The Ishango bone

 The Earliest example of Mathematics in the world found in Africa which is at least 20,000 years old.

The Ishango bone  Has an ‘arrangement of the notches engraved on the handle of the bone, and the numbers in each group, these numbers are clearly not casual. Analysis of their numerological properties led people to conclude that the artifact is not a simple tally stick, but a kind of calculator based on special number systems. Each of the groupings in the left and right columns contains an odd number of notches (9, 11, 13, 17, 19, and 21), while the numbers contained in the first column are precisely the four prime numbers between 10 and 20. From facts such as these it is thought that the groupings represent numbers and the whole design represents a system of reckoning based upon counting by digits. It has also thought that the bone could have been used for time reckoning, following the observable course of the moon over a period of about 5½ synodic (lunar phase cycle) months, based on a period of a double lunation of 59–60 days.

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the Lebombo Bone is the oldest tally stick (and oldest mathematically related artifact!) dating to around 35,000 BC.  Originally a fibula of a Baboon, it has 29 notches carved into it, possibly to keep track of the lunar cycle or a woman’s menstrual cycle, probably one of the earliest systems of calendar keeping that remains today.  It was found in Africa in present day Swaziland.


The Ishango Bone dates from before 20,000 years ago, found near Lake Edward, is a bit more cryptic in its message.  It has a piece of quartz on one end probably used for writing, and it bears a series of mostly-odd numbers etched into it, except its center column, which appears to group integers with their doubles, 4 and 8, 5 and 10.  Perhaps doubles and halves were early explorations into multiplication and division, and odd numbers being the curious ones which don’t half evenly.


Ishango Chamber Choir - John Tavener, Svyati