VEDIC MATHEMATICS - BHARAT'S SCIENTIFIC HERITAGE
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Vedic Mathematics
By Suresh Soni
Page 22/35
The Organiser
August 12, 2007 issue
Many scholars have described the journey of the Indian
numerals throughout the world. A brief mention of it has
been made by Bharti Krishna Teerthaji, the Shankaracharya
of Puri in the foreward of his amazing book on mathematics
called Vedic Mathematics.
He writes, "It gives me great pleasure to say that some
well known modern mathematicians like Prof. G. P. Halstand,
Prof. D. Morgan and Prof. Hutton, who are researchers and
lovers of truth have, in contrast to Indian scholars,
adopted a scientific outlook and have wholeheartedly
praised India's unique contribution to the progress of
mathematical knowledge."
The examples of some of the scholars will present ample
explicit proofs themselves.
1 On page 20 of his book The Foundation and Process of
Mathematics, Prof. G. P. Halstand says, "The significance
or importance of the discovery of the zero can never be
explained. Giving not just a name but authority, in fact,
power to 'nothing', is the characteristic of the Hindu
community, whose invention, it is. It is like giving the
power of the dynamo to nirvaan or salvation. No other
single mathematical invention has been more effective than
this in the general development or progress of intelligence
and power."
2 In the same context, B. B. Dutt, in his narrative, "The
modern way to express numerals" (Indian Historical
Quarterly, Issue-3, pp.53O-540) says, "The Hindus had
adopted the 'Decimal System' a long time back. The
numerical language of no other country had been able to
achieve or acquire the scientific calibre and the
completeness that ancient India had. The ancient Indians
had achieved success in expressing any number beautifully
and easily with the help of only ten symbols. The beauty of
Hindu numeral markings attracted the civilised world and
they gladly adopted it."
3 In his article 'New Light on our Numerals' published in
The bulletin of the American Mathematical Society pp. 366-
369, Prof. Ginsberg says, "In around 770 AD, Abba Sayeed
Khalifa Al-Mansur of Baghdad had invited the famous Hindu
scholar Kank of Ujjain to the famous court of Baghdad. This
is how the Hindu way of marking numerals reached Baghdad.
Kank taught Hindu astrology and mathematics to the Arab
scholars. With Kank's help they even translated
Brahmagupta's Brahma Sphut Siddhant into Arabic. French
scholar M. F. Nau's latest discovery proves that Indian
numerals were known in Syria in the 7th century and were
also praised."
4 In his essay, B. B. Dutt further writes, "These numerals
slowly reached the west via north Arabia and Egypt and by
the 11th century reached Europe. The Europeans called them
Arabic numerals because they got them from Arabia but the
Arabs themselves unanimously called them Hindu numerals."
(Al-Arkan-Al-Hind)
The Decimal System: Ekam of Sanskrit became ek in Hindi and
'one' in Arabic and Greek while the shunya became sifar in
Arabis, jeefar in Greek and 'zero' in English. This is how
Indian numerals spread throughout the world.
Arithmetic: The sequence-wise description of the numbers
can be found in the Yajurved:
Savita prathameahannagni rdviteeye vayustriteeya
Aadityenchaturthe chandramaah
Panchamarituh shashthe marootah saptame brahaspatirashtame
Mitro navame varuno dashamam indra ekaadashe
Vishwedeva dwadashe
- (Yajurved 39-6)
What is special is that the numbers are given here from one
to twelve in a sequence.
-From the aspect of counting, the largest number known to
the ancient Greeks was myriad which is equal to 104 or
10,000 and the largest number known to the Romans was 10ณ,
i.e. 1000. On the contrary, many kinds of counting were
prevalent in India. These methods were independent. The
methods described in the Vedic, Buddhist and Jain texts,
have a similarity in the names of some of the numbers but
there is a difference in the value of the numbers.
First: Next number multiple of 10: This means that the
number that comes next is 10 times more. The second mantra
in the 17th chapter of the Yajurveda Samhita refers to
this, whose sequence is given -- Ek, dash, shat, sahastra,
ayut, niyut, prayut, arbud, nyarbud, samudra, madhya,
ananta and parardh. In this way, Parardh measured 10นฒ that
is one thousand billion or one trillion (US).
Second: Next number multiple of 100: This means that the
next number is 100 times more than the earlier number. In
this context, we must refer to the conversation between
mathematician Arjun and Bodhisatva in Lalit Vistar, the
Buddhist text from the 1st century BC in which he asks what
the number after 1 crore is? In reply, Bodhisatva describes
the numbers after crore, which are multiples of 100.
Shat (One hundred) koti = ayut, niyut, kankar, vivar,
kshomya, nivaah, utsang, bahul, naagbal, titilamb,
vyavasthanapra-gyapti, hetusheel, karahu, hetvindriya,
samaaptalambh, gananagati, nikhadh, mudraabal, sarvabal,
vishagyagati, sarvagya, vibhutangama and tallakshana which
meant that tallakshana means 10 raised to the power of 53.
(i.e.1053)
Third: Next number multiple of ten million: The 51st and
52nd chapters of Katyayan's Pali Grammar has reference to
multiples of crores, i.e. the next number is a crore times
(i.e.107 times) more than the earlier number.
In this centext, the Jain text of Anuyugodwar describes the
numbers after koti as follows --
Koti koti, pakoti, kotyapakoti, nahut, ninnahut,
akkhobhini, bindu, abbnd, nirashbud, ahah, abab, atat,
sogandhik, uppalkumud, pundareek, padum, kathaan,
mahakathaan and asankhyeya.
Asankhyeya measures 10140 that means 10 raised to power of
140.
From the above description, it becomes quite clear as to
how much developed was the knowledge of numbers in India in
the ancient times while the rest of the world did not know
more than 10,000.
The above references have been given in detail in
Vibhootibhushan Dutt and Avadhesh Narayan Singh's book The
History of Hindu Mathematics.
(This book is available with Ocean Books (P) Ltd, 4/19 Asaf
Ali Road, New Delhi-110 002.)
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