Religion in India

The History of the Vedic Age

Around 1500 BC, a group of Indo-Aryan peoples came from modern day Iran to India, where they would follow the Vedic Religion. Vedism was a polytheistic sacrificial religion involving the worship of numerous male divinities (and a few goddesses), most of whom were connected with the sky and natural phenomena. They were also in procession of a collection of sacred text, known as the Vedas, and it is through these texts we gain the first literary evidence of Indian culture and hence mathematics (Ian G Pearce, Mathematics). In fact, we refer to this period as the Vedic age because of the Vedas. Additionally, the Vedas was originally transmitted orally from one guru to another for generations, up until the 5th century BC (Vedic Religion). After the 5th century, the texts were finally written down, in which the surviving texts gave us knowledge of their religion and also "certain rites that continue to be observed within the framework of modern Hinduism" (Vedic Religion). Vedism was a polytheistic sacrificial religion involving the worship of numerous male divinities (and a few goddesses), most of whom were connected with the sky and natural phenomena.

The Mathematics of the Vedic People

The Vedas are primarily religious in content, but embody a large amount of astronomical knowledge. The development of astronomy and geometry came from the need to determine the correct times for Vedic ceremonies and accurate construction of altars. One such altar was designed in the shape of a falcon. There were other constructions but they are of little mathematical interest (Joseph, 2011).

This is a Vedic sacrificial altar in the shape of a falcon. It is made up of 4 different types of bricks, 60 a-type, 46 b-type, 6 c-type, and 24 d-type (Joseph, 2011).

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The Rise of Jainism

Around the 6th century BC, the Vedic religion began to wane, this is in part due to excessive religious and social practices, so the demand for altars declined. The perception of mathematics as a concept also changed around this time, changing from "fulfilling the needs of sacrificial ritual" to "an abstract discipline to be cultivated for its own sake" (Joseph, 2011). It was at this time Jainism started to take over, it was was a new religion and philosophy, which also gave us Jaina mathematics.

Jaina mathematics

The ideas of the mathematical infinite in Jaina mathematics is very interesting indeed and they evolve largely due to the Jaina's cosmological ideas. In Jaina cosmology time is thought of as eternal and without form (Jaina mathematics). This cosmology has strongly influenced Jaina mathematics in many ways and has been a motivating factor in the development of mathematical ideas of the infinite which were not considered again until the time of Cantor.

Cosmological texts detail the quantities and proportions of parts of the universe. There are many examples of the vital part mathematics plays in traditional Jain concepts of the universe (Mathematics of the universe).

Jaina mathematics recognised five different types of infinity. infinite in one direction, infinite in two directions, infinite in area, infinite everywhere and perpetually infinite (Indian mathematics). All before infinity was "invented" by the English mathematician John Wallis in 1655 AD. "Much of the Jaina theory of infinity is extremely advanced for the time in which it was conceived" (Indian mathematics).

Also found in Jaina works:

• Knowledge of the fundamental laws of indices.
• Arithmetical operations.
• Geometry.
• Operations with fractions.
• Simple equations.
• Cubic equations.
• Quartic equations (the Jaina contribution to algebra is severely neglected).
• Formula for π (root 10, comes up almost inadvertently in a problem about infinity).
• Operations with logarithms.
• Sequences and progressions.

Finally there's also the appearance of Permutations and Combinations in Jaina works, which appears to be an early form of Pascal triangle, called Meru Prastara, many centuries before Pascal himself "invented" it; another case where Indian contributions have been neglected severely (Indian mathematics).

(Halai, 2020)

Jainism, and Jaina Mathematics, never declined suddenly like the Vedic Religion, however around the 6th century AD, India was experiencing a decline politically and even mathematically. It was at this the work of a mathematician named Aryabhata would summarize all of Indian mathematics up to his time, and brought about the Classical period of Indian mathematics, bringing the sub-continent to a new era of intellectual resurgence, which lasted for 600 years.

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Sources

Encyclopædia Britannica, inc. (n.d.). Vedic religion. Encyclopædia Britannica. https://www.britannica.com/topic/Vedic-religion

Halai, C. (2020, August 2). Pingala’s algorithm part vi: Meru Prastaar - Indic Today. Indic Today - Indic Today. https://www.indica.today/quick-reads/pingalas-algorithm-meru-prastaar/

Indian mathematics. Maths History. (n.d.-a). https://mathshistory.st-andrews.ac.uk/HistTopics/Indian_mathematics/

Jaina mathematics. Maths History. (n.d.-b). https://mathshistory.st-andrews.ac.uk/HistTopics/Jaina_mathematics/

Jainism. Maths History. (n.d.-c). https://mathshistory.st-andrews.ac.uk/Projects/Pearce/chapter-6/

Joseph, G. G. (2011). The crest of the Peacock: Non-European roots of mathematics. Princeton University Press.

Mathematics in the service of religion: I. vedas and Vedangas. Maths History. (n.d.-d). https://mathshistory.st-andrews.ac.uk/Projects/Pearce/chapter-4/#:~:text=As%20a%20result%20of%20the,Equivalence%20through%20numbers%20and%20area

Mathematics of the universe - jainpedia. (n.d.). https://jainpedia.org/themes/principles/jain-universe/mathematics-of-the-universe/