Number Theory in India

  • Takao Hayashi
Living reference work entry

It is difficult to find “number theory” in its proper sense in Indian mathematics. What I am going to describe below is how the Indians have treated kinds of numbers.

In the Vedas (ca. 1200–800 BCE), the oldest Hindu literature, a number of numerical expressions occur. Their favorite numbers were three and seven as well as a hundred and a thousand. The largest number contained in their common list of names for powers of ten is 1012 (called parārdha). Later (by the fourth century AD), those names came to be employed for denoting decimal places and became the nucleus of the Hindu list of decimal names (18 in number), while the Buddhists and the Jainas developed longer lists, which contained numbers as large as 1053 (tallakṣaṇa) or more.

The Jainas even speculated about different kinds of uncountable and infinite numbers ( Aṇuogaddārāiṃ, between the third and the fifth centuries AD). They divided the whole set of “numbers ( saṃkhyā) concerning counting ( gaṇanā)” into three subsets – (1)...


Arithmetical Operation Irrational Number Seventh Century White Mustard Favorite Number 
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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Doshisha UniversityKyoto CityJapan