The Ideas of India
Hindol Sengupta

“Did you know that the Vedic priests were using the so-called Pythagorean Theorem to construct their fire altars in 800 BCE?”[i]- so begins the review of the American Fields Medal-winning mathematician David Mumford of the book Mathematics in India written by another accomplished mathematician Kim Plofker.

The most common answer in India, indeed around the world, to this question would be – no.

Not many people know that the Pythagoras Theorem ought to “arguably be called Baudhayana’s theorem”, as Mumford writes, after the man who first composed the verses that expressed this numerical theory.

Baudhayana who? – you might ask.

"There is so much chatter in India about the idea of India but too little about the ideas of India"

The problem lies just there. There is so much chatter in India about the idea of India but too little about the ideas of India (Baudhayana, by the way, was a scholar, ascetic in ancient India); in fact, too little even about the philosophy from where the poet and writer Rabindranath Tagore may have taken the idea for the phrase - the idea of India. Tagore wrote that “the idea of India is against the intense consciousness of the separateness of one’s own people from others, which inevitably leads to ceaseless conflicts”. He could have easily said vasudhaiva kutumbakam, the Upanishadic phrase that translates to the whole world is my family.

The idea of India can perhaps be best celebrated if we pause to consider – and teach our children – where the idea for the idea of India comes from. What were the unique ideas that India gave the world?

Ideas like that is now known as Pascal’s triangle but known to ancient Indian mathematicians as meru prastara. The mathematician Pingala (third century BCE) dealt with this in detail in his Chandas-sutra.

Pingala and Panini (fifth century BCE) along with the likes of Aryabhata, Bhaskara and Brahmagupta are the pillars of ancient Indian mathematics. Astonishingly, Panini’s immortal fame is not even as a mathematician but as the definitive Sanskrit grammarian. But he also “introduced abstract symbols to denote various subsets of letters and words that would be treated in some common way in some rules; and he produced rewrite rules that were to be applied recursively in a precise order”, notes Mumford, “one could say without exaggeration that he (Panini) anticipated the basic ideas of modern computer science”.

It was the Indian scientist Aryabhata, born around 476 CE, who gave the first approximate value of ‘pi’ correct to four decimals (62832/20000; 3.1416). Indian mathematics—both in the ancient and classical period—surpassed Greek and Roman achievements, noted B.V. Subbarayappa, the first non-Westerner to be elected president of the History of Science division of the International Union of History and Philosophy of Science. Aryabhata “knew the rules for the extraction of square and cube roots, areas of triangles and trapezium, circles, volumes of sphere and pyramic, arithmetic progression and summation of series, fractions.”[ii]

"one could say without exaggeration that he (Panini) anticipated the basic ideas of modern computer science"

 In medicine, ancient India gave the Sushruta Samhita (probably sixth century BCE), which had some of the earliest and most detailed advisories on illnesses and surgery known to man. Sushruta, the medical practitioner sometimes referred to as the father of Indian medicine, described 101 types of blunt surgical instruments and twenty kinds of sharp instruments, including “forceps, tongs, scalpels, catheters, bougies, trocare, syringes, speculums, needles, saws, scissors, lances, hooks and probes.”[iii]

Indian physicians of that age knew delicate procedures like laparotomy and lithotomy. They knew the surgical procedure to remove cataract from the eyes, perform craniotomy and anal fistula operations. “Another feat,” writes Subbarayappa, “related to the joining of the lips of the wound by causing them to be bitten by ants and then cutting off the body of the ants, leaving behind the mandibles which would clamp the wound.”[iv]

The Encyclopaedia Britannica (2008) notes that the Samhita was probably the world’s first medical document to identify and record leprosy as a disease.

In chemistry, from dyes to alcohol to the use of mercury, one needs to only look at the writings of the renowned chemist Prafulla Chandra Ray and his History of Hindu Chemistry or the writings of British scientist and historian Joseph Needham to get a sense of breadth of early chemical knowledge in India. Just to give a sense of the credibility of these men: Ray’s work on a water- soluble mercurous nitrate was hailed around the world, including publication in Nature in 1912 and subsequently in the Journal of the Chemical Society. Ray, apart from writing more than 100 scientific papers, founded the Bengal Chemical and Pharmaceutical Works, and—inspired by the famous French chemist Marcellin Berthelot’s voluminous Les origines de l’alchimie’—published his magnum opus, the two-volume History of Hindu Chemistry in 1902 and 1908 (one volume each in those years). Instantly hailed as a breakthrough publication, the books were praised by Berthelot himself in a review.

"Wouldn’t it be wonderful if many, many more Indians realise that in India reason has gone hand in hand with belief?"

Needham was the first living person to hold three titles simultaneously—Fellow of the Royal Society, Fellow of the British Academy and the Order of the Companions of Honor. Needham’s seminal work defines why the East, specifically China, once had a seemingly insurmountable lead in invention and technology over the West, and why it fell behind. His work on India is equally significant, especially in revealing details about the early Indian prowess in the field of distilling alcohol.

These are just some of the scientific ideas that India gave the world. Wouldn’t it be wonderful if many, many more Indians realise that in India reason has gone hand in hand with belief – and that is why a monk like Swami Vivekananda could say, “Is religion to justify itself by the discoveries of reason, through which every other science justifies itself? Are the same methods of investigation, which we apply to sciences and knowledge outside, to be applied to the science of religion? In my opinion this must be so, and I am also of the opinion that the sooner it is done the better. If a religion is destroyed by such superstitions, it was then all the time useless, unworthy superstitions, and the sooner it goes the better.”[v]  



[i] David Mumford, Book Review: Mathematics in India, Notices of the American Mathematical Society, March 2010, p. 385

[ii] B. V. Subbarayappa, India’s Contribution to World Thought and Culture: India’s Contributions to the History of Science (Chennai: Vivekananda Kendra Prakashan Trust, 1970), p. 49

[iii] Subbarayappa, India’s Contribution to World Thought and Culture, p. 58

[iv] Subbarayappa, India’s Contribution to World Thought and Culture, p. 58

[v] Swami Vivekananda, The Complete Works of Swami Vivekananda, Vol. 1 (Mayawati: Advaita Ashram, 2007), p. 367


(Hindol Sengupta is an award-winning journalist, author of seven books, and a World Economic Forum Young Global Leader)

The views expressed above belong to the author(s) and the Narendra Modi website and Narendra Modi App does not necessarily endorse the views expressed.