Science in the Classical Hindu World

V V Raman. Science, Religion, and Society: An Encyclopedia of History, Culture, and Controversy. Editor: Arri Eisen & Gary Laderman. Volume 1. Armonk, NY: M.E. Sharpe, 2006.

The origins of Indic civilization are shrouded in the mists of very ancient history. Some archeological finds suggest that it dates back to 7000 BCE. In India too, as with all ancient science, speculations sometimes took precedence over observation, and qualitative descriptions over quantitative measurements. Yet there is much of relevance and interest in the scientific investigations and reflections of ancient Indic thinkers. In many fields of sustained research, such as mathematics, physics, astronomy, chemistry, and medicine, Hindu investigators observed and speculated insightfully.


The Vedas, which date back prior to 3100 BCE, are the classical sacred texts of mainstream Hinduism. Vedic literature prescribing rules for the construction of sacrificial altars imply a knowledge of basic geometry. The skills required for these included the fundamental operations of arithmetic and measurement, as well as abstract mathematical thinking. Already in the fifth century BCE, a text entitled Chandahashastra used what is essentially a binary system of numeration. This work also contains the Meru Prastara, an arrangement of numbers in pyramidal form that resembles the Pascal triangle in modern mathematics.

In the first centuries CE, there were references to the representation of numbers. By the seventh century, such notations became quite common in India. Indian thinkers were among the first to use the place value system of numeration. This system was imported to Europe via Arab scholars in the Middle Ages.

The decimal notation is related to the concept of zero. An important term for zero was sunya: void, emptiness. (Another was kha.) This was a metaphysical view of reality as nothingness. This speculation on the empty led to one of the most fruitful concepts in mathematical thought. The idealist extreme of regarding the world as a passing illusion provoked by the senses called for a symbolic representation of the reality behind it. Initially, this was represented by a simple dot, and the dot grew into a small circle.

Indian mathematicians had great skill in computational arithmetic, and they developed ingenious methods for arithmetical calculations. They handled numbers of incredibly large magnitudes. The Yajur Veda Samhita listed multiples of ten up to a trillion, giving names to each. Another text, the Sankhyayana Srautasutras, extends the list even further. A Buddhist text, Lalitavistara, introduces a dialogue in which a student recites powers of ten up to 1053. This number is called tallakshana.

Reducing fractions was common practice in ancient India. References to fractional numbers occur in Vedic writings. A second-century text states that the expert mathematician, “in order to simplify operations, removes common factors from the numerator and the denominator of a fraction.” Operations with fractions as well as the extraction of square and cube roots were well known in ancient India.

Hindu thinkers expressed the concept of infinity in a metaphysical way. The invocatory verse of the Isopanishad says, in rough translation: “That which is produced of the perfect, is also perfect in itself. Even if complete units emanate from the perfect, the latter still remains perfect.” If we replace the word perfect with infinity, the statement expresses the insight that infinity divided by anything is also infinity, and that infinity minus infinity is again infinity. The mathematical idea of infinity (ananta: endless) was extrapolated into other domains as well. Thus, one spoke of nominal infinity (greatness), epistemic infinity (enormous knowledge), one-dimensional infinity (observation along a line of sight), numeric infinity (a fraction with zero in denominator), and temporal infinity (eternity).

Some Hindu arithmeticians used negative numbers. Although the idea of negative numbers is fairly simple to us, at one time it was quite intriguing. The seventh-century mathematician Brahmagupta I was one of the first to use negative numbers. It may be recalled here that negative numbers came into use in Europe only from the sixteenth century with the work of Jerome Cardan and Thomas Harriot.

Hindu mathematicians explored algebra, which was called avyakta-ganita: mathematics of the unknown. They were among the first to investigate quadratic equations, recognizing both rational and irrational roots, as well as positive and negative ones. The ninth-century mathematician Mahavira, while grappling with quadratic equations, stumbled upon what we now call imaginary numbers. But he discarded them because the idea of a number whose square is negative was unacceptable.

Geometrical figures were studied systematically, often in the context of constructions for religious purposes. The Sulba Sutras, dating back to the seventh century BCE, prescribe dimensions of well-defined geometrical forms and patterns, to be used as altars. Familiarity with these enabled mathematicians to determine the midpoints of lines and to state methods for bisecting angles and evaluating areas. Rules were given for transforming rectangles into square areas, and the value of pi was approximated.

