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In 1960, a strange bone cutting tool was discovered during the
excavation of a prehistoric site in Zaire.
On the bone tool are a series of markings arranged in regular
patterns. They appear to exhibit a lot of possible mathematical
structure. There are three rows of markings; on each row the
markings are grouped into clusters as follows:
Row A: $19, 17, 13, 11$
Row B: $7, [5, 5, 1, 9], 8, 4, [6, 3]$ (we are not sure how the
scratches in the brackets were grouped)
Row C: $9, 19, 21, 11$
(In row B, the groupings of some
of the scratches is not very clear: the $[5, 5, 1, 9]$ part might
also be $[10, 10]$ or $[10, 1, 9]$ or $[5, 5, 10]$. Similarly, the
$[6, 3]$ scratchings might be grouped into $$
Investigate these numbers and their properties.
Do you think that they are just random, or can you see any
How do you think that the scratchings should be grouped?
Can you create a hypothesis as to the meaning of the scratches or
why they might have been made?
Why are you making a hypothesis and not a proof?
Would it ever be possible to be certain of the meanings of the
Imagine that you find another similar bone which was created
according to your rules. What different patterns of scratches could
NOTES AND BACKGROUND
This bone is around 20,000 years old and is one of the oldest known
artefacts exhibiting mathematical structure. Although there are
many theories about the meaning of the scratches nobody knows for
sure what their purpose is. Perhaps if another similar artefact
were found in reality then evidence for the different sorts of
hypotheses would grow. It might even be that you will come up with
a really clear explanation of all of the scratches which nobody has
yet thought about!
You might like to read about this artefact on the wikipedia
which the images were taken.
A conference was held in 2007 to discuss the Ishango bone. Read
more about this here:
. Older readers might also like to read a professional
archeological assessment of this problem
Mathematics in (central) africa before colonisation
Another interesting mathematical artefact, which has a more
convinving explanation, is analysed in the problem Babylon