While I was taking a History of Mathematics course, I came upon references to the oldest mathematical object known to exist.  Even making this statement comes with some controversy.  What makes something a "mathematical object"?  There are older examples of counting.  Some of the cave paintings and an older fragment of bone have markings suggesting the people were counting the days of the lunar cycle.  This piece is different in that it seems to have had more than just counting as its purpose.

The Ishango Bone

This piece of bone, which dates from around 20,000 years ago, has three sets of markings along its length.  Here is a diagram:

Notice the numbers in each of the three rows:

9 + 19 + 21 + 11    = 60                     

60 is one of the most "divisible" numbers below 100.  It can be evenly divided by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30.

19 + 17 + 13 + 11 = 60              

Two separate groups of numbers that add up to 60.  That cannot be an accident.

7 + 5 + 5 + 10 + 8 + 4 + 6 + 3 = 48      48 is also very divisible.  It can be evenly divided by 1, 2, 3, 4, 6, 8, 12, 16, and 24.

Look again at row a.  Do you notice anything about those numbers?  Rearranged they are 10-1, 10+1, 20-1, 20+1. 

Now look at row b. 

What is unusual about those numbers?  11, 13, 17, and 19 are all the Prime numbers between 10 and 20. 

Why were people 20,000 years ago concerned with Prime Numbers, those which cannot be divided into smaller equal parts?  How did the three sets relate to one another?  What prompted these people to create and save this object?  How did it help them to survive that it was worth the time they put into making it?

If you have some ideas on the answer to this, please contact me.