Mathematics in Africa has been Lost in the History Books – It’s Time To Remind the World Its Rich Past
- Africa is home to the world’s earliest known use of measuring and calculation, confirming the continent as the birthplace of both basic and advanced mathematics.
- The oldest mathematical instrument is the Lebombo bone, a baboon fibula used as a measuring device and so named for its location of discovery in the Lebombo mountains of Swaziland.
- The world’s oldest evidence of advanced mathematics was also a baboon fibula that was discovered in the present-day Democratic Republic of Congo and dates to at least 20,000 BC.
- The oldest known evidence of the ancient counting board game, Gebet’a or “Mancala” as it is more popularly known, comes from Yeha (700 BC) in Ethiopia, it was also used in Central Africa.
- It is impossible to quantify how much the slave trade impacted the reputation of African mathematics, but we are slowly regaining a better perspective.
Africa is home to the world’s earliest known use of measuring and calculation, confirming the continent as the birthplace of both basic and advanced mathematics. Thousands of years ago, Africans were using numerals, algebra, and geometry in daily life. This knowledge spread throughout the entire world after a series of migrations out of Africa, beginning around 30,000 BC, and later following a series of invasions of Africa by Europeans and Asians (1900 BC-present).
In Trinidad and Ghana, it’s known as susu. In Senegal and Benin, it’s tontines. In Nigeria, where it began in the 1700s, it’s esusu. Whatever you call it, this system of large-scale money-pooling for mutual benefit shows that Africa has never had a problem with mathematics.
When we learn the history of mathematics, we tend to learn about the achievements of Greek, Hindu, Chinese and Arabic civilizations. If we learn anything about African mathematics, it’s almost entirely about Egypt. But sub-Saharan Africa has a rich mathematical history too – and it is possible that the world’s museums hold the key to bringing it back to life.
Some of the evidence comes from those who were in contact with slaves and slavers. European captains of slave-trading ships, for instance, marveled at the mathematical abilities of the African traders they encountered. Sailors who made bargains with African slave dealers described them as “sharp arithmeticians” who could skillfully convert currencies and exchange rates in their heads. According to one account, a broker might have 10 slaves to sell, “and for each of these, he demands 10 different articles. He reduces them immediately by the head into bars, coppers, ounces, according to the medium of exchange that prevails in the part of the country in which he resides, and immediately strikes the balance”.
That shouldn’t surprise us when we look at the number system used in the Yoruba language spoken in what is now Nigeria. The phrase for “forty-five” translates as “take five and 10 from three twenties”. It might sound cumbersome, but it is a sign of a person’s being comfortable with subtraction and multiplication. The Yoruba started esusu too. Records of complex financial systems in pre-colonial Nigeria – banks and mutual societies, effectively – suggest that dealing with complicated accounts, loans, credits, and debits was just part of everyday life. These were not people who were uncomfortable with mathematics.
The fact that the instructions for these systems of calculation were passed on by word of mouth makes it all the more impressive, but it also meant that the slave trade decimated their use. We know, for example, that at least one brilliant African arithmetician ended up enslaved in America. His given English name, after being stolen away from Africa at the age of 14, was Thomas Fuller. However, he was also known as the Virginia Calculator because of his extraordinary arithmetical skills. It is impossible to say how many more great mathematical minds were stolen away to Europe, the Caribbean, and the Americas, their skills and tutelage lost to those who were left behind.
It is also impossible to quantify how much these losses impacted the reputation of African mathematics and contributed to 19th- and 20th-century notions of the intellectual inferiority of the African people. However, we are slowly regaining a better perspective.
Recently, for example, a French researcher has shown that the Akan people, who lived in the region we know today as Ghana and Côte d’Ivoire, developed their own number system, and did not borrow Arab and Persian systems as historians had suggested. Jean-Jacques Crappier found the evidence in the Akan gold-weights that were used to weigh gold powder – the prevailing currency of the region we know today as Ghana and Côte d’Ivoire – during trades with the Arabs, Portuguese, Dutch, and English from the 15th to the late 19th centuries.
To carry out the study, which was published last year, Crappier pulled together a team of collectors and mathematicians. Between them, they determined the masses of as many gold-weights as they could lay their hands on. The team ended up with records of 9,301 weights from museums and private collections around the world. The distribution of their masses showed that the system was based on the weights of West African seeds, not Arab measures, and they were used in sophisticated ways that helped convert between the various currencies of the Akan’s trading partners.
Measuring and Counting
Lebombo Bone (35,000 BC)
The oldest mathematical instrument is the Lebombo bone, a baboon fibula used as a measuring device and so named for its location of discovery in the Lebombo mountains of Swaziland. The device is at least 35,000 years old. Judging from its 29 distinct markings, it could have been used to either track menstrual or lunar cycles or used merely as a measuring stick.