Hindu geometry also referred to properties of similar triangles and to formulas for the solution of triangles. Hindu mathematicians were acquainted with the Pythagorean property of right triangles. A work by Baudhayana (600 BCE) contains the equivalent of the theorem associated with Pythagoras in the Western tradition.

Bhaskara II (twelfth century CE) evaluated the volume of a sphere by subdividing it into many pyramids, a technique that is akin to integration. He also introduced a concept in the study of planetary motions that suggests the notion of instantaneous velocity; and this is closely linked to the derivative. Developed in the context of astronomy, a number of trigonometric formulas were developed in India from the fifth century onward. The Paulisa Siddhanta was one of the first works to introduce a definition of the sine of an angle. Tables of this function were also constructed.

In the fourteenth through sixteenth centuries there flourished in Kerala mathematicians who developed some key notions of the calculus, gave the equivalent of series expansions of trigonometric functions, and did observational work in astronomy. It has been suggested that the early European traders to Kerala transferred some of the things they learned there to scholars in Europe.


Vedic hymns reveal astounding symmetries in their poetic meters. Careful analysis of these by some scholars suggests that their authors in evoking the gods of fire and sky were also correlating the patterns in the numbers of syllables, lines, and verses with celestial motions. Vedic rituals and sacrifices had to be performed on well-defined days of the year, and at precisely specified hours. This required exact time divisions and reckonings. Astronomy inevitably came into play. Vedic astronomical views continued to have their impact at later times. Vedic astronomy makes references to calendar divisions. The solar year, or samvatsara, had 360 days.

Hindu astronomers divided the path of the moon around the earth into twenty-seven or twenty-eight nakshatras: lunar mansions or asterisms. This was a kind of lunar zodiacal division that referred to certain constellations. The names of the months in the Hindu calendar are derived from the names of the nakshatras. The Tamil calendar in southern India has a sixty-year cycle, each year bearing a different name. The sixty-year cycle arises from the fact that Jupiter and Saturn align themselves in the same region of the sky every sixty years.

Periods involving multiples of years were considered. These were called yugas. In Vedic astronomy, one spoke of yugas made up of four, five, or even six years. In later Hindu astronomy, yugas came to mean much longer periods, involving hundreds of thousands of years. In the text Surya Siddhanta, for example, the yuga is stated as consisting of 4,320,000 years. Hindu astronomers also spoke of the kalpa, which was equivalent to 8,640,000,000 years: a day in the life of Brahma, the creator. Time scales of this magnitude do not seem to have any parallels in the history of human thought until the advent of twentieth-century cosmology.

Another idea in the yuga concept is that the world is more or less completely destroyed at the end of each yuga, to be recreated again by Brahma. At the end of each kalpa, the universe regresses into its pristine state, only to reemerge again with new law and order. The modern concept of an oscillating universe seems to echo this ancient suggestion.

The Scientific Method

The Chândogya Upanishad, dating back to the sixth century or earlier, is a very revered text. It treats of ritual chants, of the primordial significance of the sun, breath, and food, of the genesis of Vedic hymns, and much more. In the midst of all this, we encounter a personage by the name of Uddâlaka Âruni. He instructs his son on the ultimate essence of things. He refers to water as essential for physical life, and food as essential for the mind. He demonstrates this by asking his son to live only on water for fifteen days. The son obeys, and is unable to recall whatever he had learned. Then he is instructed to feed himself well and return after fifteen days. The son obeys and is now able to recite the verses he had learned. In this way Uddâlaka Âruni experimentally proves to his son what he had stated.

This is a very significant episode, but as it is buried in metaphysical musings, its unusual empirical undertone escaped the scrutiny of scholars. Debprasad Chattopadhyaha, a modern historian of Hindu science has drawn attention to its relevance and argues that it entitles Uddâlaka, rather than Thales of Miletus, to be regarded as the first scientific thinker in history.

The Physical Sciences

In their interpretation of the physical world, Hindus developed theories similar in some aspects to those of the ancient Greek and Chinese sciences, and there were certainly mutual influences. Jaina speculations dating back to the sixth century BCE reflect an atomic theory. This underwent modifications in the course of time. Ancient Indian thinkers seem to have realized the ultimate minuteness of atoms, for they stated that their existence could be only inferred, never directly put into evidence.

Hindu doctrines on the nature of the physical world were extensive and sophisticated. Ether, space, and time were the arena of the world. The ultimate material unit in the physical world was called anu. One imagined a primordial, prematerial potential, called tanmatra, pervading the universe, containing the five roots of sensations. Thus, with the tanmatra are associated shabda (which can be heard), sparsha (which can be touched), rupa (which can be seen), rasa (which can be tasted), and gandha (which can be smelled). The tanmatra evolves into innumerable anu.

