Chairman: Paulus Gerdes (Mozambique)

Secretary: Ahmed Djebbar (Algeria)


Cyprien Gnanvo (Benin)

Salimata Doumbia (Côte d'Ivoire)

Nefertiti Megahed (Egypt)

Mohamed Aballagh (Morocco)

Abdoulaye Kane (Senegal)

David Mosimege (South Africa)

Mohamed Souissi (Tunisia)

David Mtwetwa (Zimbabwe)

Associate Members: José Barrios (Canary Islands, Spain), Scott Williams (USA)



  1. Objectives of AMUCHMA
  2. Meetings, exhibitions, events
  3. Current Research Interests
  4. Notes and queries
  5. Theses
  6. Sources
  7. Have you read? (#349-#380)
  8. Announcements
  9. Addresses of scholars and institutions mentioned in this newsletter
  10. Suggestions
  11. Do you want to receive the next AMUCHMA-Newsletter

Centro de Investigação Etnomatemática, Maputo (Mozambique), 11.11.2002



2.1. Conferences of Ahmed Djebbar at the Island of Reunion (9-16 February 2002)

At the invitation of the Science-Resource Association and of the Institute for Research in Mathematics Education (IREM) of Saint-Denis (Reunion), Ahmed Djebbar (Algeria) gave four lectures on the history of mathematics:

2.2. International colloquium on Euclid's Elements (May 15-16, Lille, France)

An international colloquium on "The reception of Euclid's Elements in the Middle Age and in the Renaissance" took place at the University of Lille 3 (France). The following communications were presented:

2.3. 7th Maghrebian Colloquium on the History of Arabic Mathematics (Marrakech, Morocco, May 30 ­ June 1, 2002)

The opening session of the 7th Maghrebian Colloquium on the History of Arabic Mathematics chaired by Abdellah Saaf, Morocco's Minister of the National Education. Abdelhadi Tazi, member of the Royal Academy of Morocco, delivered the opening lecture "On intellectual activity in the medieval Maghreb." Ahmed Djebbar presented the closing lecture "On mathematics in the imperial Maghreb of the 12th and 13th centuries."

The following papers were presented at the colloquium:

At the last of the colloquium a round table was organised on History and Pedagogy of Mathematics (HPM).

2.4 Colloquium dedicated to (10-13 July, Safi, Morocco)

On the occasion of the sixtieth birthday of the mathematician Mohamed Akkar, his former students, led by Mohamed Chidami, one of the Vice-president of the African Mathematical Union (AMU), organized an international colloquium on "Statistics in functional spaces" that took place in his home town Safi. Morrocco's Minister of the National Education and Secretary of State for Scientific Research attended the opening session of the colloquium and the ceremony of honoring. About one hundred scholars mostly from Morocco but also from Algeria, Benin, Burkina Fasso, France, Germany, Poland, and South Africa took part. Jan Persens, President of AMU, gave the closing address. Twenty five papers on statistics in connection with functional analysis and four papers of general interest were presented. Ahmed Djebbar (Algeria) presented the paper entitled "Debates and controversies among Arabic mathematicians (9th-14th centuries)."

2.5 Papers presented at recent meetings

2.6 Launch of books

At a well attended ceremony chaired by Alcido Nguenha, Mozambique's Minister of Education, the new Portuguese language edition of Paulus Gerdes' book Lusona: Recreações geométricas de África [Lusona: Geometrical Recreations from Africa], was launched on April 19, 2002, in Maputo. The book (cf. #241) is simultaneously published by Moçambique Editora (Maputo, Mozambique) and Texto Editora (Lisbon, Portugal).


-none reported


This section is reserved for questions that readers would like to have answered; these are the 'queries'. The answers will be the 'notes'. If you have questions or answers about sources, dates, names, titles, facts, or other such matters related to the history of mathematics in Africa, frame them in clear and concise language and send them to the editors. If you are answering a question, make clear reference to that question. All readers may send both questions and answers. Each will be published with the name of the sender.


