Eduardo Mondlane University, Maputo, Mozambique, 25.06.1987

Chairman: Paulus Gerdes (Mozambique)

Secretary: Ahmed Djebbar (Algeria)

Members: Georges Njock (Cameroon), Maasouma Kazim (Egypt), J. Mutio (Kenya), Lawrence Shirley (Nigeria), Geoffrey Mmari (Tanzania), Mohamed Souissi (Tunisia), Claudia Zaslavsky (USA)



0. "Welcome"

1. Formation of AMUCHMA

Objectives of AMUCHMA

2. Meetings

2.1 2nd Pan-African Congress of Mathematicians
2.2 First International Colloquium in Alger on the History of Arabic
2.3 International Colloquium on the History of Fractions (Paris)
2.4 Papers Presented at Recent Meetings

3. Theses in Progress or Completed

4. Current Research Interests

5. Seminars

6. Education

7. Have You Read ?

8. Notes and Queries

9. Announcements

10. ADDRESSES of scholars and institutions mentioned in this newsletter


Do you want to receive the next AMUCHMA-Newsletter



From the President's Desk

It is my great pleasure and privilege to write this "welcome" for the first edition of the newsletter of the AMU Commission on the History of Mathematics in Africa (AMUCHMA).

Since the creation of this Commission under the dynamic leadership of Professor Paulus Gerdes by the current Executive Committee of the African Mathematical Union, the commission has demonstrated clearly its intention to make effective contribution to our knowledge of the history of Mathematics in Africa through conscientious implementation of its declared programme of activities including the publication of a Newsletter which is now a reality.

I should like to congratulate Professors Gerdes and Djebbar for the successful publication of this first newsletter which contains sections on the aims and objectives of the Commission, papers presented at recent conferences and congresses, current research interest of workers in areas related to History of Mathematics in Africa as well as an interesting section titled '1Have you read?".

In bidding this newsletter a hearty welcome, I should like to commend it very highly to the Mathematical, Historical, Archaeological and other relevant communities in Africa and other continents as a medium for exchange of news, ideas and information on various aspects of History of Mathematics in Africa.

Long Live A.M.U.!. Long Live AMUCHMA.!

Professor A. 0. Kuku

President African Mathematical Union



At the 1986 2nd Pan-African Congress of Mathematicians in Jos (Nigeria), the newly elected Executive Committee of the African Mathematical Union (A.M.U.) decided to create an A.M.U. Commission on the History of Mathematics in Africa (AMUCHMA) with the following objectives:

a) to improve communication among those interested in the history of mathematics in Africa;

b) to promote an active cooperation between historians, mathematicians, archaeologists, ethnographers, sociologists, etc., doing research in or related to the history of mathematics in Africa;

c) to promote research in the history of mathematics in Africa and the publication of its results in order to contribute to the demystification of the still dominant eurocentristic bias in the historiography of mathematics;

d) to cooperate with any and all organisations pursuing similar objectives.

The main forms of activity of the AMUCHMA- are as follows:

a) publication of a newsletter (two times a year);

b) setting-up a documentation centre;

c) organisation of lectures on the history of mathematics at national, regional, continental and international congresses and conferences.



Report by L. Shirley

One of the sections of the 2nd Pan-African Congress of Mathematicians (23-29.3.1986, University of Jos, Jos, Nigeria) was dedicated to the history of mathematics in Africa. Five papers were presented.

Enukoha, I.O.: Counting and geometry in traditional Ibibio and Efik societies
Enukoha has earlier studied traditions of Igbo mathematics and now, as he lives in the Efik-Ibibio culture area, he has begun the study of mathematics of Efik-Ibibio traditions. His paper concentrated on describing the Efik-Ibibio counting words system, which is a mixture of base five and base ten, and the local concepts of lines and shapes.

Gerdes, P.: On the reconstruction of the history of geometrical thinking in Africa
Gerdes presented a stimulating demonstration of links between Mozambique traditional basket-weaving patterns and concepts of geometry, including a remarkably novel approach to the discovery and proof of "Pythagoras" (so-called) theorem.

