Mathematics Has Emerged in Africa in Many Varied Forms Over the Millennia

World history of mathematics Mathematics in Africa Mathematics has emerged in Africa in many varied forms over the millennia. Different civilisations have employed sophisticated arrangements of weights and measures, elaborate counting systems, and have played mathematical games. Former collection of French botanist Jean Baur. Donated to the Museum of Toulouse in 2010 of Toulouse the Museum to Donated Baur. Jean botanist collection of French Former Beyond that of the North African in various forms for the next 3,000 Akan gold-weights, and a Islamic and ancient Egyptian years. Comprehensive evidence of balance (18th–20th century CE); the weight on the left depicts civilisations, the history of Egyptian mathematics is rare, since a drummer, although the arms mathematics in Africa has been little- it would have been recorded on have been removed – possibly studied, and sources are sketchy. papyrus, which has not survived. to adjust the weight Further research will undoubtedly However, the very few remaining uncover more of the details of African sources allow us to reconstruct the mathematics that have been hidden sophisticated arithmetical techniques for centuries. that Egyptian scribes used in record- keeping. We also have evidence of the British Museum © The Trustees of geometrical understanding: for example, a standard procedure for calculating the area of a circle. Alexandria in Egypt was also home, in the fourth century CE, to one of the first female mathematicians about whom we have any substantial gold trade, in the 14th century CE. The information: Hypatia, who Akan people in particular produced wrote commentaries on ancient brass weights, for weighing gold, that mathematical texts, and is said to were both elaborately and accurately Founded in 2003, the African have constructed astronomical crafted. Institute for Mathematical Sciences instruments. (AIMS) is a network of academic Mathematical Games institutions in Cameroon, Ghana, Ben2, CC BY-SA 3.0, via Wikimedia Commons BY-SA Ben2, CC Games of chance and strategy have Rwanda, Senegal, South Africa, been played throughout Africa and Tanzania. Its goal is to promote over the centuries. One example is post-graduate education, research, morabaraba, a version of the Roman and public engagement in the game of nine men’s morris, played in mathematical sciences in Africa. The Ishango bone, South Africa and Botswana. Another controversial evidence of early game that is particularly widespread, arithmetic in Africa with numerous variants and a host of Early arithmetic? different names, is mancala – alleged The Ishango bone is a tool made from to be one of the oldest games still to a baboon fibula, discovered in 1960 in be played anywhere. Indeed, mancala what is now the Democratic Republic Hypatia of Alexandria tournaments now take place around One area of mathematics that has of the Congo. It dates to between (?–415 CE), as depicted by the world. seen particular growth in African Jules Maurice Gaspard in 1908 20,000 and 18,000 BCE. Notches institutions in recent years is that carved into the bone have been Weights in West Africa of machine learning, driven by the interpreted as tally marks, evidence The small hard seeds of the rosary foundation of such organisations of an arithmetical game, a record of pea were traditionally used as as Data Science Africa and Deep lunar cycles, or simply as grooves to standard weights by various peoples Learning Indaba. aid grip and therefore entirely non- in West Africa, owing to their mathematical. consistency in size. However, metal © The Trustees of the British Museum weights became the norm following A Kenyan mancala board – The Rhind Mathematical Ancient Egypt the introduction of metal-working players take turns to move their Papyrus, the most complete playing pieces from one pit to and extensive surviving The ancient Egyptian civilisation techniques to present-day Ghana, and another, with the goal of capturing source on ancient Egyptian arose around 3,000 BCE and lasted the expansion of the trans-Saharan their opponent’s pieces mathematics © The Trustees of the British Museum World history of mathematics Mathematics in the Americas The countries of North, Central, and South America feature prominently in the modern international mathematical community. In the past, the various cultures Quipu Artur Ávila, awarded of the continent, particularly of Rather than recording information the Fields Medal in 2014 for ‘contributions South America, developed a range in a written form, some Andean to dynamical systems of number systems, which were civilisations, including the Incas of theory, which have employed most extensively in ancient Peru, developed a system changed the face of the field, using the powerful connection with time-keeping. of record-keeping using knots in idea of renormalization as a unifying principle’ bundles of wool and cotton cords © MFO The Aztecs called quipu (‘talking knots’). The use of base-20 number