Hisham Barakat Bisher (al Arish, Egypt) concluded in June 2001 his masters thesis in ethnomathematics, written in Arabic, under the supervision of Professor Massouma Kazim, former member of AMUCHMA, at the Ain Shams University (Cairo, Egypt). His thesis analyses mathematical ideas in nomad Bedouin culture and possibilities to embed them into mathematics teaching.


-none reported

7. Have you read?

7.1 On the History of Mathematics in Africa

#349 Anselin, Alain: Les gestes du nombre, in: Alain Anselin, La Cruche et le Tilapia, Une lecture africaine de l'Egypte nagadéenne, Éditions de l'UNIRAG, Abymes, Guadeloupe, 1996, pp. 103-115
Presents a comparative analysis of number words in Ancient Egypt and several African languages. The chapter analyses different ways of counting and presents a 'human ecology' of the numbers in Ancient Egyptian.

#350 Barrios García, José: Tara: A study of the Canarian astronomical pictures. Part I: Towards an interpretation of the Gáldar Painted Cave, in: Florin Stanescu (Ed.), Proceedings of the Third SEAC meeting, Lucian Blaga University, Sibiu (Romania), 1999, 24-36 [SEAC = Société Européenne pour l'Astronomie dans la Culture, European Society for Astronomy in Culture]
"The first part of the paper analyses the archaeological, ethnohistorical and linguistic evidence that led the author to propose that in the 14th ­ 15th centuries the Berber populations of Grand Canary Island systematically recorded numerical, astronomical and calendrial data by means of certain geometrical figures named tara, painted in white, red and black on wooden planks and on the walls of certain caves. One main conclusion of the study was the discovery of the use of a type of chess board of 3 vertical x 4 horizontal squares, named acano by the author, to represent 12 moons" (CF. AMUCHMA 19: 4.1).

#351 Barrios García, José: Tara: A study of the Canarian astronomical pictures. Part II: The acano chess board, in: C. Jaschek and F. Atrio Barandela (Eds.), Proceedings of the IVth SEAC meeting "Astronomy and Culture", Universidad de Salamanca, Salamanca (Spain), 1997, 47-54 [SEAC = Société Européenne pour l'Astronomie dans la Culture, European Society for Astronomy in Culture]
The paper presents the acano as a Berber lunar calendar and shows "how to number its squares to force the solstitial, equinoctial and eclipse moons to move across the board with very simple and stable patterns. These patterns provide a safe and clear mnemonic guide for performing on the acano an easy calculus of seasonal and eclipse moons over extended periods of time, just using the difference in days of the lunar year with either the solar year or the eclipse year to perform an elementary saw function on the squares. This calculus establishes the octaeteris, the metonic cycle and the 135-moon eclipse cycle as basic periods of the acano. The proposed calculus on the acano would reveal an unsuspected high level of Canarian mathematical astronomy [in the 14th - 15th centuries] and pose the question of the origin of this set of techniques" (CF. AMUCHMA 19: 4.1).

#352 DeYoung, Gregg: Astronomy in Ancient Egypt, in: Helaine Selin (Ed.), Astronomy across Cultures, The History of Non-Western Astronomy, Kluwer Academic Publishers, Dordrecht, 2000, 475-508
"Ancient Egypt had a wide-ranging but essentially qualitative understanding of the heavens. The regularity of the annual inundations removed the necessity to make extensive predictions of future meteorological or climatological events. Despite making extensive observations, the reliance on extremely simple observational devices effectively prevented the growth of any complex theories or predictive algorithms. The primary concern seems to have been connected with time measurement, both for agricultural and religious purposes, as well as articulating analogies that were taken to point toward the possibility of a future life through constant rebirth, like the celestial lights" (p. 507).

