Presidential address to the

Symposium on Ancient Indian Scientific Knowledge.

(Feb.25, 2003)


I am delighted to be here today in the midst of so many luminaries and under the benign divine presence of the most respected sage that ever walked on Earth in the twentieth century. The Samskrita Academy and the KSRI have to be congratulated for having thought of this  symposium on Ancient Indian Scientific Knowledge.  I am greatly honoured to have been asked to preside over this symposium. Since there are five expert speakers lined up to speak today, three in the forenoon and two in the afternoon, I shall restrict my presidential remarks to a few general observations, mostly as an introduction.


The Ancientness of Indian knowledge goes back not just to a few centuries  or even a few millenia, but it goes back to several yugas, where each yuga is itself several hundreds of millenia. The words ‘Scientific Knowledge’ may prompt you to think that we are talking of the Mathematics, Physics, Chemistry and Biology that we now know of from our contacts with the western world. There is a mistaken impression in some quarters that science and scientific knowledge are the prerogatives of only the past few centuries of history. It is not so. From time immemorial all knowledge in India had been scientific. When I use the word scientific, please do not think only in terms of modern laboratories where they experiment, enquire, hypothise, make further experiments and arrive at theoretical conclusions, only to be reconfirmed and revalidated by further experiment and enquiry.  It is the scientific methodology  that is the important factor here. Remembering the meaning of scientific methodology, we can safely claim that  all knowledge in India has been scientific only. One of the most ancient of all books in the world, the Taittiriyopanishad, chapter 3

adhIhi bhagavo brahmeti .... sa tapas taptvA.

The disciple is enjoined to investigate the cause of all causes by doing tapas that is, one-pointed self-negating concentration, a spiritual travail for which ancient India was legitimately famous. The disciple goes through the process step by step. At every stage of his ‘finding’  he comes back and reports to the Guru. The latter is not satisfied with the finding and exhorts the disciple to investigate again.

Punareva --- pitaramupasasAra>


The disciple proceeds from the obvious and the outer to the deeper and inward principles one by one: from matter to life, from life to mind, from mind to intelligence, and finally from intelligence to bliss;

From anna to prANa, from prANa to manas, from manas to vijnAna and from vijnAna to Ananda.


This spirit of enquiry is the sum and substance of all quest in ancient times. Whether the object of enquiry was spiritual or not, the method always incorporated this spirit of relentless enquiry and experiment. This is why I call all ancient Indian knowledge scientific.


In the beginning no distinction was made between  the so-called spiritual pursuit and the secular pursuit of material knowledge. But even in later times when such a distinction was made, the spirit of scientific enquiry continued. Whether it was the magnum opus of the 6th century B.C.E., namely, the ashTAdhyAyI of Panini the Grammarian, or the Vaiseshika sUtras of Kanada (of about the same time) about the atomic theory of matter or the vast treasures of Jain literature (around the 2nd century B.C.E.) on Infinity and the law of indices, or  Pingala’s Chandas-shAstra of the 1st century B.C.E. talking about Vedic metres, or it was Vedanga jyotisha, or the Sulva-sutras of Bodhayana and Apastambha (7th and 8th centuries B.C.E.),  or the AryabhatIya of Aryabhata, or the conceiving of the Shriyantra that goes back to even the atharvaveda, or the Surya-siddhanta of Varahamihira of the 6th century C.E.,  or the Brahmasphuta-siddhanta of Brahmagupta of the 7th century C.E., or   the Rasa-ratnAkara of Nagarjuna of the 10th century, or the Siddhanta Siromani of Bhaskara of the 12th century  -- whatever it was, the scientific quest continued.   


In spite of the significant and voluminous contributions of  the Greeks to Number Theory, Geometry and Mensuration, the credit of inventing a practically useful notation for writing and communicating with numbers goes back to the Hindu school of thinkers of the first century B.C.E. It is again an amazing fact that long before these notations were used, probably even before the time of the Mahabharata, Samskrit literature had already been using unique word names for powers of 10. Listen to a passage from Krishna Yajur Veda (4th Khanda, 4th Prashna): This is a prayer and a wish for the wealth of cows to abound in large numbers, like millions and millions.


sahasrAyatvemAme agna ishTakA dhenavassantv ekA ca shatamca sahasramcAyutamca niyutamcaprayutamcArbudamca nyarbudamca samudrashca madhyamcAntashca parArdhashcemAme agna ishTakA dhenavassantu.


The counting of cows here goes by  hundreds, thousands, and thousands and millions of hundreds. The actual sequence of powers of ten has a word for each power of ten upto the seventeenth, though not all of this is used in that passage just quoted. The actual sequence as defined in books of Mathematics like Leelavati is:


Eka, shata, sahasra, ayuta, laksha, prayuta, koti, arbuda, abja, kharva, nikharva, mahapadma, shankha, jaladhi, antya, madhya, parArdha.


