)

Manḥ al-quddūs , a didactic poem on logic drawn from the Mukhtaṣar of al-Sanūsī, on which al-Kashnāwī then wrote an extensive commentary entitled, Izālat al-‘ubū ‘an wajh minaḥ al-quddūs.

6)

 Bahjat al- āfāq (also called Mughnī al-mawāfī) a numerological work on magic square completed on 29th January of 1733.

7)

Al-Durr al-manẓūm, an abridged commentary dealing with three domains of the esoteric sciences, which he began in Mecca and completed in Cairo on 20th December 1733. It was written at the request of one of his Egyptian students; Isma‘il b. Hamza Duhaydih, to whom al-Kashnawi had been introduced by another west African scholar from Kano named Yinus b. Muhammad al-Hawsawi al-Kanawi.

8)

Durar al-yawāqīt, a commentary on Kitāb al-durr of ‘Abd al-Rahman al-Jurjanī on the science of letters and the great names of God which he completed on 6 Sep 1734.

(ALOA Vol2, pg 38-39)

Besides the travelogue and compendium, only two other works of al-Kashnāwī have been translated and studied. These are the work on esoteric sciences; Al-Durr al-manẓūm, and the mathematical work on magic squares; Bahjat al- āfāq.

The mathematical treatise of Muhammad al-Kashnāwī and his algorithm for solving complex 'magic squares'.

al-Kashnāwī treatise on 'magic squares' is a mathematical recreation based on number theory. The basic concept of the 3x3 magic square was borrowed from the Chinese by Muslim scholar Jabir ibn Hayyan (d. 975). Subsequent Islamic scholars expanded the construction of magic squares to higher numbers; 4x4, 5x5, 6x6, 7x7, 9x9, and spread them to Europe in the 12th century, where they gained the attention of men of science such as Gerolamo Cardano (d. 1576) and Johannes Kepler (d. 1630).

They are referred to as "Magic" squares in Western Europe primarily because the sum of the numbers in each row, column, and diagonal is the same, known as the "magic constant", and were considered by some to have mystical properties although al-Kashnāwī makes no mention of such. The magic square appears in several west African manuscripts, as well as amulets and decorative motifs on cloth and architecture.

(Legacy of the Loushu, pg 93-116, 159, Magic Squares: Their History and Construction pg 13-19  Africa counts, pg 137-138, Cloth in West African History pg 102, A Geography of Jihad pg 72-73)

Folios from a copy of al-Kashnāwī's mathematical treatise, at BnF, Paris, Arabe 5635

Before launching into the procedures for the construction of magic squares, al-Kashnāwī warns the reader not to be misled by appearances, and provides words of encouragement, writing: "Do not give up, for that is ignorance and not according to the rules of this art. Those who know the arts of war and killing cannot imagine the agony and pain of a practitioner of this honorable science. Like the lover, you cannot hope to achieve success without infinite perseverance."

(Africa counts: Number and Pattern in African cultures pg 139-150)

al-Kashnāwī then provides several formulas for the construction of magic squares having an odd number of rows and columns, and examples of each, including 3x3, 5×5, 9×9, and 11×11.

The systematic method (ie algorithm) which al-Kashnāwī utilizes to generate magic squares of odd orders much larger than 3x3 had just been introduced to Europe from Siam (Thailand) by the French mathematician De la Loubère in 1693, and is thus referred to in the west as the 'De la Loubère method' or the 'Siam method'. In his chapter on the 'The problem of the magical square according to the Indians,'  De la Loubère writes that "I take liberty of giving the rules and the illustration of this surprisingly simple method, with which one very easily reaches a result though deemed difficult by all our mathematicians"

The algorithm became very popular among European mathematicians studying number theory over the 18th and 19th centuries, particularly in France and England.

