Whether the vigesimal (base 20) scale of the West African Yoruba people came with them from the east (perhaps Egypt) or not it was certainly present around 1000 AD during the foundation of the Oyo kingdom. The numeral system itself weighs heavily upon subtraction.

As in our system there are different names for the numbers from one

= okanto ten= eewa. As in our system, the numbers eleven= ookanlato fourteen= eerinlacould be translated as "one more than ten" to "four more than ten." But once fifteen= aarundinlogunis reached the convention changes, so that fifteen to nineteen= ookandinlogunare expressed as "twenty less five" to "twenty less one," respectively, where twenty= oogun. Similarly, the numbers twenty-one to twenty-four are expressed as additions to thirty= ogbon. At thirty-five= aarundinlogoji, however, there is a change in hte way the first multiple of twenty is referred to: forth is expressed as "two twnenties"= ogojiwhile 60= ogota, "three twenties," and 80= ogerin, "four twenties" and so on to 200=igbafor"ten twenties." It is in the naming of some of hte intermediate numbers that the subtraction principle comes into its own. Examples:45 = (20*3) - 10 - 5

50 = (20*3) - 10

108 = (20*6) - 10 - 2

300 = 20*(20 - 5)

318 = 400 - (20*4) - 2

525 = (200*3) - (20*4) + 5

All the number from 200 to 2000 (except those that can be directly related to 400

= irinwo) are reckoned as multiples of 200. From the nameegbewa =2000, names are constructed similar to above.The Yoruba numerals are amazingly complicated in which the expression of the small terms involved considerable feats of arithmetical manipulation, and it is unclear whether it has comparative merit, as complicated arithmetic involves a weighty amount of recall.

Documentary evidence at our disposal suggests that earlier in 17th century West Africa some Ulama (scholars) of Kanem -Bornu were highly skilled in the science of Ilm al-Awfaq (the science of magic squares). By the 18th century, the Borno kingdom became the most important center of learning of Mathematics in the Central Sudan attracting peoples from adjacent areas linking this at times to the occult sciences. Muhammad ibn Muhammad al-Fullani al-Kishnawi was a Falani from northern Nigeria. In 1732 he wrote an arabic manuscript on his researches on magic squares.

There is ample evidence to prove that the scholars of Hausaland and Borno were also consulting Coptic Solar Calendars in determining their economic activities. The recovery of a book written probably in Egypt on agrarian activities, from Bauchi in 1973 points to the fact that some aspects of of the agricultural sciences were being diffused in this area.The book, which is copied in a Sudanic script, contains mathematical charts dealing with agronomic activities such as the right time of harvest; the various directions of the wind; time of germination; and the seasons during which insects appear. A conversion table to lunar months is also made at the beginning of the book as a guide for the users of the chart.

It seems that some scholars in the Central Bilad al- Sudan especially the area of Katsina, were well versed in numerology and astrology. The recovery of some books from Katsina areas such as Borno by the late Professor M.A. al-Hajj and other researchers suggests that the scholars of Katsina were versed in these occult sciences .

Education was a major preoccupation of the Sokoto Jihad and its intellectual revolution in 19th century Hausaland. There is ample evidence to suggest that Shaykh Uthman b. Fudi was teaching both simple and advanced arithmetic (al-Yasir wa al-Gharib) to his students. Another evidence of the incorporation of arithmetic and related sciences in the syllabi of the schools in 19th century Hausaland is to be found with Abd al-Quadir b. al-Mustafa who is reported to have studied medicine, astrology, arithmetic, logic and astronomy.

This is partially extracted from Ahmad Kani, Arithmetic in the pre-colonial Central Sudan

Since opening 5/25/97, visitors to

The web pages

**MATHEMATICIANS OF THE AFRICAN DIASPORA**

are brought to you by

The Mathematics Department of

The State University of New York at Buffalo.

They are created and maintained
by

Scott W. Williams

Professor of Mathematics