Combinations of anu arise from invisible factors, referred to as adrshta. Adrshta is a metaphysical notion that extends beyond gross matter to souls also. Then there was the idea of the paramanu, the rough equivalent to the Democretan (Greek) atoms. These were eternal, and of different kinds.

The mahabhutas or basic elements of ancient science were prithivi (earth), ap (water), vayu (air), and tejas (fire), and were said to be made up of paramanu. The paramanu of different substances have different qualities. The paramanu of prithivi are endowed with the qualities of color, taste, odor, and touch; those of ap with color, taste, and touch; those oftejas with color and touch; those ofvayu only with touch. The various paramanu have a number of other qualities of which number, dimension, distinctiveness, conjunction, and disjunction are common to all.

The Vaiseshika Sutra discusses the nature of motion. Motion could exist only for a few moments, as it has no intrinsic quality of its own. It ceases to exist as soon as it produces an effect. Motion is also described as something that can be both cause and effect. If we consider the kinetic energy aspect of motion, this view makes much sense. One also finds in these writings glimmers of the concepts of impetus, force, and momentum. There is even a suggestion that perpetual motion is impossible. The phenomena of falling bodies and arrows in flight are often cited as examples.

Heat and light were regarded as related because of the commonality of their source: fire. The heating of a body was analyzed in terms of different stages through which its atoms pass. Flame was regarded as a large collection of particles of light. Hindu physicists did speak of light corpuscles, but some of them also believed that such particles emanated from the eye, and that by falling on bodies, they rendered them visible.

The phenomenon of falling bodies was attributed to two of the four elements, earth and water. Calling this property gurutva, they regarded it as the qualitative attribute of all material substances, rather than as resulting from external causes. Gurutva was also looked on as a macroscopic property that the individual atoms did not possess.

Other properties of matter that were defined and studied in classical Hindu science included fluidity, viscosity, and elasticity. All these were explained in terms of the corresponding properties of the constituents. Thus atoms of water, fire, and earth were taken as having fluidity, while viscosity was a property only of water. Only earth substances were endowed with elasticity.

Hindu thinkers explored the notions of space and time. They regarded space as a substance that has its own individuality. It was all pervading, eternal, and a fundamental cause of physical phenomena. It was suggested that the sun, by its rising and setting, specified the cardinal directions. The sun was deemed responsible for our recognition of the flow of time. If the sun stood still, the day would not advance, and there would be no perception of cosmic time advancement. Some considered the notion of a time atom, called truti. This corresponded to 1.33750 seconds.

The universe was imagined to have arisen from water, an idea that is reminiscent of Thales of Miletus. In one of the Upanishads we read, “It is simply water that has solidified: the earth, the air, the sky, the gods and men; beasts and birds, grass and trees, animals and worms, flies and ants; all these are just water solidified.” The idea that everything in the universe is fundamentally interconnected in some subtle and all-embracing way is a view implicit in ancient Hindu science and is found now in quantum physics.


Our interaction with matter is as old as human culture. In the processes of shaping clay and forging metals, humans developed a keener understanding of materials and their properties. Thus did chemistry arise from the most ancient times. But substances are not only handled and molded. Some of them are also ingested. Food is an important subset of material things. We chew and swallow not only for palatal pleasures and the necessary nourishment, but also on occasions to rid ourselves of ailments. Medicinal materials need to be studied, and this becomes a topic for chemistry. Herbs, plants, and mineral concoctions can cure diseases and bestow health and strength. Can they also restore youth and prolong life indefinitely? Such were the inspirations for alchemy, the progenitor of chemistry.

Immortality is not just imperishability, but continuation without damage or decay. Some materials seem to persist forever, but even they rust and rot. But gold and silver seem beyond corruption. So they have been venerated from time immemorial, and one investigated methods for transforming ordinary substances into these immortals of the material world. Alchemy dominated the scene for at least five centuries in medieval India, from the tenth to the fourteenth century. It became wedded to mythology and mysticism; as elsewhere, it developed secret ways and some grotesque methods in attempts to achieve impossible goals.

Mercury was the supreme substance of sanctity for alchemists. Struck perhaps by its unusual state (the only metallic substance liquid at ordinary temperatures), alchemists revered it and imagined it had extraordinary powers. Mercury was called rasa (Sanskrit for essence), and alchemy was known as rasavidya: knowledge of essence.