#353 Djebbar, Ahmed: La production scientifique arabe, sa diffusion et sa réception au temps des croisades: l'exemple des mathématiques [Arab scientific production, its diffusion and reception at the time of the crusades: the example of mathematics], in: Actes du Colloque International sur "Occident et Proche-Orient: Contacts scientifiques au temps des croisades" (Louvain-la-Neuve, 24-25 mars 1997), Brepols, Brussels, 2000, 343-368
Study of the different types of circulation of mathematical knowledge since the 12th century, inside the muslim empire, between the East and the West, and outside this empire to Latin Europe.

#354 Djebbar, Ahmed: Omar Khayyâm et les activités mathématiques en pays d'Islam aux XIe-XIIe siècles [Omar Khayam and mathematical activities in the Islamic countries during the 11th­14th centuries], Farhang (Teheran), Vol. 12, No. 29-32, 2000, 1-31
Paper dedicated to the life and work of Omar Khayyâm (d. 1131), in relationship with the scientific and cultural activities of his time.

#355 Djebbar, Ahmed: La place et le rôle de l'imagination dans les activités mathématiques de la tradition arabe médiévale [The place and role of imagination in the mathematical activities of the medieval Arab tradition], in: A. Benmaïssa (Ed.), Actes du Colloque International sur "Imagination and Sciences" (Rabat, 1998), Publications de la Faculté des Lettres et des Sciences Humaines, Rabat, 2000, 153-176
Study of the different interventions of the imagination among the mathematicians of the Islamic countries, both in their scientific practice and their discours.

#356 Djebbar, Ahmed; Rommevaux, Sabine & Vitrac, Bernard: Remarques sur l'histoire du texte des Eléments d'Euclide [Remarks on the history of the text of Euclid's Elements], Archives for the History of Sciences, No. 55, 2001, 221-295
A comparative study of certain aspects of the contents of the three great traditions of Euclid's Elements, those of ancient Greece, of the Arab translators and commentators and of the medieval Latin translators and commentators.

#357 Djebbar, Ahmed: Les transactions dans les mathématiques arabes: classification, résolution et circulation [Transactions in Arab mathematics: classification, solution and circulation], in: Actes du Colloque International "Commerce et mathématiques du Moyen ge à la Renaissance, autour de la Méditerranée" (Beaumont de Lomagne, 13-16 mai 1999), Editions du C.I.H.S.O, Toulouse, 2001, 327-344
An analysis of the different transaction problems and the solution procedures included in the known Arab mathematical manuals that were published between the 9th and the 14th century.

#358 Djebbar, Ahmed: Pratiques savantes et savoirs traditionnels en pays d'Islam: l'exemple des sciences exactes [Scholarly practices and traditional knowledge in Islamic countries: the example of the exact sciences], in: Actes du Colloque International sur "Science and Tradition: Roots and wings for Development", (Académie Royale des Sciences d'Outre Mer & UNESCO, Bruxelles, 5-6 avril 2001), Brussels, 2002, 62-86
Partial analysis and reflection about the relationships between two types of knowledge that are often separated, in the discours on science, but that have known important interactions. The question is illustrated by the study of the complex relationships that existed between the oral and written transmission and the theoretic and practic aspects of scientific activity in the countries of the Islam.

#359 Djebbar, Ahmed: La phase arabe de l'histoire de l'algèbre [The Arab phase in the history of algebra], in: Actes de la Troisième Université d'Été Européenne sur "Histoire et épistémologie dans l'éducation mathématique" (Louvain-la-Neuve, 15-18 juillet 1999), Université Catholique de Louvain, Louvain, 2001, Vol. 2, 203-217
Summary of the most significant developments in algebra during the Arab phase, that is between the 9th and 15th century. An important place is given to algebraic activities in Andalusia and in the Maghreb.

#360 Djebbar, Ahmed : Las Matemáticas árabes y su papel en el desarrollo de la tradición científica europea [Arab mathematics and its role in the development of the European scientific tradition], in: Galileo y la gestación de la ciencia moderna, (La Laguna and Las Palmas de Gran Canaria, October 1999 - May 2000), Fundación Canaria Orotava de Historia de la Ciencia, Las Palmas, 2001, 23-34
Paper presented at the Universities of La Laguna and Las Palmas [Canarian Islands] in which information is given about the role of Andalusia in the development of certain mathematical activities and their diffusion to medieval Europe.

