A Brief History of Indian Science. From Mathematics to Medicine.

July 18, 2021 Authored by: Subhash Kak


The history of Indian physics goes back to Kaṇāda (~ 600 BCE) who asserted that all that is knowable is based on motion, thus giving centrality to laws and their operational analysis in the understanding of the universe.20

There are nine classes of substances: ākāśa, space, and time that are continuous; four elementary substances (or particles) called earth, air, water, and fire that are atomic; and two kinds of mind, one omnipresent and another which is the individual.

Let the basic atoms of pṛthvi, āpaḥ, tejas, and vāyu be represented by P, Ap, T, and V, respectively. Every substance is composed of these four kinds of atoms. Consider gold in its solid form; its mass derives principally from the P atoms. When it is heated, it becomes a liquid and therefore there should be another kind of an atom already in gold which makes it possible for it to take the liquid form and this is Ap. When heated further it burns and this is when the T atom gets manifested. When heated further, it loses its mass ever so slightly, and this is due to the loss of the V atoms.

The atoms are eternal only under normal conditions, and during creation and destruction, they arise in a sequence starting with ākāśa and are absorbed in the reverse sequence at the end of the world cycle. The sequence of evolution of the elements is given as V→T→Ap→P. The V and T atoms have little mass (since they do not exist in a substantive form), whereas P and Ap atoms have mass. This sequence also hides within it the possibility of transformation from V and T atoms that are energetic to the more massive Ap and P atoms.

Indian chemistry developed many different alkalis, acids, and metallic salts by processes of calcination and distillation, often motivated by the need to formulate medicines. Metallurgists developed efficient techniques of extraction of metals from ore.21


We know quite a bit about how astronomical science evolved in India. The Yajurvedic sage Yājñavalkya knew of a ninety-five-year cycle to harmonize the motions of the sun and the moon, and he also knew that the sun’s circuit was asymmetric. The second millennium BCE text Vedāṅga Jyotiṣa of Lagadha22 went beyond the earlier calendrical astronomy to develop a theory for the mean motions of the sun and the moon. An epicycle theory was used to explain planetary motions. Given the different periods of the planets, it became necessary to assume yet longer periods to harmonize their cycles. This led to the notion of mahāyugas and kalpas with periods of billions of years.

The innovations of the division of the circle into 360 parts and the zodiac into 27 nakṣatras and 12 rāśis took place first in India. The schoolbook accounts of how these innovations first emerged in Mesopotamia in the 7th century BCE and then arrived in India centuries later are incorrect because both these divisions are described in the Ṛgveda.

The Śatapatha Brāhmaṇa which was compiled soon after the Vedas says: “The sun strings these worlds [the earth, the planets, the atmosphere] to himself on a thread. This thread is the same as the wind…” This suggests a central role to the sun in defining the motions of the planets and ideas such as these must have ultimately led to the theory of expanding and shrinking epicycles.

Astronomical texts called siddhāntas begin appearing sometime in the first millennium BCE. According to the tradition there were eighteen early siddhāntas, of which only a few have survived. Each siddhānta is an astronomical system with its own constants. The Sūrya Siddhānta speaks of the motion of planets governed by “cords of air” that bind them, which is a conception like that of the field.

The great astronomers and mathematicians include Āryabhaṭa, who took Earth to spin on its own axis and who spoke of the relativity of motion and provided outer planet orbits with respect to the sun. This work and that of Brahmagupta (b. 598) and Bhāskara (b. 1114) was passed on to Europe via the Arabs. The Kerala School with figures such as Mādhava (c. 1340–1425) and Nīlakaṇṭha (c. 1444–1545) came up with new innovations of analysis based on advanced mathematics.23


The Sāṅkhya system speaks of evolution both at the levels of the individual as well as the cosmos. The Mahābhārata and the Purāṇas have material on creation and the rise of humankind. It is said that man arose at the end of a chain that began with plants and various kind of animals. In Vedic evolution the urge to evolve into higher forms is taken to be inherent in nature. A system of an evolution from inanimate to progressively higher life is assumed to be a consequence of the different proportions of the three basic attributes of the guṇas (qualities): sattva (“truth” or “transparence”), rajas (activity), and tamas (“darkness” or “inertia”). In its undeveloped state, cosmic matter has these qualities in equilibrium. As the world evolves, one or the other of these becomes preponderant in different objects or beings, giving specific character to each.

