Mathematics in North Africa

Summary: North Africa has been a major contributor to mathematics, particularly in ancient Egypt and the Islamic Golden Age.

North Africa, comprised of Algeria, Egypt, Libya, Morocco, Sudan, Tunisia, and Western Sahara, has long been geographically and culturally distinct from the rest of the continent because of the Sahara desert (which includes most of the region) and the proximity to southern Europe and the Middle East. The mathematics of ancient Egypt is among the oldest known mathematics traditions, and the Egyptian city of Alexandria was an important center of learning in the ancient world. Centuries later, Egyptian mathematicians were among the contributors to the Islamic Golden Age, translating classical works, which also helped bring about the Renaissance and Age of Enlightenment.

Mathematics historians and teachers have explored a variety of historical mathematics in the area, such as string figures and precolonial mathematics in Sudan, or the work of Gaston Julia, who was born in Algeria at the end of the nineteenth century and is known for his investigations on dynamical systems. The Julia set is named for him. Modern mathematicians and scholars in North Africa continue to take part in mathematics research and teaching.

Ancient Developments

Papyrus scrolls predating 1500 b.c.e. have been found in Egypt that discuss mathematical topics. One of the more famous is the Ahmes scroll (after the name of the scribe to whom it is attributed), currently held in the British Museum, which describes many problems in algebra and geometry and demonstrates their solutions. It is of particular interest for its use of unit fractions (fractions with a numerator of 1, such as 1/8) and for demonstrating a method of calculating circular areas.

In the Hellenistic period (c. 323–146 b.c.e.), and in the Roman period that followed, the city of Alexandria in Egypt was a center of learning, and the Great Library of Alexandria was the most important library in the ancient world. Euclid (c. 300 b.c.e.), a Greek mathematician who worked in Alexandria, is best known for his treatise Elements, which formed the basis for how geometry has been understood and taught for more than 2000 years. Eratosthenes of Cyrene (276–194 b.c.e.) was born in what is now Libya. He estimated the circumference of Earth and is known for the Sieve of Eratosthenes, which is useful in number theory.

One of the best-known Egyptian mathematicians from the Roman period was Ptolemy (c. 90–168 c.e.), a Roman citizen who lived in Egypt. One of his well-known works is the Almagest, the most comprehensive surviving ancient treatise on astronomy. Hypatia (c. 350–415), a Greek who lived in Alexandria, was a female mathematician who wrote commentaries and was also known as a teacher of astronomy and philosophy.

Islamic Period

Mathematics flourished during the Islamic Golden Age (c. mid-eighth to mid-thirteenth century). One impetus to this development was the translation of classical Greek works, such as Ptolemy’s Almagest and Euclid’s Elements. These translations were often the only surviving copies and their preservation by Islamic scholars allowed them to be reintroduced into Western thought. Besides the appreciation of knowledge for its own sake, the development of mathematical sciences had practical uses in the Islamic world; for instance, knowledge of astronomy was required to understand the phases of the moon and thus correctly observe Islamic holy days, while algebraic notation was developed in part to solve problems relating to the laws of inheritance. Geometric motifs are very common in Islamic art and design, in part because, for religious reasons, Islamic artists did not create representational art, such as portraits. Instead, complex patterns such as tessellation figures (tilings) were developed for artistic use.

Many mathematicians worked in Egypt during the Islamic Golden Age. Ahmed ibn Yusuf (c. 835–912) was born in what is now Iraq but moved to Egypt and died in Cairo. He worked with his father, Yusuf ibn Ibrahim, on mathematics and wrote a book on ratio and proportion, which commented on Euclid’s Elements and was translated into Latin in the twelfth century. Abu Kamil Shuja ibn Aslam (c. 850–930) was a mathematician who made important contributions to the study of real numbers, irrational numbers, and combinatorics, and some of whose techniques were adopted by the thirteenth-century Italian mathematician Fibonacci. Ibn Yunus (c. 950–1009) was an Egyptian astronomer and mathematician whose most famous work is a handbook of astronomical tables, which is notable for the accuracy of his observations and for his meticulous description of numerous planetary conjunctions and lunar eclipses. Abu Ali al-Hasan ibn al-Hasan ibn al-Haytham (c. 965–1039) was born in Persia but lived primarily in Egypt and died in Cairo. He worked as an engineer, reportedly attempting to develop a method to dam the Nile River, and made important contributions to optics and to the development of the scientific method. Al-Marrakushi ibn Al-Banna (c. 1256–1321) lived in Morocco and may have been born there. He worked on Euclid’s Elements and texts on algebra and arithmetic operations.

Modern Developments

In the early twenty-first century, mathematical study and research continues in North Africa. Mathematicians belong to professional organizations like the Association Mathématique Algérienne, the Egyptian Mathematical Society, the Tunisian Mathematical Society, and the Société des Sciences Naturelles et Physiques du Maroc. Egypt and Tunisia are members of the International Mathematical Union, which is a worldwide organization designed to promote mathematics. North African countries have participated in the International Mathematical Olympiad, an annual competition held since 1959 for high school students. Algeria first participated in 1977, Morocco in 1983, and Tunisia in 1981.

Bibliography

Gerdes, Paulus. African Doctorates in Mathematics: A Catalogue. Maputo, Mozambique: Research Centre for Mathematics, Culture and Education, 2007.

Gerdes, Paulus, and Ahmed Djebbar. Mathematics in African History and Cultures: An Annotated Bibliography. 2nd ed. Cape Town, South Africa: African Mathematical Union, 2007.

Joseph, George Gheverghese. The Crest of the Peacock: Non-European Roots of Mathematics. Revised ed. Princeton, NJ: Princeton University Press, 2000.

Kani, Ahmad. “Arithmetic in the Pre-Colonial Central Sudan.” In Science and Technology in African History With Case Studies From Nigeria, Sierra Leone, Zimbabwe, and Zambia. G. Thomas-Emeagwali, ed. Lewiston: Edwin Mellin Press, 1992.