#361 Gerdes, Paulus: Mathematics in Mozambique, The Mathematical Intelligencer, New York, 2002, Vol. 24, No. 2, 26-29
Short overview of the development of mathematical activity in Mozambique since the Independence of the country in 1975.

#362 Jones, Alexander (Ed.): Astronomical Papyri from Oxyrhynchus, American Philosophical society, Philadelphia, 1999, 2 Vol., xiv + 495 pp.
Translation of and commentary on astronomical papyri found in an early 20th century dig at the Roman provincial capital of Oxyrhynchus, Egypt. Offers a glimpse of the state of astronomy around the time of Ptolemy.

#363 Lumpkin, Beatrice: Mathematics used in Egyptian Construction and Bookkeeping, The Mathematical Intelligencer, New York, 2002, Vol. 24 No. 2, 20-25
Presents "examples from ancient construction and bookkeeping practices [which] indicate that the development of relatively modern concepts, such as recognition of zero as a quantity and the metricizing of space, has a long history, going back at least 4,700 years in ancient Egyptian mathematics. The examples include a bookkeeping balance sheet with many columns containing zero remainders and numbered construction lines at pyramids and mastabas. The same symbol, nfr, was used for the zero remainders and the zero reference point on the construction guidelines. A third example was a very interesting architect's diagram that gave vertical coordinates for points located on a curve. The horizontal spacing of the points appears to be one cubit apart."

#364 Rossi, Corinna & Christopher A. Tout: Were the Fibonacci Series and the Golden Section Known in Ancient Egypt, Historia Mathematica, New York, Vol. 29, 2002, 101-113
"The Fibonacci series and the Golden Section have often been used to explain the proportions of ancient Egyptian art and architecture. All such theories, however, are based on our modern mathematical system. They have never been examined in the realm of ancient Egyptian mathematics, as we understand it from studying the surviving mathematical sources. This article analyses the compatibility of the Fibonacci series with ancient Egyptian mathematics and suggests how an ancient scribe could have handled it. The conclusion is that concepts such as phi and the convergence to phi have little in common with the surviving ancient Egyptian mathematical documents and that they are quite far from the ancient Egyptian mentality" (p. 101)

#365 Snedegar, Keith: Astronomical practices in Africa south of the Sahara, in: Helaine Selin (Ed.), Astronomy across Cultures, The History of Non-Western Astronomy, Kluwer Academic Publishers, Dordrecht, 2000, 455-473
The paper presents an overview of pre-colonial astronomical practices. The paper is structured in the following sections: sources of evidence, astronomical practices in the built environment, Khoisan sky lore, time reckoning in agricultural communities, cosmology and social cohesion, astronomical practice as an indicator of cultural exchange, colonialism and the decline of African astronomical practices.

7.2 Publications on the History of Mathematics in Africa, Ethnomathematics and / or Mathematics Education

#366 Ascher, Marcia: Mathematics Elsewhere: An Exploration of ideas Across Cultures, Princeton University Press, Princeton, 2002
Some sections are related to the African continent. The first chapter is about divination and includes detailed discussions of Sikidy, as practiced in Madagascar, and Ifa, as practiced by the Yoruba (Nigeria). In the third chapter, which is about calendars. There is a brief mention of the Akan calendar. The fifth chapter includes a detailed discussion of the Gada system (essentially a system of social organization) of the Borana. And the seventh chapter has brief mentions of the Tchokwe sona (Angola) and designs of the Kuba (Congo).

#367 Barrios García, José: Sobre la existencia de censos de población entre los antiguos Canarios (Gran Canaria, Siglos XIV-XV), in: XIII Coloquio de Historia Canario-Americana, Ediciones del Cabildo de Gran Canaria, las palmas de Gran Canaria, 2000, 1697-1704
The paper analyses the sources on the existence of indigenous population census on the Canary Islands during the 14th and 15th centuries.