Kani, A.M.: The history of 'Ilm al-Hisab' (arithmetic) in Nigeria
Kani pointed out to aspects of mathematics in Islam, especially as studied by the Islamic scholars of pre-colonial northern Nigeria, and notably by Muhammed ibn Muhammed al Katsinawi (c.1740) who worked on 'magic squares' and numerological patterns.

Ojoade, J.O.: The number 'three' in African lore with foreign analogies
The paper of Ojoade had less history and more culture, a humorously comprehensive run through the many ways the number 'three' occurs in Nigeria and world culture.

Shirley, L.H.: Ethnomathematics in the history of African mathematics
Shirley had done the organisation and coordination of the history section of the Congress. In his paper he used the concept of 'ethnomathematics' to take a broader view of mathematics, including cultural aspects, local technology, and everyday applications, in considering the history of mathematics. By using such local aspects in mathematics not only does the history become more relevant to African students, but also the mathematics itself is made more real.


Report by A.Djebbar

The 1st International Colloquium in Alger on the History of Arabic Mathematics was held at the 'École Normale Superieure', Kouba-Alger, Algeria, December 1-3, 1986. The Colloquium was organized under the auspices of the Ministry of Higher Education. The opening session took place in the presence of the Minister of Higher Education, the Secretary of Culture of the F.L.N. Party and the responsible in charge of the High Council for the Arabic language. About 200 scholars, high school teachers, 4th year students, inspectors of mathematics and journalists attended the Colloquium. Television, radio and journals gave great publicity to the event.

Twelve papers (8 in Arabic, 4 in French) were contributed. They dealt with four great themes:

1. Mathematics in the Arabic-Islamic civilization (C.Bouamrane, Algeria);
2. Arabic mathematics of the East (M. Abdeljaoud & H. Hadfi, Tunisia ; R. Bebbouchi & K. Taleb, Algeria; K. Jaouiche, France);
3. Arabic mathematics of the West-Andalusia and Maghreb (M. Aballagh, Morocco; A.Djebbar, Algeria; Y.Guergour,Algeria; J. Hogendijk, Netherlands; A. Sadallah, Algeria; M.Souissi, Tunisia; T.Zemouli, Algeria);
4. The transmission of Arabic mathematics to Europe (J. Sesiano, Switzerland).

At the closing session of the Colloquium some recommendations were read and adopted. Directly related to the history of mathematics it was recommended:
1. To try to organize in Algeria every two years an International Colloquium on the History of Arabic mathematics;
2. To try to publicize a Maghrebian journal on the history of science that divulges the classic Arabic science in general and Maghrebian in particular;
3. To invite for research manuscripts owned by private individuals.

The proceedings of the Colloquium will be published in Arabic and French.
List of the contributed papers:

1. M. Aballagh: Comparative study of Talkhis and Raf al-hijab of Ibn al-Banna'

2. M. M. Abdeljaoud & H. Hadfi: "The problems that cannot be solved" according to the book Al-fawa'id al-baha'iya of Ibn al-Khawwam (1245-1324)

3. C. Bouamrane: The sciences and their development in the civilization of the Islam.

4. R. Bebbouchi & K. Taleb: The infinitely great quantities of Thabit Ibn Qurra.

5. A. Djebbar: Some aspects of algebra in the mathematical tradition of the Mussulman West.

6. Y. Guergour: A Maghrebian mathematician of the 14th century, Ibn Quufudh al-Qasantini (1339-1406).

7. J. P. Hogendijk: The Kitab al-istikmal of Al-Mu'taman Ibn Hud, an important source for the history of ancient and medieval geometry.

