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42 Ganita Manjari | Grade 9 | Part I Even more fascinating is the Ishango bone, found near the headwaters of the Nile River in the Democratic Republic of Congo, dating to around 20,000 BCE. This bone contains three columns of asymmetrical notches. What makes the Ishango bone a mathematical marvel is the specific grouping of the tallies. One of the columns groups notches into 11, 13, 17, and 19 — the prime numbers between 10 and 20. Another column seems to demonstrate the concept of multiplication by 2 (doubling). These artefacts indicate that the abstract concept of a ‘number’ is indeed tens of thousands of years old. Fig. 3.1: Representation of the prime number tally groupings found on the Ishango bone. 3.1.2 The Indian Context: Trade and Astronomy As civilisations advanced, so did the need for larger numbers. In the ancient urban centers of the Indus Valley Civilisation, such as Lothal and Harappa, standardised weights and measures were crucial for trade. A merchant trading terracotta pottery, lapis lazuli, or cotton with Mesopotamia needed a robust system of accounting. During Vedic times, Indian philosophers were fascinated by and deeply pondered large numbers. In the Vedas, which go back thousands of years, names were given to all powers of 10 up to 10 12 (which was called parārdha). In the Lalitavistara in the 4th century BCE, Buddha 53 describes names up to 10 , which is called tallakṣhaṇa. Expressing quantities in terms of powers of 10 was explicitly used in the Ṛigveda, thus setting the stage for the number system based on powers of 10 to be developed in India in the ensuing years, and which we now use around the world today. The development of the Indian numeral system in terms of place values and powers of 10 also helped pave the way for what is perhaps the most important mathematical invention in human history: the concept of zero.