The World’s Three Oldest Mathematical Objects are From Africa

The three oldest mathematical objects are from Africa. There are two ishango bones, both from the Democratic Republic of Congo. The Lebombo bone is from a cave on the border between Swaziland and South Africa.

The Ishango bones are named for the Ishango area of the North-Kivu Province located in northeastern Democratic Republic of Congo in West Africa. It lies near the shores of the Semliki River in the Virunga National Park. The site of Ishango has been populated by humans for over 25,000 years.

In 1950 excavations were begun in the area by Jean de Heinzelin de Braucourt.  Zoologist Hubert Damas located the site originally where he discovered human remains along with bones with harpoon heads on them. After publishing his findings, Damas did not explore the area further.

The second Ishango bone was discovered first in 1959. It comes from the same layer of excavation as the first bone. It is 40 cm long with 90 notches categorized as “major” and “minor” due to length. It is has a six sided shape with a broken, hollow end.

the second ishango bone
The second Ishango Bone was excavated first in 1959. The examination of the first Ishango bone led to the second bone’s reevaluation.

The first Ishango bone led to a reanalysis of the second. It is the first Ishango bone which had markings which are considered the oldest known mathematical evidence. The craftsman who made it scrapped, thinned, and polished to such an extent that the original source of the bone is difficult to determine, although it is considered to be either the bone of a baboon or lion.

the first ishango bone
The first ishango bone from the shores of the Semliki River region of the Democratic Republic of the Congo is the oldest mathematical object.

One end of the first Ishango bone has a piece of quartz embedded in it. This indicates utility as cutting device, although its exact use is still unknown. The main area of the bone has 168 notches, in 16 groups and split in three rows. They cover three sides of the bone.

Both Ishango bones have been dated to approximately 20,000 before the present.

Near the border between South Africa and Swaziland, can be found Border Cave. The cave is located in the Lebombo Mountains at an elevation 365 m above sea level.

border cave from open street maps
Map showing Swaziland to the east near the Indian Ocean. Border Cave is in the lower east area of Swaziland near the border of South Africa.

The Lebombo bone is a baboon fibula found during an excavation done in the early 1970s. It has been dated to between 42,300 and 43,000 years old. The Lebombo bone has 29 markings along one edge. The notches have been allude to as being related to the cycle of the moon. Additionally, the notches have been suggested to identify a woman’s menstrual cycle.

lebombo bone
SI Figure 8. Baboon fibula from 1BS Lower B-C presenting an incomplete sequence of 29 notches
along the interosseous crest, and oblique incisions on the other aspects (top). Note the changes in the
section of the notches (bottom) indicating the use of different cutting edges. Scale = 1 cm.