Since my childhood, I have been conscious of two things related to the realm of mathematics, viz. that India has quite an impressive mathematical heritage dating back to Vedic times and that a book entitled Vedic Mathematics exists. Any layperson is bound to correlate the two and assume that the above-mentioned book deals with the profound mathematics that evolved from the time of the Vedic era. Nothing could be farther from the truth. In recent times the interesting and even somewhat entertaining contents of the book have been making waves in various quarters connected with the teaching of school mathematics and therein lies the need to introduce some clarifications.
Let me first talk a little about the extraordinary mathematics that grew from the time of the Vedas. Most of us are generally aware of the well-known theorem of Pythagoras in plane geometry. What many of us may yet be unaware of is the fact that the theorem was known in India since much before the time of Pythagoras. The theorem is clearly recorded in several texts that predate the time of Pythagoras by many centuries. In fact, the debate on the dating of ancient Indian knowledge and discoveries is far from settled and has suffered much damage at the hands of many zealous historians from schools of thought that lean to the left or to the right.
Perhaps mathematicians should take a greater interest in these matters to keep the record straight and neutral. Lest we stray from the matter at hand, I must iterate that a whole body of important mathematical knowledge grew around the practice of the Vedic rituals through fire sacrifices. This corpus of mathematical knowledge was recorded in texts known as the Sulba-Sutras. There are other texts too. The Sanskrit word Sulba stands for a piece of cord or string and the word sutra translates to formula or an aphorism. Hence, the Sulba-Sutras stand for mathematics that grew out of the use of lengths of cord for the purposes of construction of sites for sacrificial altars associated with the practice of Vedic rituals.
Anyone who is familiar with any construction work in modern times shall recognise at once that the cord referred to in the Sulba-sutras is essentially the same sort of cord that a mason uses even now for construction purposes. There are many important ideas of geometry that are recorded in these ancient texts. Each Sulba-Sutra is ascribed to a mathematician and the Sulba-Sutra of Baudhayana that predates Pythagoras by a few hundred years at least—as agreed by all experts—clearly records the theorem of Pythagoras. Incidentally, what many may not know is that Pythagoras visited India in search of knowledge. Voltaire says this clearly when he records, “All the world knows that Pythagoras, when he resided in India, attended the school of the Gymnosophists.” There is other hard evidence that indicates that Pythagoras had visited India.
I am not indicating that he stole the idea of the theorem. However, the theorem was much in vogue in India much before Pythagoras came to India. There have been plenty of other great mathematical principles that India developed during the Vedic age. This includes Pingala’s Meru prastara rediscovered in Europe 1800 years later as Pascal’s triangle. Of course, we are aware that the decimal system is India’s contribution, with zero playing a central role. The story is very impressive and India’s achievements, derived from the Vedic tradition, were phenomenal in terms of substance and breadth. I must also mention that calculus—one of the finest inventions of the human mind—was discovered in India by Bhaskaracharya in the 12th century AD. Many important ideas of calculus were invented in India from the time of Bhaskaracharya to the time of Madhavacharya in the 15th century AD, a good two hundred years before Newton.
I wish to contrast the above with what is in the book Vedic Mathematics. This book has been authored by the late Swami Bharati Krishna Tirtha, who served as the Shankaracharya of the Govardhana matha at Puri from 1925 till his demise in 1960. The venerable Shankaracharya says in the preface that he has been inspired by the Vedas. Significantly, he does not state anywhere that the contents of the book are taken from the Vedas. Are the contents in any significant manner related to the Vedas or to the great mathematics that came about during the Vedic period or thereafter in direct continuity of the grand Vedic tradition? I am afraid the answer to this question is emphatically in the negative. One can infer this also from the fact that the sutras of the book cannot be found in any ancient text, let alone the Vedas. In addition, the Sanskrit of the Shankaracharya is distinctly different from the Sanskrit found in the Vedas.
This has also been stated in the foreword to the Shankaracharya’s book, written by Dr Agrawala, who was the General Editor of the series under which the book was published. What the book offers are methods that facilitate quick arithmetical and algebraic computations in special cases. To that extent it has some value as it helps make some computations easier, but there is nothing magical or mysterious there and the methods are of limited practical value for various valid reasons. The main point to be recognised is that the book does not carry any mathematical ideas in the real sense that can be compared to the idea of the theorem of Pythagoras or to the idea behind the Meru prastara or even the binomial theorem that was discovered in India by Halayudh in 1200 AD via the Meru prastara. Thus it is wise to keep in mind that the book has very limited use in true mathematical learning at the level of schools.
A whole body of important mathematical knowledge grew around the practice of the Vedic rituals through fire sacrifices. This corpus of mathematical knowledge was recorded in texts known as the Sulba-Sutras ... There have been plenty of other great mathematical principles that India developed during the Vedic age. This includes Pingala’s Meru prastara rediscovered in Europe 1800 years later as Pascal’s triangle
Dinesh Singh is the Former Vice-Chancellor, Delhi University, and Adjunct Professor of Mathematics, University of Houston Email: firstname.lastname@example.org