Indian mathematicians invented negative numbers: the British mathematician Lancelot Hogben, grudgingly acknowledging this, suggested ungraciously that “perhaps because the Hindus were in debt more often than not, it occurred to them that it would also be useful to have a number which represents the amount of money one owes.” (That theory would no doubt also explain why Indians were the first to understand how to add, multiply, and subtract from zero — because zero was all, in Western eyes, we ever had.)
The Sulba Sutras, composed between 800 and 500 B.C., demonstrate that India had Pythagoras's theorem before the great Greek was born, and a way of getting the square root of two correct to five decimal places. (Vedic Indians solved square roots in order to build sacrificial altars of the proper size.) The Kerala mathematician Nilakantha wrote sophisticated explanations of the irrationality of pi before the West had heard of the concept. The Vedanga Jyotisha, an astrological treatise written around 500 B.C., declares: “Like the crest of a peacock, like the gem on the head of a snake, so is mathematics at the head of all knowledge.” (Our mathematicians were poets, too!) But one could go back even earlier, to the Harappan civilization, for evidence of a highly sophisticated system of weights and measures in use around 3000 B.C.
Archaeologists also found a “ruler” made with lines drawn precisely 6.7 millimeters apart with an astonishing level of accuracy. The “Indus inch” was a measure in consistent use throughout the area. The Harappans also invented kiln-fired bricks, less permeable to rain and floodwater than the mud bricks used by other civilizations of the time. The bricks contained no straw or other binding material and so turned out to be usable five thousand years later when a British contractor dug them up to construct a railway line between Multan and Lahore. And though they were made in fifteen different sizes, the Harappan bricks were amazingly consistent: their length, width, and thickness were invariably in the ratio of 4:2:1.
“Indian mathematical innovations,” writes Teresi, “had a profound effect on neighboring cultures.” The greatest impact was on Islamic culture, which borrowed heavily from Indian numerals, trigonometry, and analemma. Indian numbers probably arrived in the Arab world in 773 A.D. with the diplomatic mission sent by the Hindu ruler of Sind to the court of the Caliph al-Mansur. This gave rise to the famous arithmetical text of al-Khwarizmi, written around 820 A.D., which contains a detailed exposition of Indian mathematics, in particular the usefulness of the zero. With Islamic civilization's rise and spread, knowledge of Indian mathematics reached as far afield as Central Asia, North Africa, and Spain. “In serving as a conduit for incoming ideas and a catalyst for influencing others,” Teresi adds, “India played a pivotal role.”
For a nation still obsessed by astrology, it is ironic that Indians established the field of planetary astronomy, identifying the relative distance of the known planets from the sun, and figured out that the moon is nearer to the earth than the sun. A hymn of the Rig Veda extols “nakshatra-vidya”; the Vedas’ awareness of the importance of the sun and the stars is manifest in several places. The Siddhantas are among the world's earliest texts on astronomy and mathematics; the Surya Siddhanta, written about 400 A.D., includes a method for finding the times of planetary ascensions and eclipses. The notion of gravitation, or gurutvakarshan, is found in these early texts. “Two hundred years before Pythagoras,” writes Teresi, “philosophers in northern India had understood that gravitation held the solar system together, and that therefore the sun, the most massive object, had to be at its center.”
The Kerala-born genius Aryabhata was the first human being to explain, in 499 A.D., that the daily rotation of the earth on its axis is what accounted for the daily rising and setting of the sun. (His ideas were so far in advance of his time that many later editors of his awe-inspiring Aryabhattiya altered the text to save his reputation from what they thought were serious errors.) Aryabhata conceived of the elliptical orbits of the planets a thousand years before Kepler, in the West, came to the same conclusion (having assumed, like all Europeans, that planetary orbits were circular rather than elliptical). Aryabhata even estimated the value of the year at 365 days, six hours, twelve minutes, and thirty seconds; in this he was only a few minutes off (the correct figure is just under 365 days and six hours). The translation of the Aryabhattiya into Latin in the thirteenth century taught Europeans a great deal; it also revealed to them that an Indian had known things that Europe would only learn of a millennium later.
If Aryabhata was a giant of world science, his successors as the great Indian astronomers, Varamahira and Brahmagupta, have left behind vitally important texts that space does not allow me to summarize here. The mathematical excellence of Indian science sparkles through their work; Indian astronomers advanced their field by calculations rather than deductions from nature. Teresi says that “Indian astronomy, perhaps more than any other, has served as the crossroads and catalyst between the past and the future of the science.” Inevitably, Indian cosmology was also in advance of the rest of the world. Teresi's book has a fascinating section relating Hindu creation myths to modern cosmology; he discusses the notion of great intermeshing cycles of creation and destruction and draws stimulating parallels with the big bang theory that currently commands the field.
The ancient Indians were no slouches in chemistry, which emerges in several verses of the Atharva Veda, composed around 1000 B.C. Two thousand years later, Indian practical chemistry was still more advanced than Europe's. The historian Will Durant wrote that the Vedic Indians were “ahead of Europe in industrial chemistry; they were masters of calcination, distillation, sublimation, steaming, fixation, the production of light without heat, the mixing of anesthetic and soporific powders, and the preparation of metallic salts, compounds, and alloys.” An Indian researcher, Udayana, studied gases by filling bladders and balloons with smoke, air, and assorted gases. The ancient Jain thinkers predicted the notion of opposite electrical charges and advanced a notion of the “spin” of particles, which would not be discovered by the West till the twentieth century.
So what about physics? Indian metaphysicists came upon the idea of atoms centuries before the Greek Democritus, known in the West as the father of particle physics. In 600 B.C. Kanada established a theory of atoms in his Vaisesika Sutra; the Jains went further in later years, expounding a concept of elementary particles. Indians also came closer to quantum physics and other current theories than anyone else in the ancient world.
The Upanishadic concepts of svabhava— the inherent nature of material objects — and yadrchha (the randomness of causality) are startlingly modern. The Upanishads developed the first classifications of matter, evolving into an awareness of the five elements and later of the five senses. When the Samkhya philosophers explained, in the sixth century B.C., that “the material universe emanates out of prakriti, the rootless root of the universe,” they anticipated Aristotle. And when Indian philosophers spoke of maya, or that which gives illusory weight to the universe, they did so in terms that evoke the twentieth-century idea of the Higgs field, the all-pervasive invisible field so beloved of particle physicists, which gives substance to illusion.