#368 Bleicher, Michael N.: Egyptian fractions, in: Anatole Beck, Michael N. Bleicher & Donald W. Crowe, Excursions into Mathematics. The Millennium Edition, A. K. Peters, Natick MA, 2000, 421-434
Presents a "number of solved and unsolved problems" related to Egyptians fractions. The problems which "arise from the oldest known mathematical manuscripts" are "easily acessible to the mathematical novice" (p. 421).

#369 Gerdes, Paulus: Lusona: Recreações geométricas de África [Lusona: Geometrical Recreations from Africa], Moçambique Editora, Maputo (Mozambique) and Texto Editora, Lisbon (Portugal), 2002, 128 pp.
New Portuguese language edition (original edition Maputo, 1991). Presents examples of traditional pictograms, called '(lu)sona', from north-eastern Angola and geometrical recreations inspired by them. The reader is presented with certain figures in the style of the 'sona' and invited to find the missing figure(s) (cf. #109, 120, 172-174, 236, 273, 279 and the latest bilingual edition English / French: #241).

#370 Tuchscherer, Konrad: The lost script of the Bagam, African Affairs, The Journal of the Royal African Society, London, 1999, 98 (390), 55-77
The paper presents new information on the Bagam script, an autochthonous writing system from Cameroon, which has now fallen into extinction. On page 73 are illustrated the numerals for one to ten. On page 77 the author notes the possible connection of the Bagan numerals to the Bamum numerals.

#371 Verran, Helen: Science and an African logic, The University of Chicago Press, Chicago, 2001, 277 pp.
The author, who taught at Obafemi Awolowo University in Ile-Ife (Nigeria) between 1979 and 1986, reflects on how science, mathematics, and logic come to life in Yoruba primary schools. She describes how she "went from the radical conclusion that logic and math are culturally relative to a new understanding of all generalizing logic."

#372 Zaslavsky, Claudia: Math Games and Activities from around the World, Chicago Review Press, 1998, 146 pp.
Book for children for ages 9 and up. Includes several examples of mathematical games or activities from Africa, like: [three-in-a-row games] Shisima from Kenya (4-5), Tsoro yematatu from Zimbabwe (8-9), Dara from Nigeria (18-19); [Mankala board games] Easy oware from Ghana (22-23), The real oware game from Ghana (24-25), Giuthi from Kenya (28-29); [More board games] Yoté from West Africa (42-43); [Games of chance] Igba-ita from Nigeria (52-53); [Puzzles with numbers] Magic squares from West Africa (64-65), Dividing the camels from North Africa (73-74), The Ishango bone from Congo (75); [Puzzles without numbers] Crossing the river in Liberia (81), Crossing the rive with jealous husbands from Kenya (82), The snake and the swallow's nest from Angola (84), The Chokwe story tellers from Angola (85-86), Decorations on the walls from Angola (87), How the world began from Angola (88-89), Children's networks from Congo (90-91); [Geometry all around us] Round houses in Kenya (100), Cone-cylinder houses in Kenya (101-102), The pyramids of ancient Egypt (105-106); [Repeating patterns] African patterns from Congo (127-129), Adinkra cloth from Ghana (133-134).

#373 Zaslavsky, Claudia: Jogos e Atividades Matemáticas do Mundo Inteiro Editora Artes Médicas Sul, Porto Alegre (Brazil), 2000
Translation into Portuguese of #372 by Pedro Theobald.

#374 Zaslavsky, Claudia: Math Games and Activities from around the World [in Chinese], Yuan T. Lee Foundation, Taipei, Taiwan, 2002
Chinese language edition of #372.

7.3 Other publications on the History of Mathematics by African mathematicians

None were reported.

7.4 Publications on the History of Mathematics and the African Diaspora

None were reported.