8. K. Jaouiche: Analysis and synthesis in the Arabic-Islamic mathematics: the book of Ibn al-Haytham.

9. A. Sadallah: Some Scientific practices in Algeria during the period of scientific retardation.

10. J. Sesiano: The "Liber Mahamaleth", a Latin mathematical treatise composed in the 12th century in Spain.

11. M. Souissi: The Maghrebian mathematical school: some examples of its works and certain of its particularities.

12. I. Zemouli: The Uriuza of Ibn al-Yasamin on irrational quadratic numbers.


report by A.Djebbar

An International Colloquium on the History of Fractions, entitled "Histoire des fractions et fractions d'histoire" was held at the Center for Juridical and Historical Studies, Paris (France),January 30-31 ,1987. The colloquium was organized by P. Benoit, K. Chemba and J. Ritter. The following were contributed papers concerning the history of mathematics in Africa:

1. J. Ritter: Metrology and the prehistory of fractions.
2. E. M. Bruins: The construction of numerical tables in Egypt and Babylonia.
3. M.Caveing: The arithmetical statute of Egyptian "quantieme".
4. M.Guillemot: Do the operational notations and practices permit us to talk about Egyptian fractions?
5. M. Aballagh: Fractions between theory and practice with Ibn al-Banna' al-Marrakushi (1256-1321).
6. A. Djebbar: The treatment of fractions in the mathematical tradition of the Maghreb.


At the Nairobi session (10-15.11.1985) of the Special Committee on Africa of the United Nations University: L'Afrique, berceau de la mathématique mondiale? (Africa, the cradle of world mathematics, 11 pp.) by the first president of the African Mathematical Union (1976-1986), Henri Hogbe-Nlend. This paper is intended as an introduction on the contribution of Ancient Africa to world mathematics. After underlying the negro-African character of pharaonic Egypt and analyzing the dialectics of intuitive and deductive reasoning, it is stated that mathematics in pharaonic Africa was intuitive, demonstrative and rational; Africa is the mother of Geometry.

At the Annual General Meeting of the Mathematics Association of Tanzania (May 1986): The history of mathematics in Tanzania (12 pp.) by Beniel R. Seka. The paper describes the development of the mathematics curriculum in Tanzania since Independence. A distinction between three periods is made: "the traditional mathematics era, the modern era and the present era which lends from both traditional and modern mathematics".

At the 5th Symposium Association of the Southern African Mathematical Sciences Association, Maseru Lesotho (15-19.12.1986), On the history and teaching of geometry in Africa: the Pythagorean Proposition as an example by Paulus Gerdes. Some African cultural contexts (sand drawings, decorative motifs, plaiting and knotting patterns) are shown that could have led in the past to the discovery of the so-called Pythagorean proposition and can be used in the classroom to stimulate 'reinvention' by the students of this important theorem.


Abdoulaye Elimane Kane (Department of Philosophy, University of Dakar, Senegal), will complete a doctoral dissertation this year ('These d'état') on "Oral numeration systems in west sub-Saharan Africa". Probable defense: June 1987.

Youcef Guergour (École Normale Supérieure, Alger, Algeria) is preparing a thesis ("Magistère") on "The life and works of the Maghrebian mathematician Ibn Ounfudh". Probable defense: October 1987.

Touhami Zemouli (École Normale Supérieure, Alger, Algeria) is preparing a thesis ("Magistère") on "The life and the mathematical work of Ibn al-Yasamin". Probable defense: October 1987.

Mohamed Aballagh, a Moroccan researcher, is completing a doctoral thesis ("Nouvelle Thèse") in Paris (France) on "The philosophical-mathematical treatise of Ibn al-Banna': Raf al-Hijab an Wujuh a mal al-Hisab". Probable defense: June 1987.

Mamman Musa (Ahmadu Bello University, Zaria, Nigeria) completed an M.Ed. thesis, entitled: "The mathematical heritage of the Hausa People: a resource guide for mathematics teaching". Data gathered from library research plus extensive interviews with various local experts. He summarizes mathematics in daily life, measures, art, religion, etc. for the Hausa culture of northern Nigeria. Illustrated.

