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India’s Scientific Heritage-XIX
Vedic Mathematics
By Suresh Soni
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.
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 nirvana or salvation. No other single mathematical invention has been more effective than this in the general development or progress of intelligence and power.”
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.”
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.”
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 Yajurveda:
Savita prathameahannagni rdviteeye vayustriteeya
Aadityenchaturthe chandramaah
Panchamarituh shashthe marootah saptame brahaspatirashtame
Mitro navame varuno dashamam indra ekaadashe
Vishwedeva dwadashe
—(Yajurveda 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 10³, 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 10¹² 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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