Development of Mathematics

Indian mathematics has a hoary past and the history of ancient Indian mathematics dates back to several millennia. We shall discuss the history of Indian mathematics in terms of the following broad periodization:

1. The Ancient period (Prior to 600 BCE)
2. The Early Classical period (600 BCE to 400 CE)
3. The Later Classical period (400 CE to 1200 CE)
4. The Medieval period (1200 CE to 1750 CE)

There have been significant contributions to mathematics by Indians in the modern period (post 1750 CE) also. The legendary Indian mathematician Srinivasa Ramanujan (1887-1920 CE) and many other stalwarts have contributed significantly to the world of mathematics in the 20th and 21st century.

The Ancient Period (Prior to 600 BCE)

The oldest available work of mankind is the ṛg-veda. It contains 1,028 sūktas with 10,462 mantras. These mantras were compiled in the millennia prior to 2000 BCE. Historians call it the Vedic period. According to historians, the ancient period is the period prior to 600 BCE. In this period, the Vedas and the canonical texts of Vedāngas were composed.

There are four Vedas - ṛg, Yajur, Sāma and Atharva. The Vedas are composed of mantras. There are several mathematical aspects contained in these Vedic mantras. Some of them are listed below.

• Enumeration of numbers in powers of 10 till 10¹⁹ (Taīttirīya-saṃhitā, 7.2.20)
• Decimal place value nomenclature for numbers.
• Odd number series (Taīttirīya-saṃhitā, 7.2.11)
• Even number series (Taīttirīya-saṃhitā, 7.2.13)
• Arithmetic Progression with common difference 4, 5, 10, 20 and 100 (Taīttirīya-saṃhitā, 7.2.20)

To understand the import of the Vedic mantras, six supporting disciplines evolved. They are

1. Śikṣā which deals with classification and pronunciation of sounds (phonetics)
2. Vyakaraṇa which deals with grammar.
3. Chandas which discusses prosody or the study of metres.
4. Kalpa which discusses performance of yajñas and construction of altars and other accessories.
5. Nirukta which deals with etymology of words and their meanings.
6. Jyotisa which is the science of astronomy

These six are called as Vedāngas.

The body of literature called Sulbasūtras was composed in this period. They form a part of the Kalpa Vedānga. The Samskrit word Sulba means 'a rope'.