The investigation of mercury is elaborated in the tenth-century text Rasarnava (Sea of Mercury). Here it is stated that the material is to be treated in eighteen different ways before its full potential can be realized. These include steaming, grinding, distillation, and blending. Rules prescribed the construction of the room where alchemical inducements were to be carried out. The laboratory had to be in a region blessed with medicinal plants. There were to be four principal doors, furnaces had to face the southeast, the instruments had to be in the southwest. The chemical laboratory contained a variety of apparatuses such as sieves, bellows, crucibles, pans, and retorts.

Chemistry apart from alchemy flourished in India in the arts of metallurgy and ceramics, in smithies and idol factories. One also explored substances to beautify the body and add fragrance to the skin. Explosive salts were prepared for pyrotechnic spectacles. Candles were made and oils extracted.

Hindu chemistry had significant metallurgical achievements. There stands to this day near New Delhi an impressive iron pillar, over twenty-four feet tall and weighing more than six tons, that is known to have been erected sometime in the fifth century. Chemical analysis reveals that it contains minute proportions of carbon, silicon, sulfur, and phosphorus. The pillar has not suffered from the passage of time. V. Ball, an English geologist in the late nineteenth century, had this to say about this marvel of ancient metallurgy: “It is not many years since the production of such a pillar would have seemed an impossibility in the largest foundries of the world, and even now there are comparatively few places where a similar mass of metal could be turned out.”

Medicine and Psychology

The goal of medicine being good health and longevity, the ancient Hindus called their medical science Ayurveda: science of longevity. Ayurvedic treatises date back to the early centuries of the Christian era. But their framework was already laid in Vedic literature. The two most outstanding names that occur in the classical medical texts are Charaka and Sushruta. Their works have survived almost in their entirety and are the sources of our knowledge of ancient Hindu medicine. The age in which these men lived and practiced is not known with certainty. The samhitas (treatises) by these authors suggest that medical practice was much more ancient than their names. Somewhat like Galen in the European tradition, Charaka and Sushruta were the spiritual masters of Indian medical writers for many generations. Their analyses of medical knowledge and rules governing good health and medical practice have inspired Hindu physicians from time immemorial. In 150 short chapters, Charaka covered a long list of topics that included prognosis, pathology, the influence of environmental factors, and such various complications as tetanus, convulsions, nasal catarrh, insanity, abdominal pains, disgust of foods, jaundice, swelling of the scrotum, and ingestion of poisons.

One ancient Hindu theory of diseases is that a human being is made up of three components: soul, mind, and body. As long as all three are in equilibrium, we are in good health. Any perturbation in their mutual balance results in a disease. Such perturbations may be caused by abnormal correlations between time, mind, and the senses. These are described as adverse, null, or excessive. Time refers not only to clock or calendar time, but also to internal, personal time: one’s age and stage in life. When a youth runs for an hour without stopping, he may not be affected at all, whereas when an old man does the same, unpleasant consequences may follow. Here we have cases of null and excessive correlations.

There are three factors in the body which must also be in proper balance: vayu (wind), pitta (bile), and kapha (phlegm). These terms do not refer to products within the body, but to certain overall states of the body. Any disturbance in their equilibrium is called a dosha. Specific medications are prescribed for each dosha.

The origin of diseases is traced to three factors. First, there are factors that come from conception and birth. These give rise to constitutional (genetic) diseases. Next, diseases could arise from unexpected events over which the sufferer has no control, such as snakebites or epidemics. These are accidental diseases. Finally, there are diseases arising from the wrath of a god or a demon, or from time and old age. These are inevitable and incurable.

Although the physical basis of diseases was recognized, there was also a strong belief that magical influences were present in all cases. Hence, associated with all medicines were spells and incantations, prayers, and pilgrimages. In many instances, these did have therapeutic effects, if only because of the psychological basis of many common diseases.

Careful diagnosis was stressed. Charaka warned that the “physician who, without carefully ascertaining the disease, commences his treatment, seldom meets with success even if he be well conversant with medicines and methods of application.” He went on to say that the cure of an ailment results from the physician’s effective manipulation of the patient, and from the drugs and the nurse.

Several hundred concoctions of plant, mineral, and animal origin are listed in medical works. Mercury and gold, herbs, salts and gems, the urine of animals, milk, and marrow was used in preparing a whole range of medications.

Sushruta was the greatest of ancient Hindu surgeons. His treatise discusses surgery with references to the dissection of cadavers. He has left behind an impressive listing and classification of surgical instruments. Razors, forceps, pincers, needles, and hooks were among the many tools of the surgeon mentioned in this text.