(Magic Squares: Their History and Construction pg 32-34, Legacy of the Luoshu pg 118-119)

>> the actual calculations used by al-Kashnāwī' are explored in greater detail in Claudia Zaslavsky's book 'Africa Counts: Number and Pattern in African Cultures' and by Jacques Sesiano's article; 'Quelques méthodes arabes' see link in references, the links to both are added in the references below <<

The American mathematician Claudia Zaslavsky who identified al-Kashnāwī's algorithm as similar to the 'Siam method' concludes that she can't say whether or not al-Kashnāwī made original contributions to number theory. The swiss mathematician Jacques Sesiano who also studied al-Kashnāwī's algorithm notes that it was an innovation from older methods utilised by the Persian Asfizarı (d. 1121) and the Egyptain Shabramallisı in 1600, but applied to larger squares of odd numbers. With another important innovation being the solution for magic squares where one square is left empty. Sesiano notes that al-Kashnāwī presents all his explanations with "great clarity".

(Magic Squares: Their History and Construction pg 16, 29, 35-36, 38-39,   Quelques méthodes arabes pg 53-76)

This mathematical treatise evidently shows that al-Kashnāwī was a scholar of high standing in Egypt, something that was repeatedly mentioned by several of his peers in the later years, especially al-Jabarti, who describes the west African mathematician as the authority in the field of magic squares, and as the teacher of his father. Another prominent Egyptian scholar Muḥammad Makhlūf (1890-1990) describes al-Kashnāwī as having ‘had a long hand in most sciences and complete knowledge of the subtleties of secrets and illuminations.’

(Quelques méthodes arabes pg 54, Islamic scholarship in Africa pg 44)

Conclusion: the intellectual contribution of an African scientist in the diaspora.

 Muhammad al-Kashnāwī's career and his writings encapsulate the historian Zachary Wright's recent argument that "sub-Saharan African scholars were active participants in a sphere of scholarship linking West Africa with Morocco and Egypt."

It's important to note that besides Muhammad Bello's mention of Al-Kashnāwī as a prominent scholar, the mathematical treatise described above is by far the only manuscript of Al-Kashnāwī that has been found in West Africa itself (rather than Egypt). It was part of the library of the Tukulor ruler Umar Tal at Segou, Mali, from where it was seized by the French and deposited at the 'Bibliothèque nationale de France' in Paris. Indicating that al-Kashnāwī left a larger intellectual impact in Egypt than he did in West Africa, buttressing my earlier argument that scholarly exchanges between "north Africa" and the rest of the continent were not unidirectional.

Al-Kashnāwī’ contributed significantly to the established tradition of scholarship in Egypt during the 18th century, connecting him to various important intellectual currents and figures of the time. His education in Hausaland indicates the establishment of various disciplines in the region, including mathematics, which was once thought to be underrepresented in the corpus of Africa's scientific manuscripts but was doubtlessly part of the intellectual heritage of the region, and the scientific contribution of Africans in global history.

 Explanations of Problems in Arithmetic with Examples by Ahmad ibn Sulayman al-Rasmuki (d. 1639) on the work of the medieval mathematician al-Samlali, Library of Congress.

(Other commentaries by al-Rasmuki regarding the subject of Arabic syntax also appear in a number of West African libraries at Segou and Chinguetti, see: The Trans-Saharan Book Trade, pg 159)

Ethiopian manuscript with a Magic square,  (British library Or 12034, f.64v)

References:

ALOA, Vol2 (Arabic Literature of Africa: The writings of central Sudanic Africa Vol.2) by John Hunwick

Islamic Scholarship in Africa: New Directions and Global Contexts

edited by Ousmane Kane

Al-Azhar and the Orders of Knowledge by Dahlia El-Tayeb M. Gubara

Legacy of the Luoshu: The 4,000 Year Search for the Meaning of the Magic Square of Order Three by Frank Swetz

Magic Squares: Their History and Construction from Ancient Times to AD 1600 By Jacques Sesiano

Africa Counts: Number and Pattern in African Cultures

By Claudia Zaslavsky

Cloth in West African History By Colleen E. Kriger

A Geography of Jihad: Sokoto Jihadism and the Islamic Frontier in West Africa By Stephanie Zehnle

Quelques méthodes arabes de construction des carrés magiques impairs by Sesiano Jacques

The Arabic Literature of Nigeria to 1804 by ADH Bivar

Link