Harnessing African science and technology: Part Six…African mathematics foundation for modern mathematical sciences

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IN this article, we shall continue to explore the scientific achievements of Africans in the area of mathematical sciences as part of efforts to re-assert Africa’s pride of place among the human races on earth.
To obtain more documented examples of African science, we have accessed various internet sources including Wikipedia and others.
Interestingly, several websites make a point of stating that very little has been done to explore and document African science and technology.
That does not mean Africans have no science footprint on the sands of time; on the contrary, Africa’s achievements in the mathematical field have largely been ignored, down-played or mis-attributed to other races.
Needless to say part of the reason for marginalisation of African mathematics and other sciences is the reluctance of Western authors to acknowledge African achievements out of bias as they have historically striven to depict Africa as a land of backwardness and under-achievement.
The downright refusal by Westerners to accept African scientific and other achievements must be countered by continuously highlighting black Africa’s large science footprints on the sands of time.
That some of the African scientific achievements have been blurred or even covered by the shifting sands of time should not diminish their greatness.
African scholars must do more research and deliberately increase the volume of publications that document Africa’s scientific heritage.
In this series we shall continue to give readers narratives of African scientific achievements based on historical information from books and internet sources.
The aim is to exorcise the ghost of false perceptions that black African societies have no scientific heritage and also to build the confidence of Africans so that they continue to boldly harness science and technology for the continent’s socio-economic development.
We have previously highlighted African achievements in areas like medical sciences.
A recent perusal of the Wikipedia websites revealed some interesting details on African achievements in science areas like mathematics, metallurgy, maritime technology, agriculture, irrigation, textile technology and architecture.
In this episode, we shall look at mathematics, one of the key subjects in the STEM curriculum.
Virtually all human endeavour is premised on quantifying the phenomena around us.
The basic questions of how much, how far, how high, how big, how heavy, how fast and so on require a form of measurement requiring a mathematical operation in order to answer.
Some form of measurement/calculation is required to quantify the various phenomena in our environment.
This is essentially the field we call mathematics.
Even so-called illiterate unschooled persons all have a clear quantitative/mathematical appreciation of the things around them.
For the countless millennia over which Africans have interacted with their natural environment, they have evolved various strategies to quantify and therefore be able to manipulate and exploit the natural phenomena and environment around them.
In this article, we shall also highlight some mathematical concepts that Africans have developed and used.
We also will highlight areas where African mathematicians have led the rest of the world.
In Wikipedia reference is made to the ‘Lebombo bone’ discovered in the mountains of Swaziland and thought to be probably the oldest mathematical artefact on record dating back to 35 000BCE (Before Christian Era).
It consists of 29 distinct notches cut into a baboon’s fibula.
The ‘Ishango bone’ tool discovered in the Democratic Republic of the Congo is dated between 18 000-20 000 BCE.
It is also a baboon’s fibula thought to have been used as a ‘tally stick’ because it has a series of tally marks carved in three columns running the length of the tool.
Some scientists think the groupings of notches indicate a mathematical understanding far beyond counting. It has been suggested the ‘Ishango bone’ could have been used as a tool to carry out mathematical calculations (addition, subtraction, multiplication, division), a six-month calendar or for tracking a woman’s menstrual cycle.
In the Nile Valley, during the pre-dynastic ‘Naqad’ period, Africans had already developed a numerical system.
That mathematics was important to Egyptians is indicated by a narrative where a proposal was made for two people to compete in doing calculations in accounting for land, labour and grain yields.
The contest was between two mathematically literate contestants.
The ‘Rhind’ and ‘Moscow Mathematical Papyruses’ show that Ancient Egyptians, who were of course black Africans, could carry out mathematical operations such as multiplication, division, use fractions, compute volumes of boxes and pyramids, calculate surface areas of rectangles, triangles, circles and even spheres.
The ancient Egyptians understood basic Algebra, Geometry and could solve simple simultaneous equations.
There is evidence to show these ancient Africans used a decimal mathematical notation based on hieroglyphic signs for each power of 10 up to one million.
In writing numbers, each symbol was written as many times so as to add to the required total.
For example, for 80, the symbol for the number 10 would be written 8 times.
Ancient Egyptian wrote fractions as sums of several fractions. For example 2/5 was resolved to (1/3 + 1/15).
They had standard tables of values. Common fractions were written in a special ‘glyph’.
Egyptian mathematicians were familiar with the Pythagorean Theorem where a triangle had a right angle opposite the hypotenuse when its sides are in a 3:4:5 ratio.
They could estimate the area of a circle by subtracting 1/9 from its diameter and squaring the result.
Thus: Area = [(8/9)D]2 = (256/81)r2 = 3.16r2
The above is a reasonable approximation of pi.r2; formula for area of a circle.
The mathematical education of the Islamic world was said to be largely advanced by Timbuktu scholars.
Timbuktu University in West Africa was a leading centre of learning in those ancient times where black scholars excelled in the development of mathematical sciences such as arithmetic, algebra, geometry and trigonometry, among others. The Ghana and Mali empires housed these great centres of African learning.
Unfortunately, the illiterate barbarians from Europe and the Middle East, who had very little or no education, civilisation or culture, invaded and destroyed most of the centres of black African learning, destroying universities and libraries housing Africa’s accumulated wisdom of thousands of years.
Those developments set back African civilisation by centuries. The slave trade and European colonialism finished off what little scientific progress was still left in black Africa. The rest is poorly documented history!
From ancient times, Africans were in possession of advanced knowledge of fractal geometry and mathematics. Fractal geometry knowledge is found in a wide range of aspects of African life from art, social design structures, architecture, games, trade and divination systems.
The discovery that fractal mathematics was widespread in African societies led Ron Eglash, a Western writer, to remark that:
“When Europeans first came to Africa, they considered the architecture very disorganised and thus primitive. It never occurred to them that the Africans might have been using a form of mathematics that they had not even discovered”.
Binary numerical system was widely known in Africa before it was known in much of the world. It has been theorised that it influenced Western geomancy which is later thought to have led to the invention of the digital computer.
In short, mathematics has been an integral part of African science and philosophy. Great African mathematicians in both West and Northern Africa (Egypt) pioneered most of the mathematical concepts attributed to Greeks who only learnt them from compatriots who were schooled in the great African universities such as Timbuktu as well as in Egypt and Sudan.
Most other African societies have been employing highly sophisticated mathematical concepts which Western science has been most reluctant to accept or recognise.
In the next episode we shall look at engineering science and the construction of Africa’s great monuments by its indigenous peoples.

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