Science and Mathematics in Ancient India: Scholars and Texts

Ancient India produced a body of work in mathematics, astronomy, medicine and metallurgy that examiners return to year after year, because the questions are easy to set and easy to check: a scholar, his book and his field. This note arranges that material in the order a student can remember it, first the mathematicians and astronomers, then the physicians, then the metal workers, and finally a table that pairs every name with its text.

Mathematics, from the Sulbasutras to the Kerala school

The oldest Indian mathematics is geometry written for ritual. The Sulbasutras, appendices to the Shrauta Sutras composed by Baudhayana, Apastamba, Katyayana and Manava, give rules for building sacrificial altars of a fixed area and shape, and the Baudhayana Sulbasutra states the proposition that the square on the diagonal of a rectangle equals the sum of the squares on its two sides, the result Europe knows as the theorem of Pythagoras. Pingala, in his Chandahshastra on metre, worked out how to count the arrangements of long and short syllables, which makes his text the earliest Indian work on combinations and on a two-symbol, that is a binary, notation.

The decimal place-value system, in which the same digit means a different amount depending on where it stands, and the use of zero both as a placeholder and as a number in its own right, are India's largest contribution to mathematics. Brahmagupta, in the Brahmasphutasiddhanta of 628 CE, was the first to set out rules for arithmetic with zero and with negative quantities, which he called fortunes and debts. Aryabhata, born in 476 CE, wrote the Aryabhatiya in 499 CE in four parts, the Gitikapada, the Ganitapada, the Kalakriyapada and the Golapada; he gave a value of pi equivalent to 3.1416 and described it as approximate, drew up a table of sine differences, and invented the kuttaka method for solving indeterminate equations. Mahaviracharya, a Jain mathematician of the ninth century at the Rashtrakuta court, wrote the Ganita Sara Sangraha. Bhaskara II, also called Bhaskaracharya, composed the Siddhanta Shiromani in 1150 CE, whose four parts are the Lilavati on arithmetic, the Bijaganita on algebra, the Grahaganita and the Goladhyaya on astronomy. Much later, Madhava of Sangamagrama founded the Kerala school, which obtained infinite series for pi and for the sine and cosine functions, and Nilakantha Somayaji of that school wrote the Tantrasamgraha in 1501.

Astronomy

The Vedanga Jyotisha is the oldest surviving Indian text on astronomy, written to fix the times of sacrifices. The Surya Siddhanta is the best known of the later siddhantas, the treatises that set out planetary positions and eclipse calculations. Varahamihira, who lived in the sixth century, summarised five such schools in his Panchasiddhantika and wrote the Brihat Samhita, an encyclopaedia covering astronomy, omens, architecture and the finding of water, as well as the Brihat Jataka on horoscopy. Aryabhata explained day and night by the rotation of the earth on its axis, and held that a solar eclipse is the moon's shadow and a lunar eclipse the earth's, in place of the older story of Rahu and Ketu swallowing the luminaries. Brahmagupta argued that heavy bodies fall because the earth attracts them, and Bhaskara II used a notion close to the instantaneous motion of a planet.

Medicine and surgery

Ayurveda has eight branches, from which it is called Ashtanga Ayurveda. Its three great texts, the Brihat-trayi, are the Charaka Samhita, the Sushruta Samhita and the Ashtanga Hridaya. Charaka, whom tradition places in the court of the Kushana king Kanishka, revised the older Agnivesha Tantra into the Charaka Samhita, a work on internal medicine, diagnosis, diet and ethics, and he is called the father of Indian medicine. Sushruta's Sushruta Samhita is a manual of surgery, shalya chikitsa, describing surgical instruments, the cutting of the cataract, the stitching of wounds and the rebuilding of a severed nose, so that Sushruta is remembered as the father of surgery and of plastic surgery. Vagbhata wrote the Ashtanga Hridaya and the Ashtanga Sangraha. The Laghu-trayi, the lesser triad, consists of the Madhava Nidana on diagnosis, the Sharngadhara Samhita and the Bhavaprakasha. Jivaka was the physician of the age of the Buddha, and Patanjali's Yoga Sutras gave yoga its classical form.

Chemistry, metallurgy and physics

Kanada, the founder of the Vaisheshika school of philosophy, held that matter is made of indivisible particles called paramanu, an atomic doctrine arrived at by reasoning rather than by experiment. Nagarjuna's Rasaratnakara belongs to rasashastra, the Indian alchemy that worked with mercury and other metals. In metalwork the evidence is in the objects themselves: the iron pillar at Mehrauli in Delhi, which carries an inscription of a king named Chandra, identified with Chandragupta II, has resisted rust for some sixteen centuries; wootz steel from south India was exported to west Asia and admired for its edge; zinc was distilled at Zawar in Rajasthan; and the bronze dancing girl of Mohenjo-daro shows that the lost-wax process was known in the Harappan period.

Scholars and their works

How the knowledge travelled

Indian numerals and the decimal system passed to the Arab world, where they were called the Hindu numerals, and from there to Europe as the Hindu-Arabic numerals, the system every calculation now uses. The Brahmasphutasiddhanta and other siddhantas were translated into Arabic at Baghdad in the eighth century, and Indian medical works were translated with them. India has acknowledged this inheritance in the names of its satellites: the first Indian satellite, launched in 1975, was named Aryabhata, and later satellites were named Bhaskara and Rohini.