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Perhaps the oldest mathematical artifact in existence, the Ishango Bone

Os_d'Ishango_IRSNB

The Ishango Bone (above) was unearthed in 1950 in the then Belgian colony of the Congo (now the Democratic Republic of Congo). It was discovered by the Belgian anthropologist Jean de Heinzelin de Braucourt (1920-1998) and named after the region in which it was found. The bone, probably a fibula of a baboon, large cat, or other large mammal, has been dated to the Upper Paleolithic Period of human history, approximately 20,000-25,000 years ago. It is 10 cm long and bears an articulated, organized series of notches readily identifying it, to many observers, as a tally stick. However, its original purpose remains a subject of debate. The Ishango Bone is now housed at the Museum of Natural Sciences in Brussels, Belgium, with whose cooperation the image above was obtained.

The artifact was first estimated to have originated between 9,000 BC and 6,500 BC.  However, the dating of the site where it was discovered was re-evaluated, and it is now believed to be more than 20,000 years old.  The Ishango bone is on permanent exhibition at the Royal Belgian Institute of Natural Sciences, Brussels, Belgium.

Mathematical calculations

Left column

Center column

Right column

Some believe the three columns of asymmetrically grouped notches imply that the implement was used to construct a numeral system. 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 anddivision by two. The bone may therefore have been used as a counting tool for simple mathematical procedures. 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.    In the book How Mathematics Happened: The First 50,000 Years, Peter Rudman argues that the development of the concept of prime numbers could only have come about 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 that “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.”

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Civilization

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