The ethical framework of physicians is illustrated in a passage from the Charaka Samhita: “Of all the physicians, he is best who practices medicine, not for wealth or personal gratification, but purely out of compassion for life. Those who exploit medical knowledge as just another commodity, purely for monetary gains, run after a heap of dust while ignoring the real mound of gold. None offers greater blessings, moral or material, than the physician who severs the death-noose, and restores life and health to the victims of fierce disease. He who performs the healing art with care and compassion, regarding this as the noblest of professions, is entitled to the greatest happiness.”

Ancient texts list diseases of the eye, lungs, heart, and urinary tract. There are references to skin eruptions, rheumatism, asthma, epilepsy, tuberculosis, leprosy, simple headache, and loquacity. Other items mentioned in some of the medical works include amputation, rhinoplasty, and trepanning. Strict rules of hygiene were prescribed. Principles governing sexual encounters were enunciated. Even hypnotism seems to have been practiced for curative purposes.

Hindu science also probed into psychology and consciousness. Some modern theories in psychology have been influenced by Hindu insights into the nature of the human mind. One detects in the works of Carl Jung and Ken Wilber, for example, reformulations of Hindu views. In the Hindu framework, experienced consciousness is part of a grander consciousness that is freed from ordinary experience. Science explores experienced consciousness with its methodological and conceptual tools. But for many ages, Hindu experimentalists have probed the mystery of other dimensions of consciousness through sophisticated yogic disciplines.


Hindus approached grammar as a subject matter for scientific study. Careful and systematic analysis of spoken Sanskrit as well as of the Sanskrit hymns must have been carried out from the most ancient times. The works of generations of scholars culminated in a classic treatise called Ashtadhyayi (Eight Chapters) by Panini. This work was most probably composed during the fourth century BCE. Panini’s chapters consist of nearly 4,000 aphorisms that describe and prescribe the correct use of the language. It has been suggested that Panini himself, if not some earlier grammarian, gave literary language the name Sanskrit, which essentially means “that which has been elaborated or cultured,” in order to distinguish it from vulgar speech.

Panini’s great insight was the recognition that the words of a language spring from some basic roots by means of inflections and other modifications. He listed 2,000 such roots for Sanskrit. He stated strict rules for the combination of words in accordance with the laws of euphony. In Panini’s analysis of phonology, morphology, and syntax, modern investigators have detected parallels with concepts in computer programming.

Hindu Science in a Global Context

Ancient and classical India made impressive progress in craft, technology, and science. In astronomy and in mathematics, in alchemy and in medicine, inquiring minds have been active in the Indian subcontinent from time immemorial. There were exchanges and interactions with contemporaneous science and civilization in other parts of the world, notably with China, Greece, and later the Arab world. The overall framework of science in the Hindu context was that the cosmic divisions of earth (lower/material), atmosphere (connecting region), and sky (higher/immaterial) are mirrored in the human body, breath, and mind.

One may wonder why such an intellectually alert people did not bring about the scientific and industrial revolutions. But then, the same questions may be asked with respect to Egypt, Babylon, and other cultures. In general terms, it may be said that no people or nation continues with a high level of progress and creativity indefinitely. External or internal forces arise, overtly or subtly, to stifle the victories and vitality of a people after a span of robust activity. In the case of India, inordinate reverence for ancient writings because of their inseparable association with religious practice carried over to scientific matters as well. This tended to diminish independent thought and the spirit of questioning. Also, in one phase, excessive preoccupation with spiritual liberation tended to draw the energies of people to metaphysical realms. It has also been suggested that the scientific development of medicine was a threat to the highly organized religious orthodoxy. Because of this, the more rationalistic and secular aspects of medical theories were condemned by an establishment that would rather stress the ritualistic and mystic sides. This self-serving preoccupation of the priestly class, contends one scholar, thwarted the full blooming of science in ancient India.

Then again, a series of external forces in the form of invaders often put the people on the defensive. Foreign cultural intrusions have the effect of pushing a people even more ardently to whatever they can claim as their own. This too is not conducive to the development of new ideas and perspectives. Finally, in order for science in the modern sense to arise, knowledge must become more widespread, rather than be confined to a handful of pundits who guard it jealously. This could not be achieved before the invention of printing and other social changes.

After India’s contact with Europe, Indian scientific minds were drawn to the mainstream of modern science. Since that time, scientists from India have grown in numbers. Their contributions to international science have been increasing in quantity and in quality.