It is rather interesting to note the significance of the 29 markings (roughly the same number as the lunar cycle, i.e., 29.531 days) on the baboon fibula because it is the oldest indication that the baboon, a primate indigenous to Africa, was symbolically linked to Khonsu, who was also associated with time. The Kemetic god, Djehuty (“Tehuti” or “Toth“), was later depicted as a baboon (also an ibis) and is usually associated with the moon, math, writing, and science. The use of baboon bones as mathematical devices has been continuous throughout all of Africa, suggesting Africans always held the baboon as sacred and associated with the moon, math, and time.
Ishango Bone (20,000 BC)
The world’s oldest evidence of advanced mathematics was also a baboon fibula that was discovered in the present-day Democratic Republic of Congo and dates to at least 20,000 BC. The bone is now housed in the Museum of Natural Sciences in Brussels. The Ishango bone is not merely a measuring device or tally stick as some people erroneously suggest. The bone’s inscriptions are clearly 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, and the right column containing added and subtracted numbers. When both columns are calculated, they add up to 60 (nearly double the length of the lunar or menstrual cycle).
Gebet’a or “Mancala” Game (700 BC-present)
Although the oldest known evidence of the ancient counting board game, Gebet’a or “Mancala” as it is more popularly known, comes from Yeha (700 BC) in Ethiopia, it was probably used in Central Africa many years prior. The game forces players to strategically capture a greater number of stones than one’s opponent. The game usually consists of a wooden board with 2 rows of 6 holes each, and 2 larger holes at either end. However, in antiquity, the holes were more likely to be carved into stone, clay, or mud-like the example from Medieval Aksum, shown at right. More advanced versions found in Central and East Africa, such as the Omweso, Igisoro, and Bao, usually involve 4 rows of 8 holes each.
Fractions, Algebra and Geometry
“Moscow” Papyrus (2000 BC)
Housed in Moscow’s Pushkin State Museum of Fine Arts, the so-called “Moscow” papyrus, was purchased by Vladimir Golenishchev sometime in the 1890s. Written in hieratic from perhaps the 13th dynasty in Kemet, the papyrus is one of the world’s oldest examples of the use of geometry and algebra. The document contains approximately 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 of solving for unknowns.
“Rhind” Mathematical Papyrus (1650 BC)
Purchased by Alexander Rhind in 1858 AD, the so-called “Rhind” Mathematical Papyrus (shown below) dates to approximately 1650 BC and is presently housed in the British Museum. Although some Egyptologists link this to the foreign Hyksos, this text was found during excavations at the Ramesseum in Waset (Thebes) in Southern Egypt, which never came under Hyksos’ rule. Written by the scribe, Ahmose, in the “Hieratic” script, the text reads as follows:
“Accurate reckoning for inquiring into things, and the knowledge of all things, mysteries…all secrets… This book was copied in regnal year 33, month 4 of Akhet, under the majesty of the King of Upper and Lower Egypt, Awserre, given life, from an ancient copy made in the time of the King of Upper and Lower Egypt Nimaatre. The scribe Ahmose writes this copy…”
The first page contains 20 arithmetic problems, including addition and multiplication of fractions, and 20 algebraic problems, including linear equations. The second page shows how to calculate the volume of rectangular and cylindrical granaries, with pi (Π) estimated at 3.1605. Tere 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.
Timbuktu Mathematical Manuscripts (1200s AD)
Timbuktu in Mali is home to one of the world’s oldest universities, Sankore, which had libraries full of manuscripts mainly written in Ajami (African languages, such as Hausa in this case, written in a script similar to “Arabic“) in the 1200s AD. When Europeans and Western Asians began visiting and colonizing Mali from the 1300s-1800s AD, Malians began to hide the manuscripts in basements, attics, and underground, fearing destruction or theft by foreigners. This was certainly a good idea, given Europeans’ history of stealing and/or destroying texts in Kemet and other areas of the continent. Many of the scripts, such as the one shown below, were mathematical and astronomical in nature. In recent years, as many as 700,000 scripts have been rediscovered and attest to the continuous knowledge of advanced mathematics and science in Africa well before European colonization.
We can see the legacy of centuries of African mathematics in some of the games that are still played throughout the continent. One, known by various names such as Ayo, Mankala, or Lela, might look to western eyes a little like backgammon, but it involves using lightning-fast arithmetic skills that have long daunted casual observers.
There is almost certainly much more to bring to light. Crappier is now looking to collaborate with African scholars to delve deeper into the implications of his team’s discovery about the Akan gold-weights, for example. There are plenty of open questions, he says: how did the Akan people develop their sophisticated trading system? How did they manufacture the necessary weights and balances, and just how sensitive and accurate were they? The answers to these and other questions, which may still be scattered among the world’s museum collections, will surely help us rediscover the impressive but forgotten truth about African mathematical innovation.
Michael Brooks’s latest book is The Art of More: How Mathematics Created Civilisation