The Ishango Bone: Craddle of Ancient Mathematics

Ishango Bones
Ishango Bones

Today, I would like to talk about the Ishango bone, or rather the first evidence of a calculator in the world.  Named after the place where it was found in the Democratic Republic of Congo (DRC), the Ishango bone is what is called a bone tool or the craddle of mathematics.  Dating as far back as 22000 years ago, in the Upper Paleolitic era, the Ishango bone is a dark brown bone which happens to be the fibula of a baboon, with a sharp piece of quartz affixed to one end for engraving It is the oldest attestation of the practice of arithmetic in human history. 

The Belgian geologist Jean de Heinzelin de Braucourt uncovered the bone buried in layers of volcanic ashes on the shores of Lake Edward in the Ishango region in DRC, near the border with Uganda.  The Ishango bones are actually two (2) bones of baboon, 10 to 14 cm long, with several incisions on each faces.  The smallest of the two bones was the first to be exposed at the Royal Belgian Institute of Natural Sciences in Brussels; it carries several incisions organized in groups of three columns.

The location of Ishango
The location of Ishango

The left column can be divided in 4 groups, with each group possessing 19, 17, 13, and 11 notches.  The sum of these being 60.  Those are the 4 successive prime numbers between 10 and 20.  This constitutes a quad of prime numbers.

The central column is divided in groups of 8.  By an approximate count, one can find (in the parenthesis, is the maximum number): 7 (8), 5 (7), 5 (9), 10, 8 (14), 4 (6), 6, 3.  The minimal sum is 48, while the maximal sum is 63.

The right column is divided into 4 groups, where each group has 9, 19, 21, and 11 notches.  The sum of these 4 numbers is 60.

The second bone has not been well-studied.  However, we know that it is composed of 6 groups of 20, 6, 18, 6, 20, and 8 notches.

The Ishango bones with their notches and the numbers
The Ishango bones with their notches and the numbers

The first bone has been subject to a lot of interpretation.  At first, it was thought to be just a tally stick with a series of tally marks, but scientists have demonstrated that the groupings of notches on the bone are indicative of a mathematical understanding which goes beyond simple counting.  In fact, many believe that the notches follow a mathematical succession. The notches have been interpreted as a prehistoric calculator, or a lunar calendar, or a prehistoric barcode.

Jean de Heinzellin was the first to consider the bone as a vestige of interest in the history of mathematics.  For instance, he noted that the numbers in the left column were compatible with a numeration system based on 10, since he saw that: 21 = 20 + 1, 19 = 20 – 1, 11 = 10 +1, and 9 = 10 -1.  These numbers are also prime numbers between 10 and 20: 11, 13, 17, 19.

The Ishango bones
The Ishango bones with the notches

Some other scientists such as the Belgian physical engineer proposed that the bones were probably a slide rule. While Alexander Marshack has indicated that the bones could refer to the oldest lunar calendar on earthClaudia Zaslavsky thinks that the author of the Ishango bone must have been a woman following the lunar phases to calculate her menstrual cycle.  However, the second bone completely rules out the lunar calendar theory, and favors more the numeration system.

All said, it is amazing to realize that there were mathematicians 20,000 years ago on the African continent.  It is so great to realize that my ancestors, on the shores of Lake Edouard, were actually brilliant scientists playing with prime numbers.  Whether it was a woman calculating her menstrual cycle, or some brilliant tribe astronomer, it feels so good to know that the paleo-mathematicians of Ishango already knew prime numbers.  They were a great civilization long before the pharaohs of Egypt. Thus, in reality, the Ishango bone is the oldest table of prime numbers in the world. To read more, check out Mathematicians of the African Diaspora,, the Prime Glossary, and Wolfram Mathworld.

30 thoughts on “The Ishango Bone: Craddle of Ancient Mathematics

  1. Pingback: SCIENCE + VIDEO: The Ishango Bone | Neo-Griot

  2. Brilliant. Having been trained in both Prehistory and Anthropology, the analysis of this find scotches two widely held misapprehensions in one grand sweep: that Paleolithic man’s intellect can be equated with the simplicity of his toolkit, and that African cultures are in some way inferior. Let’s hear a big cheer for the ingenuity of humankind that evolved in, and dispersed from the Great Rift – because that means all of us.

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  6. Riyad

    Actually, very few mathematicians looked at it, and the fact that they do not agree should make us suspicious. Olivier Keller has written an article which should temper the enthousiasm:

    Click to access ishango-analysis.pdf


    The big problem here is : “what you desire to see, you will see”. You desire to see higher mathematics? Then your mind will make you see it, even if it is not there.

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      1. steve neblett

        So blacks possessed mathematics twenty thousand years ago, while at that time whites in Europe and the uk were crawling on their hands and knees eating their own excrement! The evil tragedy is, when whites eventually came in to contact with mathematics they would come to use it to count African slaves as they were boarded on to ships bound for America and Europe. its a fucking disgrace.

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  10. B.Mann

    Good job, just stop of the iceberg for any further information, feel free to contact us about any question of your own choice.

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  14. I just recently heard about that bone when I did research for concepts which involve innovators. That’s phenomenal that something my ancestor’s used to do math problems millennia before Pythagoras was even born. Strike that as a tally on the Ishango bone for something I didn’t learn in school. Just think that calculators or calendars could’ve started out with this baboon bone. Wow.

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