African Mathematics

[Auset32]

AFRICAN MATHEMATICS
Pre-colonial Northern Nigeria


AHMAD KANI



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.
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 .

The 19th century Jihad movement in Hausaland has been rightly described as an intellectual revolution which threw the door of academic pursuit open in all its ramifications. Education was a major preoccupation of the Sokoto Jihad. 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. --------------------------------------------------------------------------------

Extract from
Ahmad Kani, Arithmetic in the pre-colonial Central Sudan in
Gloria Emeagwali (ed) Science and Technology in African History, Edwin Mellen, NY, 1992



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Dr Kani is Professor of History. He has taught at Ahmadu Bello University and also served as the Dean of Arts at the University of Sokoto.

Africa-related sites on Maths (Ohio State Univ)


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See related material and bibliography on African Mathematics:

The Newsletter of the Commission for the History of Mathematics in Africa


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See also works by Ron Eglash:
When Math World Collide: Intention and Invention in Ethnomathematics, Science, Technology and Human Values, vol.22.no.1.Winter 1997, 79-97;
Ron Eglash, Bamana Sand Divination: Recursion in Ethnomathematics, American Anthropologist, 99 (1) 112-122;
Ron Eglash, African Fractals, Modern Computing and Indigenous Design, Rutgers University Press,

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1999

[terrence]

Thank you for the story. I like researching topics related to the advances in Math from past Africans. Here is another interesting piece of history from Dr. Joesph Bailey:

His web-site can be found at;
http://www.jablifeskills.com/modules...tid=182&page=1

Africans Invented Arithmetic and Algebra

Joseph A. Bailey, II, M.D.

The earliest treatise on algebra is the Egyptian Rhind Papyrus (c.1700 BC). But in c.3000 BC Egyptians called it “aha Calculus” because “Aha,” “Ahe,” or “Ahau” was the name of the second pharaoh of the first dynasty. Meaning mass, quantity, or heap (a pile of many things), it was used as an abstract term for the unknown in an equation. Originally, the word “algebra”—(“al” “from Egypt”--“al-Kemit”)--meant the reuniting of broken parts and was later defined by the Arabs as “restoration”, including “bone setting”. Note that Yin and Yang are also about the union of separate parts.

Now, algebra deals with math structures—the solution of equations and the general relations among numbers. It embraces calculus, logic, theories of numbers, equations, functions, and their combinations. Both arithmetic and algebra are branches of mathematics and both are ways of figuring. Figuring involves discovering answers (e.g. establishing values) to problems using the amount or value given in numbers, using unknown numbers, or using letters or symbols standing for quantities. A letter or symbol for any number is called a Variable. Quantities of matter have size, weight, number, mass, height, depth, width, length, capacity, extent, endurance, time duration, and volume. They can be counted, weighed, and measured geometrically (e.g. lines, curves, angles)—and these may be added to or lessened.

Arithmetic (“the science of numbers”; “the art of calculation”) applies numbers to answer questions such as “how many?” –how much?” --and how far?” Algebra is the next step up and features letter or symbol “shorthand” in expressing quantities. With arithmetic the simple job of adding can be expressed as 3+4=7 or three + four = seven.

However, in algebra the same could be written T + F = S—i.e. using the first letters of the words to stand for the numbers. This is called an Equation-- a statement that two things are equal. Equations have many governing rules—rules which allow discovering unknown numbers that appear in an equation with known numbers—and rules which make calculation with big numbers just as easy as calculation with small numbers. For example, “x” (or any other letter of the alphabet) stands for an unknown quantity. As in arithmetic, addition is shown by + and subtraction is shown by —. When you put one letter over the other--like a/b-- you are dividing b into a. Putting two symbols together-- as ab—means to multiply them. In algebra the multiplication sign is not used when two symbols are placed side by side. T x F is written TF and 3 x T is written 3T.

Although certain symbols, marks, and letters customarily represent quantities and operations, seldom would the letters T, F, and S (see examples above) be used. Usually the early letters of the alphabet—a, b, c, etc.—are applied to stand for constants (fixed or known numbers) and the late letters—x, y, z—to stand for variables.

Variables are quantities that may have various values or that are unknown. The letter “n” is used to mean “any given (or known) number”. A Power of a number is the product or result you get when you multiply the number by itself, one or more times. It is expressed by an Exponent (a small number written after and higher than the number). When you read it aloud as “three squared,” this means 3 x 3 =9; or “two to the fifth power is 2x2x2x2x2 or 32. Roots, the opposite of a power, must be multiplied by itself to produce a given number. The cube root (using a number three times as a factor—4x4x4) of 64 is 4. A Series is a group of numbers related by some rule. In an arithmetic series—1, 4, 7, 10—a constant number (here, 3) is added to each term to give the next. Africans found a place for arithmetic and algebra during their on-going activities on such vast construction projects-- as in building temples, pyramids, irrigation works, and obelisks.

Joseph A. Bailey, II, M.D.

[love2talk]

If I'm not wrong, I recall hearing that geometry is another type of mathematics developed in Africa (Egypt).

[Samoon]

You are correct. For Geometry WAS developed in Ancient Egypt. However mainstream scholars continue in refutting this.

[sephari]

i thought this thread was about fractal architecture.

you know what here:
http://www.rpi.edu/~eglash/eglash.di...l/afractal.htm

i was blown away the first time i saw this.

[catwoman]

One has only to study the piramides. They are still standing today!!. Still one of the archeological wonders of the world. The geometry they used is still mind blowing to modern day mathematicians. They had knowledge of squared roots for e.g. because it can be found in measurements.

[jimihaze]

this is great info. I see I have some reading to do on this.