Number Names – Indian Tradition

In the Indian tradition, Ganitha was not an independent field of study. It was part of Jyotisha which was one of the 6 Upavedas. Jyotisha included Mathematics, Astronomy & Astrology.

The original number names were – eka, dvir, tri, chatur, pancha, sat, sapta, ashta & nava. The multiples of ten were dasa, vimsati, trimsat, chatvarimsat, panchasat, sasti, saptati, ashti & navati.

The numeral shapes were evolving and were in the final form only around the 15th century,

Mathematics in Verse Form

In ancient India all knowledge was rendered in verse form, set to certain meter so that they can be chanted musically. This also made memorization easier. Slokas are an example of verse form.

Math in the Western Tradition

Even in Europe, until the Middle Ages, mathematics was written in textual form which we can call as Rhetoric Math.

In those days, mathematical symbols, including numerals, were not standardized. Manuscripts were copied by hand. Copying text was less error-prone than copying symbols.

With the invention of the printing press, large number of copies of books could be printed and symbol shapes also got standardised. Hence slowly symbolic math replaced rhetoric math.

Today we write mathematics in what has been borrowed from the western tradition.

Modified Number Names

Numbers, operations and even infinite series were rendered in verse form. The original number names may not fit into the meter of a particular verse.

Hence numbers were replaced with words, which may or may not have a direct connection with the numbers themselves. There was also a choice available in choosing words which will fit into the meter needed for that verse.

Two of the systems for choosing words for numbers were Bhoota Sankhya & Katapayadi Sankhya systems.

In Bhoota Sankhya system numbers were related to certain people, events or physical things which could be related to mythology.

Each of these words, say Netra, also had a large number of synonyms. Any of the synonyms which fitted the meter of the verse could be used.

In Katapayadhi system, the 25 consonants were mapped on to the numbers zero to nine. The consonants were divided into certain groups like Ka group, Ta group etc. This is what gave rise to the name Ka-Ta-Pa-Ya-Adi.

This is very similar to the system available on a phone to convert numbers to words.

Each number is associated with certain letters of the alphabet. These letters are printed along with the number itself. For example, 2 can be A, B or C, 3 can be D, E or F and so on. Depending on the number we want to convert to a word, we can form a word with the above letters so that it forms a word which is easy to remember. For example, post office number could be POST 1234 etc where P, O, S & T stand for certain numbers.

Naming Very Large Numbers

Vedic literature and mythology were already using very large numbers which were conceptualized as powers of ten. These were given separate names as shown below.

Place Value

In Vedic ritual mantras, powers of ten from ten to trillion were recited, each power having a different name, some of which have been given above.

In Patanjali’s Yogasutra and Sankara’s bhashya there are specific verses which seem to refer to this idea. The idea conveyed is that the same digit acquires a value of a hundred or ten depending on where it occurs.

Sankara says that it is similar to the same person being referred to as a son, husband, brother etc by different people depending on their relation to him. The these are quoted as examples to make a point in philosophy, is an indication that by their time the idea of place value seems fairly well established.