systems was widespread across South The colours of the cords and the However, the mathematical America, both linguistically and Maya numerals in a spacing of the knots were crucial to communities of other countries are notationally. The Aztecs, for example, rare surviving text of the the encoding of information on the now growing. In 1995, the Unión 13th or 14th century CE employed a non-positional base-20 quipu. Although much of the content Matemática de América Latina y el number system with separate signs of the surviving quipu remains to Caribe was created, with the initial for 1, 20, 400, and 8000. These Dates in the long count were written be deciphered, we know that one of involvement of Argentina, Brazil, numerals may be found in surviving using a base-20 positional numeral their major uses was the recording of Chile, Colombia, Cuba, Mexico, survey documents, which record system, where a dot and a bar stood numerical information. Uruguay, Venezuela, and Peru; in areas and perimeters of fields – but for ‘1’ and ‘5’, respectively; a picture 2018, Rio de Janeiro became the first we do not know how these were of a shell often indicated an empty The Americas in the present day city in the southern hemisphere to measured or calculated. position. During the past two centuries, the host an International Congress of mathematical focus of the Americas Mathematicians. The study of the has been on Canada and the United recent history of mathematics in the These images are obtained through the courtesy of the World Digital Library. The codex itself is held by the National Library of France itself is held by the National Library The codex Library. Digital of the World the courtesy through obtained These images are States. US-based mathematicians Americas is also changing: it has hold the largest number of Fields usually concentrated on white male Medals; so far (2020) only one mathematicians, but the contributions South American has won the award: of other, previously-overlooked groups Artur Ávila of Brazil. are now being recognised. Illustration from El The 2010 book primer nueva corónica Hidden Figures: y buen gobierno The American Dream (The First New and the Untold Story Chronicle and Good of the Black Women Government), 1615, Who Helped Win the by Peruvian Felipe Space Race Guaman Poma de Ayala; this is one of the few surviving accounts of the use of quipu An early 16th-century land survey, annotated in both Spanish and the Aztec language Nahuatl The Maya The Maya culture emerged in Mesoamerica around 2,000 BCE, and elements of it survive to the present day. From around the fifth century BCE, the Maya employed an elaborate calendar, consisting of cycles within cycles. In the calendar, a 260-day count was combined with a year of 365 days; the two came back into step every © Paul Johnson © Paul 52 years, known as a Calendar Round. For dates on monuments, the Long Count was used; this was constructed An inscription displaying a date in the An Incan quipu consisting of around much larger units of time, Maya Long Count; numerals appear above coloured and knotted cords, some spanning centuries. the respective signs for units of time encoding numerical information World history of mathematics Mathematics in China Mathematics has a long pedigree in China, both as an accomplishment expected of Confucian literati, and as a subject that was key to training as a civil servant. The Nine Chapters on the Mathematical Art One of the most influential of the traditional Chinese mathematical texts was the Jiǔzhāng suànshù 九章算術 (The Nine Chapters on the Mathematical Art), probably dating originally from c. 300 BCE, but in use for over 1,000 years as a manual for the training of administrators. TheJi ǔzhāng suànshù consists of 246 arithmetical problems and their methods of solution. Its seventh and eighth chapters, for example, deal with the solution of systems of up to five simultaneous equations in five unknowns. The method used, fāngchéng 方程, is equivalent to the process known in the West Page from an edition of the Sūnzĭ suànjīng The Yang Hui triangle 杨辉三角形 (a.k.a. as Gaussian elimination, and may printed more than 1,000 years after the Pascal’s triangle), as found in the Sìyuán yùjiàn original text was written; beyond his name, we 四元玉鉴 (Jade Mirror of the Four Unknowns, have been influenced by the use of know nothing about the alleged author, Sun Zi 1303) by Zhū Shìjié 朱世傑 (1249–1314) counting boards in China. Wang Zhenyi Although mathematical learning in Jean-Claude Martzloff and Stephen S. Wilson, A history of Chinese mathematics, Springer, Berlin, 1997 Berlin, of Chinese mathematics, Springer, S. Wilson, A history MartzloffJean-Claude Stephen and China was confined largely to men, some women did also engage in scientific studies. Most notable was https://math-physics-problems.wikia.org/wiki/Liu_Hui CC-BY-SA Wang Zhenyi 王貞儀 (1768–97), who wrote treatises on both astronomy (the procession of the equinoxes) and mathematics (trigonometry).

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