The Lebombo Bone
The Lebombo bone is one of the oldest mathematical artifacts known to man. The bone has been dated to about 35,000 B.C. and was discovered near Border Cave in the Lebombo Mountains between South Africa and Swaziland.
The Lebombo bone is a small piece of the fibula of a baboon marked with 29 clearly defined notches.
The artefact's use is not known but the tally marks on the bone suggests it may have been used as a lunar phase counter would make AFRICAN WOMEN the first mathematicians since keeping track of menstrual cycles requires a lunar calendar.
Interestingly the Lebombo bone resembles calendar sticks still used by Bushmen in Namibia.
The Ishango Bone
The Ishango bone,is the second oldest mathematical artifact in existence .and it is now believed to be more than 20,000 years old The Ishango bone is a dark brown length of bone, the fibula of a baboon with a sharp piece of quartz affixed to one end.
It was discovered in the area of Ishango near the Semliki River (which forms part of the headwaters of the Nile River) in the Democratic Republic of the Congo. The bone was found among the remains of a small community that fished and gathered in that area of Africa, buried after a volcanic eruption.
The Ishango bone was first thought to be a tally stick, as it has a series of as tally marks carved into three columns running the length of the tool. The central column begins with three notches, and then doubles to 6 notches. The process is repeated for the number 4, which doubles to 8 notches, and then reversed for the number 10, which is halved to 5 notches.
These numbers may not be purely random and instead suggest some understanding of the principle of multiplication and division by two.
Furthermore, the numbers on both the left and right column are all odd numbers (9, 11, 13, 17, 19 and 21). The numbers in the left column are all of the prime numbers between 10 and 20 (which form a prime quadruplet), while those in the right column consist of 10 + 1, 10 − 1, 20 + 1 and 20 − 1. The numbers on each side column add up to 60, with the numbers in the central column adding up to 48.
Claudia Zaslavsky an ethnomathematician (studies the relationship between mathematics and culture) has suggested that this may indicate that the creator of the tool was a woman, tracking the lunar phase in relation to the menstrual cycle.
Another researcher Alexander Marshack examined the Ishango bone microscopically, and concluded that it may represent a six-month lunar calendar but it was debated that Marshack over interprets the data and that the evidence does not support lunar calendars.
Interestingly, author Peter Rudman argues that the development of the concept of prime numbers could have come about only after the concept of division, which he dates to after 10,000 BC, with prime numbers probably not being understood until about 500 BC. He also writes "no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of 10."
The Ishango bone is on permanent exhibition at the Royal Belgian Institute of Natural Sciences, Brussels, Belgium.
References:
Ian Stewart: Taming the Infinite: The Story of Mathematics from the First Numbers to Chaos Theory
http://www.math.buffalo.edu/mad/Ancient-Africa/lebombo.html
https://originalpeople.org/ishango-bone-worlds-oldest-math-tool/
https://www.daviddarling.info/encyclopedia/L/Lebombo_bone.html
https://proofwiki.org/wiki/Book:Ian_Stewart/Taming_the_Infinite
