Africa is known as the continent that gave birth to basic and advanced mathematics. Historians of Africa and mathematics have written extensively on the use of numerals, algebra and geometry in the daily lives of Africans. The mathematical knowledge spread throughout the entire world, firstly through migrations out of Africa beginning around 30,000 BC, and secondly, through invasion of Africa by Europeans and Asians from 1700 BC.
The following are examples of ancient African mathematical instruments and devices upon which modern mathematics is based:
Lebombo Bone (35,000 BC)
The Lebombo Bone is the oldest known mathematical instrument, found in the Lebombo Mountaints in Swaziland. This 35,000-year old instrument is a baboon fibula turned into a measuring device with 29 distinct markings. It is believed that the 29 markings were used to track the lunar or menstrual cycles, or alternatively it could have been used as a measuring stick. The use of baboon bones as mathematical devices has been consistent across African cultures, suggesting that Africans held the baboon as sacred and associated the animal with the moon, mathematics and time.
Ishango Bone (20,000 BC)
Dating back to 20,000 BC, the Ishango Bone was discovered in the Democratic Republic of Congo. This bone is also a baboon fibula, but unlike the Lebombo Bone, the inscriptions are separated into clusters of markings that represent various quantities. When the markings are counted, they are all odd numbers with the left column containing all prime numbers between 10 and 20. The right column contains added and subtracted numbers. When both columns are calculated, they add up to 60.
Gebet’a ‘Mancala’ Game (700 BC to present)
This ancient counting board game, comes from Yeha in Ethiopia. However, it is believed that it may also have been used in Central Africa many years prior to its usage in Ethiopia 700 BC. The game is one of strategy. The objective is to capture a greater number of stones than the opponent. The game usually consists of a wooden board with two rows of six hole each, with two larger holes at either end.
‘Moscow’ Papyrus (2000 BC)
This papyrus derives its name from Moscow’s Pushkin State Museum of Fine Arts, where it is housed. It was purchased by Vladimir Golenishchev in the 1890s. The papyrus is written in hieratic from the 13th dynasty in Kemet, and is the world’s oldest example of use of geometry and algebra. The document contains about 25 mathematical problems, including: how to calculate the length of a ship’s rudder, the surface area of a basket, the volume of a frustum (a truncated pyramid), and various ways for solving unknowns.
‘Rhind’ Mathematical Papyrus (1650 BC)
The “Rhind’ Mathematical Papyrus dates back to 1650 BC. It was purchased by Alexander Rhind in 1858 and is presently housed in the British Museum. The text was found during excavations at the Ramesseum in Waset (Thebes), Southern Egypt. The first page contains 20 arithmetic problems, including addition and multiplication of fractions, 20 algebraic problems including equations. The second page shows how to calculate the volume of rectangular and cylindrical granaries, with pi (Π) estimated at 3.1605. There are also calculations for the area of triangles (slopes of a pyramid) and an octagon. The third page continues with 24 problems, including the multiplication of algebraic fractions, among others.
Timbuktu Mathematical Manuscripts (1200s AD)
Timbuktu in Mali may be the better known of ancient African knowledge. Timbuktu houses Sankore, one of the world’s oldest universities, which had libraries full of manuscripts written in Ajami (script similar to ‘Arabic’) in the 1200s AD. When Europeans and western Asians began visiting and colonising Mali from 1300s to 1800s, Malians began to hide the manuscripts in basements, attics and underground, fearing destruction and theft by foreigners. Many of the Timbuktu scripts were mathematical and astronomical in nature. The texts have recently been rediscovered and are being digitised and preserved with the assistance of the Government of South Africa. The texts, as many as 700,000 scripts, attest to the advanced mathematics and science in Africa well before European colonisation.
These are but a few examples that attest to the foundation of mathematics and science in Africa. It is through increasing awareness of this history that Africa can claim its rightful space in mathematical, scientific and technological developments. It will start once Africans respect their history and give it an appropriate place in their historical and cultural knowledge.