Friday, 4 August 2017

A Sanskrit anthem for Mathematics

தமிழில் இந்த கட்டுரை

In the ninth century, most of today’s Karnataka was ruled by a king of the Rashtrakuta dynasty called Amogavarsha Nrpatunga. One of his inscriptions says that his kingdom extended from the Godavari to the Kaveri, so his territory was not confined to modern Karnataka.This king was also a very special scholar – he composed the oldest surviving great literature in the Kannada language, Kavirajamarga

In his court lived a great mathematician, Mahavira, who composed a book titled GanitaSaraSangraha. This is as remarkable as Kavirajamarga, because this is the oldest book in Sanskrit,exclusively dealing with mathematics. Hundreds of books  were composed in previous centuries in Sanskrit, including the famous books of Apastambha, Baudhayana, Aryabhata, VarahaMihira and Brahmagupta. But those books were either sulba sutras or jyotisha sutras, and mathmatics was one of the components of those books. 

GanitaSaaraSangraha is the first book where mathematics is the primary subject. Several later astronomers like Madhava, Parameshvara, Bhaskara and Nilakanta Somayyaji wrote books on Astronomy, which had chapters on Mathematics, so the older practice did not fade out.

Prof Rangacharya of Presidency College, Madras translated GanitaSaraSangraha into English in 1912. The book was translated first into Telugu by Pavuluri Mallana, in the eleventh century and most recently in 2000, to Kannada by Prof Padmavathamma, of the University of Mysore. To my knowledge, there is no Tamil translation, except perhaps my own translation of a mere three stanzas.

Mahavira, was a Jain. The first stanza of the GanitaSaraSangraha has the phrase namastasmai jInendrAya mahAvirAya नमस्तसमै जिनेन्द्राय महावीराय (Salutations to Jinendra Mahavira), a reference to the last Jain tirthankara, Vardhamana Mahavira. Interestingly, in their first slokas the Hindu astronomers Aryabhata salutes Brahma, Brahmagupta salutes Siva, and Nilakanta Somayyaji salutes Vishnu. An interesting  comparison may also be made to the famous Meguti inscription of Chalukya king Pulikesi in Aihole, which begins with a similar salutation to Jinendra (Jayati Bhagavaan JinendraH जयति भगवान् जिनेन्द्रः) 

This is the other remarkable aspect, because the book is in Sanskrit, not Prakrit. Popular belief is that most works by Jains and Buddhists were written in Prakrits (Jain works in Ardha Magadhi, and Buddhist works in Pali). While this is true of several Jain and Buddhist compositions of the first few hundred years, not just for philosophy or religion, but also for sciences, later Buddhists and Jains wrote in Sanskrit, which became the lingua franca not just for people who followed the Vedic religion, but also for the sciences and the arts. 

This is an extensive topic, which is not well-known to learned Indians, and I wont discuss it here. But this is very similar to how Latin was used in Europe, after the fifteenth century, not just as the language of the Christian clergy, but also of science and arts. Hence, Linnaeus developed Latin nomenclature for naming plants and animals by genus-species, Newton wrote his book book on physics Principia Mathematica de Naturalis in Latin, chemists from Lavoisier onwards, used Latin words to name most of the elements. And since the laws of Europe use Roman law to guide them, which thence guide the Constitution and laws of former European colonies like India, Pakistan, USA, Australia, most of Africa and the Americas, Latin is the primary language of global law, except in Islamic countries and China.

But in this blog, I wont discuss the new mathematical concepts expounded by Mahavira, but merely quote three stanzas of his poem, which I believe should be declared the Anthem of Mathematics, and included in every mathematics school text book, not just in India, but in every culture broadminded enough to enjoy and agree with this poem. Here is the Sanskrit source and my English translation. My Tamil translation is here