The Purāṇas (such as Viṣṇu, Garuḍa, Skanda) speak of 8.4 million species on the earth and in the oceans, which, astonishingly, turns out to be nearly identical to modern estimates.24


Indian geometry began very early in the Vedic period in altar problems, as in the one where the circular altar is to be made equal in area to a square altar. The historian of mathematics, Abraham Seidenberg, saw the birth of geometry and mathematics in the solution of such problems.25 Two aspects of the “Pythagoras” theorem are described in the texts by Baudhāyana and others. Problems are presented with their algebraic counterparts.26 The solution to planetary problems led to the further development of algebraic methods.

The sign for zero within the place value decimal number system that was to revolutionize mathematics and facilitate development of technology appears to have been devised around 50 BCE to 50 CE. Indian numerals were introduced to Europe27 by Fibonacci (13th century) who is now known for a sequence that was described earlier by Virahaṅka (between 600 and 800), Gopāla (prior to 1135) and Hemacandra (~1150 CE).

Nārāyaṇa Paṇḍit (14th century) showed that these numbers were a special case of the multinomial coefficients.28

Bharata’s Nāṭya Śāstra has results on combinatorics and discrete mathematics, and Āryabhaṭa has material on mathematics including methods to solve numerical problems effectively. Later source materials include the works of Brahmagupta, Lalla (eighth century), Mahāvīra (ninth century), Jayadeva, Śrīpati (eleventh century), Bhāskara, and Mādhava.29 In particular, Mādhava’s derivation and use of infinite series predated similar development in Europe, which is normally seen as the beginning of modern calculus.30 Some scholars believe these ideas were carried by Jesuits from India to Europe and they eventually set in motion the Scientific Revolution.31

A noteworthy contribution was by the school of New Logic (Navya Nyāya) of Bengal and Bihar. At its zenith during the time of Raghunātha (1475–1550), this school developed a methodology for a precise semantic analysis of language. Navya Nyāya foreshadowed mathematical logic and there is evidence that it influenced modern machine theory.32


Pāṇini’s grammar Aṣṭādhyāyī (Eight chapters) of the fifth century BCE provides four thousand rules that describe Sanskrit completely. This grammar is acknowledged to be one of the greatest intellectual achievements of all time. The great variety of language mirrors, in many ways, the complexity of nature and, therefore, success in describing a language is as impressive as a complete theory of physics. Scholars have shown that the grammar of Pāṇini represents a universal grammatical and computing system. From this perspective, it anticipates the logical framework of modern computers.

The Aṣṭādhyāyī contains a meta-language, meta-rules, and other technical devices that make this system effectively equivalent to the most powerful computing machine. No grammar of similar power has yet been constructed for any other language. The famous American scholar Leonard Bloomfield called Panini’s achievement as “one of the greatest monuments of human intelligence.”


Āyurveda, the Indian medicine system, is a holistic approach to health that builds upon the tripartite Vedic approach to the world. Health is maintained through a balance between three basic humors (doṣa) of wind (vāta), fire (pitta), and water (kapha). Each of these humors had five varieties. Although literally meaning “air,” “bile,” and “phlegm,” the doṣas represented larger principles.33

Caraka and Suśruta are two famous early physicians. According to Caraka, health and disease are not predetermined, and life may be prolonged by human effort. Suśruta defines the purpose of medicine to cure the diseases of the sick, to protect the healthy, and to prolong life. The Saṃhitās speak of organisms that circulate in the blood, mucus, and phlegm. In particular, the organisms in the blood that cause disease are said to be invisible. It is suggested that physical contact and sharing the same air can cause such diseases to spread. Inoculation was practiced for protection against smallpox.

