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