African Mathematics History - the earliest counting system
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African Mathematics

African people were the first people anywhere in the world to use counting to keep track of their things, or maybe to keep track of time. Around 35,000 BC, somebody in South Africa made the earliest known counting stick, or tally stick, and left it in Lebombo Cave. Somebody cut 29 notches into the stick.

Lebombo tally stick
Lebombo tally stick (35,000 BC)

We don't know what they were counting. Some people think maybe they were counting the days from one full moon to the next full moon, but it could just as well have been 29 people, or 29 baskets of nuts, or something else. But we can see that by 35,000 BC people in South Africa had the idea of keeping records by making marks.

Ishango tally stick
Ishango Tally Stick

Further north, in East Africa, people were also using tally sticks. About 20,000 BC, somebody at Ishango, at the head of the Nile River, made another tally stick. This one has groups of marks. Possibly someone used the same stick to keep track of a bunch of different things. Or, maybe the person was doing some kind of math, or keeping some kind of calendar.

Around 7000 BC, people in Egypt and further south in Sudan began to use clay tokens to count things. They probably got the idea from West Asia, where people began using tokens earlier.

By 3000 BC, people in Egypt were using hieroglyphs to write down very large numbers. Soon afterwards, they were also using geometry to figure out how to build the Pyramids.

cone and plane
A cone intersecting a plane

When the Phoenicians colonized North Africa about 800 BC, they brought with them West Asian systems of counting and writing numbers that were used for many centuries all over North Africa. Then when the Romans came, they opened schools that taught North African students about Greek geometrical proofs. One important teacher and researcher from the Roman period was Hypatia, a woman from Alexandria in Egypt who worked on proving things about the geometry of cones and what happened when a cone was intersected by a plane. In 415 AD angry Christians killed Hypatia (hi-PAY-sha) because she would not become a Christian.

Arab invaders took over most of North Africa and East Africa by about 900 AD. The Arabs brought with them their religion, Islam, and new ways of counting that they had learned through trade with India. At Kairouan, in the 800s AD, Ab Sahl al-Qayrawn, a mathematician, wrote a book called the "Book on Indian Calculation" that explained how to use zero as a place-holder. This was the most important change that the Arabs brought. Zero made it much easier to do math. Soon most people in North Africa and East Africa used the Indian number system. The combination of Greek geometry with Indian numbers led to many new mathematical ideas.

Not all Africans used the Arab counting system. Around 1000 AD, people in West Africa were using a number system which was partly in base ten and partly in base twenty. For instance, in order to say "50", Yoruba people said "Twenty times three, take away ten". Or to say "318", people said "400-(20x4)-2". The Indian/Arab system expressed all of their numbers using addition (twenty+four), but Yoruba (your-OO-bah) people also used subtraction to express numbers. People in West Africa also used cowrie shells for counting, much like the clay tokens of ancient West Asia. They fastened these cowrie shells together in strings of forty shells.

The new Indian number system led mathematicians to many new exciting discoveries. In the 1100s and 1200s, several mathematicians were working in North Africa whose names we know. The earliest was al-Qurash, who worked on algebra, and wrote a commentary on the work of the Egyptian mathematician Abu Kamil. Al-Qurash also invented a new method for reducing fractions. Al-Qurash died in 1184 AD.
Another North African mathematician, al-Hassar, about the same time developed the modern way of writing fractions, with a bar separating the top from the bottom, like 1/2 or 2/7. Al-Hassar also wrote textbooks in Arabic about how to add whole numbers and fractions, how to calculate square roots and cube roots, and prime numbers. These are probably the books that Fibonacci used when he learned math in North Africa, to bring back to Europe and teach people there.
Ibn al-Yasamin was a black Berber mathematician from Marrakech who wrote about how to use the new Indian number system in geometry, to calculate areas. He also lived in the 1100s AD. In the 1200s AD, Ibn Muncim and Ibn al-Bann did some research on the use of number systems other than base ten, possibly influenced by their country's interaction with the Yoruba people to their south, who counted using base twenty as we have seen.

Many mathematical books travelled south from Marrakesh and Kairouan to Timbuktu in West Africa, so that these algebraic ideas were also known there. Some mathematicians probably also worked in Timbuktu, but we don't know their names or their work.

Numbers in ancient Mesopotamia
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