Indian surgery was quite advanced. The caesarian section was known, as was plastic surgery, and bone setting reached a high degree of skill. Suśruta classified surgical operations into eight categories: incision, excision, scarification, puncturing, probing, extraction, evacuation and drainage, and suturing. Suśruta lists 101 blunt and 20 sharp instruments that were used in surgery. The medical system tells us much about the Indian approach to science. There was emphasis on observation and experimentation.


Vedic deities represent cognitive centers.34 It is asserted that parā-vidyā or ātma-vidyā (science of consciousness) cannot be described in words or design. In the Śrī-yantra, which is a representation of the cosmos, consciousness (Śiva) is shown as an infinitesimal dot in the middle.

The interaction between matter and consciousness is postulated in terms of an observation process called dṛṣṭi-sṛṣṭi (creation through observation), which is consistent with a universe governed by laws.35

Indian texts assert that the phenomenon of consciousness cannot be studied directly as a material property. Their analysis of consciousness using indirect methods may very well be relevant for further progress of this question in contemporary science.


Indian thought is unique in the breadth and scope of its scientific speculations that are scattered within its high literature. These range from airplanes (Rāmāyaṇa) to weapons that can destroy the world (Mahābhārata), and to the most astonishing abstract ideas in the Yoga-Vāsiṣṭha.

The Mahābhārata has an account of an embryo divided into one hundred parts each becoming, after maturation in a separate pot, a healthy baby. There is also mention of a conception in one womb transferred to another. It also has a major section on battle with a space ship whose occupants wear airtight suits (Saubha Parva).

Universes defined recursively are described in the famous episode of Indra and the ants in Brahmavaivarta Purāṇa. These flights of imagination are more than a straightforward generalization of the motions of the planets into a cyclic universe.

The context of modern science fiction is clear: it is the liberation of the earlier modes of thought by the revolutionary developments of the 20th century science and technology. But why were speculations integrated into the mainstream Indian literary tradition over two thousand years ago?


Concluding, India’s civilization valued science and knowledge above all and created some of the most extraordinary conceptual advances. These include a cosmos with many solar like systems, the earliest astronomy, geometry, number theory, the ten-digit number system, the idea of physical laws and invariance, the earliest formal system to describe a complex natural phenomenon (as in Pāṇini’s computer program-like grammar that was not rivaled for 2,500 years), a very subtle Yoga psychology, the idea of immunization in medicine, and above all a framework that includes consciousness.

Modern science has been unable to explain the phenomenon of consciousness. Philosophy cannot reconcile our sense of freedom and agency with the framework of machine-like laws, and in physical theory there is no place for the observer. On the other hand, the Indian scientific framework, by integrating consciousness into the material world, has within it the potential to provide new insights of value to mainstream science, and its ideas have continued to provide key notions36 in the advance of modern science.


This is an expanded version of my essay titled “Science” for Stanley Wolpert’s Encyclopedia of India (Charles Scribners & Sons, 2005), and a later version that appeared in Medium. Much of this research is based on numerous journal articles thatmay be accessed here: https://www.academia.edu/46341155/Bh%C4%81rat%C4%AB_Bibliography

20. Kak (2016a), Kak (2016d)

21. Ray (1909), Biswas (1986), Balasubramanian (2002) 

22. Sastry (1985); Kak (2016e)

23. Shukla and Sarma (1976), Raju (2001), Ramasubramanian and Srinivas (2010)

24. Mora et al. (2011); this is a most astonishing coincidence.

25. Seidenberg (1962), Seidenberg (1978)

26. Saraswathi Amma (1979)

27. Ifrah (2000)

28. Srinivasiengar (1967), Seshadri (2010)

29. Datta and Singh (1962), Selenius (1975), Joseph (2000)

30. Joseph (2000), Pearce (2000)

31. Joseph (2000) with addition references in Kak (2018)

32. Rao and Kak (2016); also see Kak (2018)

33. Patwardhan (2012), Jaiswal et al. (2016), and Raghava Varier (2020)

34. Kak (2002)

35. In the orthodox interpretation of quantum theory, consciousness is a separate category as in Vedanta and the quantum Zeno effect is consistent with dṛṣṭi-sṛṣṭi.36.

36. See Kak (2018)


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