784 numbers and counting: Africa The zero was a sketch of a seashell, while the other numbers were additive, with a dot representing and bars representing 5, so that 18 was rendered by three horizontal bars with three dots on top Numbers were written in columns from the bottom up, such that the places were marked by rows rather than columns For example, 404 would be written with four dots in the 1s row, a zero above that in the 20s row, and a single dot in the 400s row The Mayan and Indian inventions of zero were quite independent Africa by Olutayo C Adesina The medieval period in Africa was a time of unprecedented advances in the idea of mathematics and a sense of arithmetic as both a cultural and an economic phenomenon Through the fresh introduction of ideas, Africans contributed significantly to human cultures of numbers and counting This development was manifested in several ways, one of which was in the area of computing roots of difficult equations During the medieval period the system of numbering and counting in Africa had undergone evolution that reflected the metamorphosis from lower to higher forms of social development through political and cultural contacts with diverse parts of the world Numerous numbering and counting systems began to exist side by side These had a variety of origins, forms, and consequences Therefore, in a sense, a distinction is sometimes drawn between indigenous number and counting systems and imported systems Ancient Africans developed and adopted systems and instruments of numbering and counting, such as counting glyphs, tally marks on bones, base-10 counting systems, the quinary and denary scale of numeration (counting by fingers and toes), and games and puzzles as part of their system of numeration For more than 10 centuries, however, from about 300 to 1450, Africa experienced major influences from other parts of the world, with diverse impacts on developments on the continent and in other parts of the world Despite the contacts with other parts of the world, there were marked contrasts in the development of different societies in Africa, ranging from highly organized kingdoms and empires, such as Egypt, Ghana, Mali, Ethiopia, Kongo, Ile-Ife, and Benin, with the knowledge of basic concepts of mathematics, to lower social formations, such as the huntergatherer societies of the Kalahari Desert, the Mbuti of the Congo forests, and the remnants of other such Stone Age communities in which changes appeared to be slow or even nonexistent Nevertheless, in more developed social formations that experienced contacts with the outside world, it was also still possible to distinguish between what was uniquely indigenous to Africa and what appeared to be borrowed from elsewhere Africa in the medieval period experienced major influences from the Romans, the Arabs, and the Iberians From then on, numbers and counting developed in tandem with indigenous African systems These became the precursors of many modern practices and systems in Africa The influence of the Roman Empire, which by 200 included North Africa, contributed to transformations in the age Thus, in the northern part of Africa the number system borrowed from or took after the Roman system The system created by the Romans had a total of seven symbols and could be used to express numbers from to million These include I for 1, V for 5, X for 10, C for 100, D for 500, and M for 1,000 The Roman numerals are read from left to right, and the symbols standing for the largest quantities are placed at the left The Hindu-Arabic numeral system was part of the culture introduced into Africa from other areas This system was represented by the use of positional notation of 10 symbols from to 9, with individual symbols assuming specific values according to their position in the numerals This system made it possible to differentiate between, for instance, the numbers 2, 202, and 2,002, all without the use of additional or cumbersome symbols The first recorded use of the system in Europe was in 976, and this followed European explorers, navigators, and adventurers into Africa in the age of European contact and exploration The transmission of mathematical knowledge from other cultures into Africa after the Roman conquest can be traced from Iraq into Egypt, then to Morocco, and on into the Iberian world There is no disputing the fact that the influence of the Romans and the Arabs in the expansion of mathematics in Africa remains very important However, there is evidence to show that some of the central ideas of calculus reached Europe from Africa Africans continued to make profound expansions in the world of mathematical ideas Some of the basic ideas of calculus were already known in Egypt before Sir Isaac Newton (1642–1727) created his own version between 1665 and 1670 Egyptians had been able to combine ideas under the unifying themes of the derivative and the integral to show the connection between the two and then evolve the calculus into a problem-solving tool In particular, the idea of the sums of integral powers and the area formula were developed in Egypt in the 11th century, when Caliph al-Hakim invited Ibn al-Haytham (965–1039), a native of Basra in Iraq, to work on a Nile-control project Not all mathematical ideas appeared as numerate skills The indigenous population in Africa retained the capacity for mathematical ideas—ideas that they retained in informal ways and manners The general consciousness of an arith-