After Darwin, Albert Einstein became the next victim of India’s present fascist regime. At the 105th edition of Indian Science Congress (ISC), in front of roughly 5000 research scholars, our Union Science Minister Dr. Harsh Vardhan shamelessly claimed that recently died cosmologist Dr. Stephen Hawking “emphatically said on record that our Vedas might have a theory superior to that of Einstein’s E = mc2”. However, in a usual way he did not provide any evidence supporting his claim. Earlier, in the month of January, the Junior Education Minister Satyapal Singh, the self-proclaimed “Man of Science”, claimed ‘Darwinism’ is a myth. In recent times, it all started with the Narendra Modi’s deliberate attempt to link the birth of a mythological figure Karna with genetic science, and Lord Ganesh with plastic surgery, to glorify ancient India. These were further followed by the claim of Rajasthan Education Minister Vasudev Devnani that cow is the only animal that inhales and exhales Oxygen, and similar nonsensical and unscientific claims. Even in the 102nd ISC, a lecture claimed the existence of ancient aviation technology along with inter-country and inter-planet journeys with the help of it, in the time of Vedas.
In this background, it will not be irrelevant if we try to point various misconceptions centering the so-called ‘Vedic Mathematics’. The popular notion of it is actually a pernicious attempt to popularize certain calculation techniques. The primary aim of this is generating revenue to some people by creating a false myth centering the Vedic period. As S. G. Dani (professor of IIT Bombay and former chairman of the National Board of Higher Mathematics) pointed out, this has nothing to do with the actual mathematical development in the Vedic age. Rather, it was in the first half of the twentieth century, when among many, Swami Bharathi Krishna Thirthaji Maharaj of Puri mutt, attempted to popularize few quick calculation tricks by using the term ‘Vedic Mathematics’. In his propaganda, he mentioned 16 mathematical rules (sutras) such as Ekadhikena Purvena, Ekanyunena Purvena, Shunyam Saamyasamuccaye etc. For example, the sutra Ekadhikena Purvena instructs to follow few steps to find the square of a number. Let, the number is 65. Then, first we need to add 1 to the number preceding the last 5, i.e. 6 in this case. Here the sum is 7. Next we need to multiply these two numbers, i.e. 6 and 7. The multiplication is 42. Then, to get the answer, we need to write 25 after this. Hence, the square of 65 is 4225. It is true that it is a quick method, however, we must also need to know that this is only applicable for numbers ending with 5. In case of other numbers we need to remember other such methods, which implies that it is not at all reducing labor.
However, the real concern is the Vedic-ness of these sutras. The techniques used in these so-called Vedic mathematical sutras include the notion of zero. For example, the sutra Shunyam Saamyasamuccaye indicates that if the sum of one number with another is same, then the later number is zero. However, the discovery of zero took place in the Buddhist period, which is much after the Vedic age. The mythical claims rose to such an extent that many of these sutras employ decimal fractions, which is a very recent development in the history of mathematics. According to the claim of the author these sutras are present in the parishishta (appendix) of the Atharvaveda, and are applicable to every branch of mathematics such as arithmetic, algebra, geometry, trigonometry, conics, astronomy, and calculus. More interestingly, according to him, after eight years of “concentrated contemplation of forest solitude” he was able to unveil these sutras. Prof. K S Shukla, a renowned scholar of ancient Indian mathematics, tried to locate these sutras in the parishishta of Atharvaveda, as mentioned by Swamiji. However, he could not find any, and finally met Swamiji in 1950 and asked him regarding this. Swamiji replied: “they occurred in my own Parishishta and not any other”.
The actual mathematical development in late Vedic period and early Buddhist period can be found in the Shulvasutras (800 BC and 200 BC). Shulvasutra literally means ‘rules of the cord’, and as the name suggests, these sutras explains the laws of measurement with the aid of a rope. For example, the people on Vedic age faced problems such as the identification of East-West line for the preparation of yagna-vedi. Shulvasutras solved this problem with the help of sunrise, a vertical pole, and a rope. It also prescribed a method of drawing a perpendicular bisector using a rope. Even, critical problems like geometric area-preserving transformations from one geometric shape to another, was solved by Shulvasutras. The Boudhayana Shulvashutra, which was the oldest among all the sutras, proposed an interesting method to obtain a square of the same area as a given circle. It results into, a = 0.87868 * d (a = side of the square, d = diameter of the circle), whereas the result as per our modern calculation is a = 0.886228 * d. One shloka in this particular sutra also mentioned a mathematical expression of square root of 2. The result is accurate to five decimal places if compared with the correct value of square root of 2. Even, mention of number sets that form ‘Pythagorean triplets’ such as (3,4,5), (5,12,13), and a general statement resembling the Pythagoras theorem (without any mathematical proof) can be traced in the Shulvasutras. However, it is absolutely unfortunate that few mythical propaganda have superseded the real mathematical achievements of the late Vedic age.