Aryabhata was an astronomer and the earliest Hindu mathematician whose work and history are available to modern scholars.(1) He belonged to the ruling class of Hindus, called Brahmans, and only the Brahmans were allowed to receive a mathematical education.

 

 

Mathematics–Number Notation System

 

 

Aryabhata took some of the first steps toward a positional number system with his “syllable-numbers.” The vowels in each syllable of these words indicated ones, tens, or hundreds. For example, Aryabhata wrote the number 3,336 as:

 

Ca  ya  gi  yi

6     3    3   3

 

beginning with the ones on the left, as all Hindus did. Aryabhata gave numerical values to the 33 consonants of the Indian alphabet to represent 1, 2, 3, …, 25, 30, 40, 50, 60, 70, 80, 90, 100. The higher numbers are denoted by these consonants followed by a vowel to obtain 100, 10000, …. In fact the system allows numbers up to 1018 to be represented with an alphabetical notation. George Ifrah in his book, A Universal History of Numbers, argues that Aryabhata was also familiar with numeral symbols and the place-value system. He writes:

 

“…it is extremely likely that Aryabhata knew the sign for zero and the numerals of the place value system. This supposition is based on the following two facts: first, the invention of his alphabetical counting system would have been impossible without zero or the place-value system; secondly, he carries out calculations on square and cubic roots which are impossible if the numbers in question are not written according to the place-value system and zero.”(2)

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Aryabhata’s method may seem an awkward, confusing one; however, it laid the groundwork for Bhāskara I (so called to distinguish him from a later mathematician with the same name). This mathematician, who lived from c. 598 to c. 665, introduced an improved system that was positional. In Bhāskara’s poetry, syllables that stood for 3 could also stand for 30 or 300, depending on their place in the word. Bhāskara’s system has a zero as well.

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Footnotes:

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(1) Encyclopaedia Britannica, Micropaedia, Volume 1, 1993, 15th Edition, p. 611.

(2) Georges Ifrah, The Universal History of Numbers (New York, 2000), p. 447.