an old Mathematical Object

Most histories of mathematics devote only a few pages to Ancient Egypt and to northern Africa during the 'Middle Ages´. Generally they ignore the history of mathematics in Africa south of the Sahara and give the impression that this history either did not exist or, at least, is not knowable, traceable, or, stronger still, that there was no mathematics at all south of the Sahara. In history, to Europeans, even the Africanity of Egyptian mathematics is often denied or suffers eurocentric views of conceptions of both 'history' and of 'mathematics' form the basis of such views.

High in the mountains of Central Equatorial Africa, on the borders of Uganda and Zaire lies Lake Edward, a source of the Nile. It is a small lake (about 30 miles by 60 miles).

click map to download an expanded view

Though the area is sparsely populated today, approximately 25,000 (update from 9,000) years ago by the shores of the lake lived a small community that fished, gathered, and grew crops The settlement only existed a few hundred years before being buried in a volcanic eruption. The place where their remains were found (1960) has a name now given to these people - Ishango. Among their remains is the second oldest mathematical object (the oldest is here) in Africa.

Some say that the Ishango Bone is the oldest table of prime numbers. Marshack later concluded, on the basis of his microscopic examination, that it represented a six-month lunar calendar.

prime numbers or menstral calendar

The most interesting, of a large number of tools discovered in 1960 at Ishango, is a bone tool handle called the Ishango Bone (now located on the 19th floor of the Royal Institute for Natural Sciences of Belgium in Brussels, and can only be seen on special demand). At one end of the Ishango Bone is a piece of quartz for writing, and the bone has a series of notches carved in groups (shown below). It was first thought these notches were some kind of tally marks as found to record counts all over the world. However, the Ishango bone appears to be much more than a simple tally. The markings on rows (a) and (b) each add to 60. Row (b) contains the prime numbers between 10 and 20. Row (a) is quite consistent with a numeration system based on 10, since the notches are grouped as 20 + 1, 20 - 1, 10 + 1, and 10 - 1. Finally, row (c) seems to illustrate for the method of duplication (multiplication by 2) used more recently in Egyptian multiplication. Recent studies with microscopes illustrate more markings and it is now understood the bone is also a lunar phase counter. Who but a woman keeping track of her cycles would need a lunar calendar? Were women our first mathematicians?

Ishango Bone Exhibition

Space Odessy of the Ishango bone

Ishango Operation in Brussels

BACK TO The Ancients in Africa

The following dating information was sent by email from Professor Charles Finch:

The site where the Ishango Bone was found was re-dated by Alison Brooks more than a dozen years ago and found to be 25,000 years old rather than the original estimate of 8,500 years. However, the Lembombo Bone in Swaziland is still 10,000 years older, consistent with iron ore mining there going back 43,000 years ago. Proto-mathematics begins in Paleolithic Central and Southern Africa.

references:

Shreeve, "The Dating Game," Discover, September 1992, pp. 76-83.
Alison Brooks, "Dating and Contex of Three Middle Stone Age Sites with Bone Points in the Upper Semliki Valley, Zaire," Science, 4/28/95, pp. 548-52.

references for this web page:

AMUCHMA-NEWSLETTER-9: http://www.math.buffalo.edu/mad/AMU/amu_chma_09.html
J. de Heinzelin, Ishango, Scientific American, 206:6 (June 1962) 105--116.
J. Shurkin, Engines of the mind: a history of the computer, W. W. Norton & Co., 1984., p21
J. Bogoshi, K. Naidoo and J. Webb, The oldest mathematical artifact, Math. Gazette, 71:458 (1987) 294.
Claudia Zaslavsky, Women as the First Mathematicians, the Women in Mathematics Education Newsletter,Volume 7 Number 1, January 1992.

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Most histories of mathematics devote only a few pages to Ancient Egypt and to northern Africa during the 'Middle Ages´. Generally they ignore the history of mathematics in Africa south of the Sahara and give the impression that this history either did not exist or, at least, is not knowable, traceable, or, stronger still, that there was no mathematics at all south of the Sahara. In history, to Europeans, even the Africanity of Egyptian mathematics is often denied or suffers eurocentric views of conceptions of both 'history' and of 'mathematics' form the basis of such views. High in the mountains of Central Equatorial Africa, on the borders of Uganda and Zaire lies Lake Edward, a source of the Nile. It is a small lake (about 30 miles by 60 miles).			click map to download an expanded view
Though the area is sparsely populated today, approximately 25,000 (update from 9,000) years ago by the shores of the lake lived a small community that fished, gathered, and grew crops The settlement only existed a few hundred years before being buried in a volcanic eruption. The place where their remains were found (1960) has a name now given to these people - Ishango. Among their remains is the second oldest mathematical object (the oldest is here) in Africa. Some say that the Ishango Bone is the oldest table of prime numbers. Marshack later concluded, on the basis of his microscopic examination, that it represented a six-month lunar calendar. prime numbers or menstral calendar



The most interesting, of a large number of tools discovered in 1960 at Ishango, is a bone tool handle called the Ishango Bone (now located on the 19th floor of the Royal Institute for Natural Sciences of Belgium in Brussels, and can only be seen on special demand). At one end of the Ishango Bone is a piece of quartz for writing, and the bone has a series of notches carved in groups (shown below). It was first thought these notches were some kind of tally marks as found to record counts all over the world. However, the Ishango bone appears to be much more than a simple tally. The markings on rows (a) and (b) each add to 60. Row (b) contains the prime numbers between 10 and 20. Row (a) is quite consistent with a numeration system based on 10, since the notches are grouped as 20 + 1, 20 - 1, 10 + 1, and 10 - 1. Finally, row (c) seems to illustrate for the method of duplication (multiplication by 2) used more recently in Egyptian multiplication. Recent studies with microscopes illustrate more markings and it is now understood the bone is also a lunar phase counter. Who but a woman keeping track of her cycles would need a lunar calendar? Were women our first mathematicians?

Ishango Bone Exhibition	Space Odessy of the Ishango bone
Ishango Operation in Brussels
	BACK TO The Ancients in Africa