लौकिके वैदिके वापि तथा सामायिकेऽपि य: |
व्यापारस्तत्र सर्वत्र संख्यानमुपयुज्यते || ९
कामतन्त्रेऽर्थतन्त्रे च गान्धर्वे नाटकेऽपि वा|
सूपशास्त्रे तथा वैद्ये वास्तुविद्यादिवस्तुषु || १०
छन्दोऽलङ्कारकाव्येषु तर्कव्याकरणादिषु |
कलागुणेषु सर्वेषु प्रस्तुतं गणितं परम् || ११

laukikE vaidikE vaapi tathA sAmAyikepi yaH
vyApArastatra sarvatra sankhyAnam upayujyate
kAmatantre artatantre ca gAndarve nAtakepi vA
sUpashAstre tatA vaidye vAstu vidyAdi vastushu
cando alankAra kAvyeshu tarka vyAkranAdishu
kalA guneshu sarveshu prastutam ganitam param


In worldly life, in Vedic learning, in religious practice,
In business, in everything, Mathematics is useful.

In romance, economics, in music dance and drama,
In cooking, medicine and in architecture,

In prosody, poetry, logic and grammar,
In all the arts, Mathematics reigns supreme.

You can here this anthem rendered as a song by Sudarsanam here 

Meaning by words
laukikE – In worldly life
vaidikE – In Vedic learning
vaapi – also
tathA – likewise
sAmAyikepi – in religious practice
vyApAraH – in business
tatra – there
sarvatra – in everything
sankhyAnam – mathematics
upayujyate – is useful

kAmatantre – in romance
artatantre –in economics
ca – and
gAndarve – in music, the art of gandarvAs
nAtake – in dance and drama
api vA - also
sUpashAstre – in cooking
vaidye – in medicine
vAstu vidyAdi vastushu – in architecture and construction

cando alankAra – in prosody and poetry
kAvyeshu – in epic poetry
tarka – logic
vyAkrana- grammar
Adishu – in these
kalA guneshu – in arts
sarveshu – in everything
prastutam – is established (reigns)
ganitam – mathematics
param – supreme

If you liked this essay, you may enjoy reading these related blogs:

0. My Essays on Astronomy
  1. Video of Prof MS Sriram lecture on GanitaSaaraSangraha
  2. The Peacock’s Tail A interesting blog on GanitaSaraSangraha
  3. Field's medallist Manjul Bhargava on Sanskrit and Mathematics
  4. Some astronomy/mathematics slokas in Sanskrit
  5. Nilakantha Somayyaji’s Sanskrit mathematical pun
  6. Atyantakama Pallava’s poem (also sung by Sudharsanam)
  7. Aryabhata’s sloka for pi
  8. Varahamihira’s salutation to Agastya
  9. My essay on Aryabhata in The Week
  10. A comparison of timelines - Tamilnadu and Karnataka


  1. Sanskrit was the lingua franca of the scholorly world in Asia till a few centuries back. Dominic Goodall, a French Indologist based in Pondicherry has succinctly nailed :

    We hope too that it will remind readers of the diversity of the Sanskrit literary tradition. Sanskrit for many people in India today is associated with conservative social agendas held by those who often think that a return would be desirable to some imaginary golden past of religious righteousness in accordance with precepts that sages of the past expressed in brahminical treatises in Sanskrit. But the Sanskrit literary tradition is in fact astonishingly plural. For while Sanskrit is of course the language of many Hindu religious works, it is also the language of rejoinders and refutations by Buddhists and materialists and many others, indeed of all manner of philosophical debate, and it is at the same time so very much more than that as well. For it is also the language chosen for treatises on every kind of knowledge, both religious and secular, as well as a language of imagination, of poetry in verse and prose, resorted to by countless generations of readers and writers of many backgrounds who wished to receive or to communicate ideas. It is, in short, the language in which the bewilderingly diverse cultural memory of millions is stored. Certainly, it is the language of the relativising moral vision of the Bhagavad-­‐Gîtâ and of the caste-­‐bound strictures of the Manu-­‐smriti; but it is also that of neutral or sometimes decidedly amoral writings on medicine, on gemmology, on archery, on political acumen (the Arthashâstra), on the care of elephants (the Pâlakâpya), on music and stagecraft and on almost anything else you might care to think of besides.

    From On_The_Bawds_Counsel_2014 – Dominic Goodall (downloadable from
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  2. Thanks for this anthem on Mathematics by Mahavira and the rest of the interesting details on the little known facts which are otherwise difficult to find on our own.