Here parArdha is 10 to the power of 17. It is the number of human years in one half of  Brahma’s life. The very fact that these words are picked and used in the veda itself shows how ancient the concept is. These names have been freely used both in literary and scientific writings  from the mahAbhArata times onward.


I dare not invade into the topic of the first speaker today, Prof. M.S. Rangachari. But having enjoyed all my life the charms and beauties of Mathematics I cannot resist the temptation of quickly  and briefly summarizing for you the greatness of our ancients in the Mathematical field.  The number zero,   one of the most significant inventions,   is the subtle gift of the Hindus of antiquity to mankind.. To it must be credited  the enormous usefulness of its counterpart, the place value system of expressing all numbers with just ten symbols. And to these two concepts we owe all the arithmetic and mathematics. The mathematical climate among the Hindus, was congenial for the invention of zero and for its use as the null-value in all facets of calculation. Then there is Vedic Mathematics which has caught the rapt attention of the whole world as a pedagogical short-cut to manipulatory mathematics. Among the Sulba sutras, the Bodhayana Sutras  (800 - 600 B.C.)  contains among other things a general statement of the Pythagorean theorem, an approximation procedure for obtaining  square roots and a number of geometric constructions  that  include an approximate squaring the circle, and construction of rectilinear shapes whose area was equal to the sum or difference of areas of other shapes. To the Jaina thinkers must be given  the credit of being  the first, in the chronology of scientific thinking, to have recognised  that all infinities were not the same.  They also were aware of the Theory of indices. The Bakshali manuscript has the unique distinction of having, for the first time, in the entire history of Ancient Indian mathematics, the subject matter organised in the sequence: a rule; a relevant example in word form; the same in notational form; the solution and finally the demonstration or the proof.. It was from here the  Rule of Three  was taken to Europe via the Arabs and it was then known as the Golden Rule. It became very popular in Europe after the Renaissance. The apex of mathematical achievement of ancient India  occurred during the so-called classical period of Indian Mathematics. The great names are: Aryabhata I (b.476 A.D.) ; Brahmagupta (b.598 A.D.); Bhaskara I (circa 620 A.D.) ; Bhaskara II (b.1114  A.D.); Aryabhata gave  the formula for the area of a triangle. His Aryabhatiyam is a monumental work. It was partly through a translation of the  work of Brahmagupta, who was himself inspired by Aryabhata,   that the Arabs became aware of Indian astronomy and mathematics. The sheer ingenuity and versatility of Brahmagupta's approach to indeterminate equations of the second degree  is the climax of Indian work in this area.  It was not until 1767 A.D. that the western world had a complete solution to such types of equations, wrongly called Pell's equation, by Lagrange's method of continued fractions. Bhaskara II introduces the notion of instantaneous motion of a planets. He clearly distinguishes between average velocity and accurate velocity in terms of differentials. His work on fundamental operations, his rules of three, five, seven, nine and eleven, his work on permutations and combinations and his handling of zero all speak of a maturity, a culmination of five hundred years of mathematical progress.


Not only in Mathematics but in other fields also the ancients of India showed excellence.  Take Chemistry for example. The excellence in the smelting of metals that was achieved in India as early as two millenia ago (as is validated by the 1500-year-old non-rusting iron pillar at Delhi),  the distillation of perfumes and fragrant ointments, the making of dyes and pigments, the extraction of sugar – all these point to a good understanding of the rudiments  of chemical knowledge that surpassed the corresponding knowledge that was obtainable in the rest of the world at the time. One can go on listing the scientific glories of ancient India. In fact the speakers of today are going to do exactly that job. But after all the wonder that India was in ancient times, as the centuries advanced and as we bent back to successive generations of invading seekers of imperial glory and exploiters of the country’s wealth as well as knowledge, by the time of the nineteenth century, India was a country, in Rabindranath Tagore’s words, ‘enveloped in dense and deep darkness, as at the deadly midnight hour, afflicted by many ills and in a state of stupor..’. These words occur in the same poem of his, the first stanza of which we nowadays sing with great pride, as our national anthem. In the fourth stanza of the same poem, he says: ‘ghora-timira-ghana-nibiDa-nishithe –pIDita-mUrcita-deshe ...’. Why did this fall happen? Why this all-round decline? I hope the speakers will give some of their time to this.


I congratulate every one of the experts who are going to share with us today their findings on this interesting topic of Ancient Indian Scientific Knowledge. I am glad I have this opportunity  and responsibility to listen to all of them. And I  look forward to a thought-provoking symposium. In the process I expect to learn a lot from them. Thank you.  


Copyright © V. Krishnamurthy  1 Jan. 2007    Homepage