7.5 Reviews

#376 Ascher, Marcia (Ithaca, USA): Paulus Gerdes' 'Geometry from Africa', Mathematical Reviews, MR2000e:01009 (cf. #279)
#377 Ashbacher, Charles (Hiawatha, USA): Paulus Gerdes' 'Geometry from Africa', Journal of Recreational Mathematics, 2000, 30(1), 59 (cf. #279)
#378 Gingerich, Owen: Alexander Jones' 'Astronomical Papyri from Oxyrhynchus', Mathematical Reviews, MR2001j:01009 (cf. #362)
#379 Wertheim, Margaret, (USA): Helen Verran's 'Science and an African Logic', The Los Angeles Times, Dec. 23, 2001 (cf. #371)
#380 Zaslavsky, Claudia (New York, USA): Paulus Gerdes' 'Geometry from Africa', Humanistic Mathematics Network Journal, 2000, 23, 55-57 (cf. #279)

7.6 Mathematical books published in Africa

None were reported.

7.7 Books published by African mathematicians outside Africa

None were reported.

8. Announcements


SMCI Symposium

The Mathematical Society of Côte d'Ivoire (SMCI, Ivory Coast) is organizing a symposium on "Probability, Statistics and Applications", to take place at the University of Cocody, Abidjan, Côte d'Ivoire (May 5-10, 2003). For more information, contact:

Modeste N'zi, UFRMI, Université de Cocody Abidjan, 22 BP 582 Abidjan 22, Côte d'Ivoire (E-mail:, Fax: 225 / 22 48 64 00), or
Etienne Desquith, IRMA, Université de Cocody Abidjan, 22 BP 2030 Abidjan 22, Côte d'Ivoire (E-mail:,

SAMSA Symposium

The next Symposium of the Southern African Mathematical Sciences Association (SAMSA) will be held at the University of South Africa (Unisa, Pretoria) from 9 to 13 December 2002. The themes of the symposium are: Research in mathematics; Applications of mathematics in industry and finance; Mathematics education. For more information, contact:

Zwelethemba Mpono, Unisa, Pretoria, South Africa (E-mail: 64), or
Temba Shonhiwa, SAMSA Secretary, University of Zimbabwe (E-mail:


22nd International Congress on the History of Science

The 22nd International Congress on the History of Science will take place in China in 2005. The preparatory secretariat is housed at the Institute for the History of Natural Science, Chinese Academy of Sciences, 137 Chao Nei Street, Beijing 10001, People's Republic of China (Fax: 86-10-6401-7637). Web site:


* International Association for Science and Cultural Diversity (IASCUD)

IASCUD launched it website in october 2002. The book "Science and Cultural Diversity: Filling a gap in the History of Science", edited by Juan Saldaña can be downloaded from IASCUD's website:

* Indigenous Knowledge World Wide (IKWW)

The Indigenous Knowledge World Wide Newsletter, published by NUFFIC (PO Box 29777, 2502 LT The Hague, The Netherlands) is also available online:


Indilinga: African Journal of Indigenous Knowledge Systems

The first issue of the Indilinga: African Journal of Indigenous Knowledge Systems was launched on the 2nd of March 2002 at the 4th African Renaissance International Conference in Durban, South Africa. The second issue will have as theme "research methods for indigenous knowledge systems." For more information, contact the editor:

Queeneth Mkabela, Private bag x10, Isipingo, 4110 South Africa (Fax: 27-31-90 93 011; E-mail:


* AMUCHMA's secretary Ahmed Djebbar, former Minister of Education of Algeria, has been appointed full professor of mathematics and history of mathematics at the University of Lille 1 (France)
* AMUCHMA's associate member José Barrios Garcia has been promoted to full professor of mathematical analysis at the University of La Laguna, Tenerife, Canary Islands (Spain)

9. Addresses of scholars and institutions

Do you have any SUGGESTIONS?



Thanks to Scott Williams, the English language edition of all issues of the AMUCHMA Newsletter is also accessible on the following website:

Please note the address of the above website changed to the present with AMUCHMA 21.