*By Zulumathabo Zulu © 2015*

**Introduction and Background**

There is a very interesting numerical concept among the Basotho of South Africa known as Tshelela which means the crossing. The immediate question that arises is: crossing to where? They are crossing over to the new base of ten from the old base of five. This then begs another question. Does it actually mean that they have two number bases of five and ten? What is the function of these number bases? If number systems were useful among the Basotho ancients, are they still useful today in this new age of electronic calculators and digital computers? What can we learn from indigenous African numerical concepts?

The popular myth according to Eurocentric version of history, is that there was no mathematics in Africa until the advent of the Europeans. Nothing could be further from the truth. We are debunking that myth in this paper by providing concrete analytical accounts of African origin of mathematics long before the advent of colonization. As a specific example, a small village of Matamong in the Eastern Free State Province of South Africa has inspired the book Sesotho Dictionary of Mathematics by this writer which boasts more than 500 pages of mathematics text from an African perspective. For the first time in the mathematics history of South Africa, a book documenting an indigenous mathematical knowledge of the Africans is born.

**Analysis Methods**

A number of analytical techniques have been used to produce this article namely Lewatsepa (algorithm analysis), Sefofatsepa (superset analysis) and Sedikakgubu (surround analysis) using the Basotho as a reference point. Before diving into the deep of the analytic and interpretive discussion, we briefly provide a background definition of the analysis methods used.

Lewatsepa (algorithm analysis), is about the computational merits of the mathematical method. How does the algorithmic method respond or behave with respect to the input size of a problem? Does the method experience a polynomial increase as the input size grows or does the algorithm remain well behaved like a logarithmic system despite a large input size? These are kinds of questions that were considered when developing this paper.

Sefofatsepa (superset analysis), was used to perform a superset analysis of mathematical knowledge. The premise of superset analysis is to look at the externals of the object and look at how that object fits in the big picture with respect to other objects. How the object relates to other objects? What is the network analysis of the object with respect to other objects? This gives us a helicopter view of a phenomenon or mathematical knowledge as is the case here.

Sedikakgubu (surround analysis), is about the surround of the object. What kinds of things surround the object and how the object gets expressed or suppressed as a result of a surround configuration? The surround refers to the contextual factors of the object or mathematical knowledge as is the case in this paper. The analysis is driven by the cultural context of the origin of mathematical knowledge.

In this paper we address the questions raised above by exploring and analyzing the African history of mathematics, the number systems, the number bases and how this connects with African cosmology.

*Excerpt from the scholarly paper* **The African Origin of Mathematics.
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