Alberta H. Carmichael (Ahmadu Bello University, Zaria, Nigeria) completed an Ph.D. thesis, entitled: "The development of mathematical concepts and skills among un-schooled Nupe children". A Piagetian-type study of children of the Nupe group of Central Nigeria. With Piagetian interviews of 336 children, she found skills developing better than concepts, and some interesting differences by sex and urban-rural distinctions.


Beniel R.Seka is preparing a monograph on the history of the Mathematics Association of Tanzania.

Dorothy Washburn prepares a monograph on the two-dimensional symmetries on the raffia cloths of the Bakuba, Zaire. Her past studies of pattern symmetry have been on ceramics from Neolithic Greece, the American Southwest Pueblo cultures, pre-Columbian Peruvian textiles, and California Indian basketry.

Gay Robins and Charles Shute are preparing a commentary on the Rhind Mathematical Papyrus (Ancient Egypt), to be published in 1987. It is intended to offer an up-to-date appraisal of the early Egyptian contribution to mathematics, emphasizing numerological as well as practical aspects.

U. Rebstock (University of Tübingen, F. R. of Germany) is preparing a book entitled "Katalog arabischer Handschriften in Mauritanien", that contains a catalogue of Arabic manuscripts in Mauritania, including some repertories on mathematics.

Jacques Navez (University of Burundi) is doing research on pre-colonial numeration systems and on the evolution of mathematics curricula at secondary level.



A research seminar, entitled 'Ibn al-Haytham' on the history of Arabic mathematics took place in 1986/1987 at the Mathematics Department of the 'École Normale Supérieure' (Kouba-Alger, Algeria). It was organized by A. Djebbar with the support of Y. Guergour and T. Zemouli. The following lectures were delivered:

M. Aballagh (4.11.86): An example of bio-bibliographic work in the history of mathematics: the life and the works of Ibn al-Banna'(1256-1321).

A. Djebbar (28.2.87): The research instruments used in the history of mathematics.

Y. Guergour (1.3.87): Some aspects of magic squares in the Maghreb mathematical tradition.

T. Zemouli (28.3.87): Heritages and mathematics: the example of the 3rd chapter of the algebra book of Al-Kwarizmi (780-850).

Y. Benrebia (29.3.87): The perfect compasses and the tracing of the conic sections by the mathematicians of the l0th-12th centuries.

M. Zerrouki (10.4.87): Fractions in the mathematical tradition of the Maghreb through an anonymous manuscript.

A. Djebbar (11.4.87): The contribution of Arab mathematicians to the elaboration of the real number concept.

A. Bouzari (16.5.87): The epistle of Al-Rhazin (10th century) on the utilization of conic sections in Arabic mathematics of the 10th century.

A. Laib (17.5.87): Some aspects of infinitesimal analysis in the 11th century through the epistle of Ibn al-Haytham on the volume of a sphere.


A 1 semester course on the history of mathematics started, for the first time in Algeria, in February 1987 for the 4th year students of the 'École Normale Supérieure' (Kouba-Alger). The course is given by A. Djebbar, with the assistance of Y. Guergour and T. Zemouli to lead the work sessions. The programme touches different aspects of mathematics in all societies (Babylonian, Egyptian, Chinese, Indian, Greek, Arab, with some modest information on mathematics in sub-Saharan Africa and in the America of the Aztecs and Incas). This year, privileged attention has been given to Arabic mathematics, in order to respond to a pressing demand of the students who discovered - sometimes with real and profound emotion - a whole scientific and cultural world, unknown to them.

About l20 people - among them the Deputy-Minister of Education, mathematician João C. Beirão - attended a series of three public lectures, at the Eduardo Mondlane University in Maputo (Mozambique), delivered by Paulus Gerdes, on the history of mathematics in Africa. These lectures were organized under auspices of the Mozambican Association of Friends of Mathematics and were devoted to:
1. The awakening of geometrical thinking in Africa (13.8.86);
2. Mathematics in Ancient Egypt (27.8.86);
3. Mathematics in the regions of Islamic influence (10.9.86).

NEWSLETTER 1 (continued)





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