How Aryabhata turned Mathematics into Poetry

We know that India have had an oral tradition of transmitting knowledge. Oral transmission of knowledge requires one to remember knowledge in the form of a poetry. Now one subject of knowledge which seems farthest from poetry is mathematics, however in our civilization these two have been combined together. In this article, we will learn how Aryabhata achieved this feat.

In Indian knowledge tradition the knowledge has been transmitted through sutras. Sutras as most of you know are small sentences in which a lot of information is packed. In the ancient times when there was no printing press, Brahmins used to memorize all these sutras and then transmit it from one generation to the next. In order to make the memorization of the sutras easy it important that they are poetical.

In the current times when we have printing press, we can write numbers as they are. However, it is very difficult to put these numbers into a poem, especially when the numbers are large. Imagine putting a number 3 crore 17 lakh 87 thousand 423 into a poem, it will be quite difficult. Sure, with the representation 31787423 you can write it in a compressed format, but if you have to recite it then this representation will not work. What you need is some way to change this number into a single word, which can then be inserted into a sutra.

In order to do that Aryabhata came up with a unique set of rules to change numbers into words. These set of rules he called dasagitika. For representing numerals, he took the Devanagiri alphabets and divided them into three categories a) classified consonants ( varga consonants) b) unclassified consonants ( avarga consonants) and c) vowels ( swara).

The varga consonants start from क and go to म. The avarga consonants start from य and go to ज्ञ and the vowels we all know are अ to अः. Here the total varga consonants are 25 and represent numbers 1 to 25. The avarga consonants from य to स represent numbers 30, 40, 50, 60, 70, 80 and 90. The avarga consonants ह is used to represent addition if needed. The vowels are used to represent successive integral powers of 10 starting from 100. आ represents 100 and subsequent vowels then represent higher powers of 10.

This is the overall layout of the dasagitika system. Now let us have a look at a few examples to really understand how this system worked. So let us go back to the number 31787423 we talked about previously. This number in dasagitika system will become

23 + 400 + 7000 + 80000 + 700000 + 1000000 + 30000000

Now by the dasagitika rule we will have the following

ब + (घ + आ) + (छ + इ) + (ज + ई) + (छ + उ) + (क + ऊ) + (ग + ए) which will become बघाछिजीछुकूगे

So as you can see the number 3 crore 17 lakh 87 thousand 423 has been converted into a rhyming word बघाछिजीछुकूगे, which is so much fun to speak and can be inserted into a sutra quite easily. This is the beauty of the dasagitika system.

Originally published at on June 27, 2020.

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