A Brief History of SciencePart 8: The Development of Science in

Ancient India

Soumitro Banerjee∗

IN THIS INSTALMENT of the essay I shalldeal with the development of science that

happened in ancient India. At the presenttime it has become all the more neces-sary for the people to understand the richheritage of science in ancient India, be-cause some unauthenticated claims are be-ing made from different quarters that areundermining the actual contributions ofancient India in science and technology.

The term “ancient” is somewhat vague,as it can mean any time in the past. So,to make our discussion more concrete, weshall divide the time-span into three parts:(a) the period of the Indus Valley civilization,(b) the Vedic age, and (c) the post-Vedic pe-riod.

The Indus Valley Civilization

The ancient civilization discovered throughexcavations in Harappa, Mahenjo-Daro,Dholavira, Lothal, and about a hundredother sites in Western India and Pakistanwas, in the opinion of many experts, themost advanced civilization of the BronzeAge. Radiocarbon dating has revealed thatthis civilization, also known as the IndusValley civilization, existed over a periodfrom about 3500 BC to about 1800 BC, outof which the period from 2800 BC to 2500

∗Dr. Banerjee is a Professor at the Indian Instituteof Science Education & Research, and General Secre-tary of Breakthrough Science Society .

BC was the time of maximum development.

Archaeologists were particularly sur-prised to see the planned layout of these an-cient cities. Large and small roads (9 feet to34 feet wide), brick houses built over squareand rectangular plots of land, large gra-naries, public baths, arrangements of light-ing the streets — all these indicate that civilengineering, town planning, and architec-ture were quite advanced in this civilization.There are many remarkable items of civilengineering, such as, drainage systems forwater (open and closed), irrigation systems,river dams, water storage tanks carved outof rock, moats, homes with private bath-rooms and drainage, multiple-storied build-ings with stairs, and even a dockyard.

Such architecture requires knowledge ofgeometry, especially the construction ofsquares, rectangles, and rectangular par-allelepiped. The Indus Valley people de-signed a ruler (Mahenjodaro ruler) that wasdivided into ten equal parts. All bricks hadthe ratio 1:2:4, regardless of their size andlocation. The seals also show intricate ge-ometric patterns. It was an agriculture-based society. But the artefact discoveredin these sites indicate significant advance-ment in textiles, pottery, and metallurgy(copper and brass) also.

Archaeological evidence indicates that byabout 1700 BC, the Harappan civilizationwas on the verge of decline. The causes of

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Picture of the Mohenjo-Daro ruins, with the great public bath in the foreground.

its decline are not certain. Climatic changesand long spells of draught (or flooding) mayhave led to the decline in agriculture. Theincrease in population and the decrease inagricultural output may have created eco-nomic problems leading to a gradual decayof culture. The physical existence of thecivilization possibly ended when the inhab-itants were forced to abandone the cities tomove to other areas with better prospectsof livelihood. Such decline and extinctionof a culture are not uncommon in ancientcivilizations; Inca and Maya civilizations ofSouth America offer similar examples.

The Vedic Age

Some tribes speaking Proto-Indo-Iranianlanguages migrated from Asia Minor intoWest Asia and Europe from around 2500BC and a few influxes occurred into North-Western India sometime between 1800 BCand 1500 BC. These were horse-ridingpastoral migratory tribes whose livelihoodcame mainly from animal husbandry. Theydid not create urban civilizations likeHarappa and Mahenjo-Daro (cities grew inAryan-speaking land only after 600 BC);they did not have a written script; theywere also significantly backward in terms

of science and technology in comparison tothe people in the Indus valley civilization.But they fought and won against the non-Aryans, settled in the Indian subcontinent,and slowly gave birth to a very rich culturethat was to have tremendous impact on thehistory of the subcontinent.

The thousand year span from the migra-tion of the Aryan-speaking people till theonset of the Buddhist era (approximatelyfrom 1500 BC to 500 BC) is called the Vedicage. The Vedas are the highest cultural cre-ations of that period. Even though ritu-als, worship, chants and hymns constitutea lion’s share of the Vedas, these are alsoour prime sources for an objective assess-ment of the actual progress of science inthat period.

From these works we see that the lateVedic people wrote numbers in a systemthat had 9 basic number-symbols. Zerohad not been discovered and the place-value system has not been invented at thattime. So they needed new symbols for 10,20, 30, · · · 100, 1000, etc. There werealso names for higher powers of 10. His-torians are surprised by the fact that theycould conceive large numbers in spite ofthe handicap of not being able to write

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such numbers. In the Taittiriya Samhitaand Shulvasutra we see mention of arith-metic progression and geometric progres-sion. They could add, subtract, multiplyand divide simple fractions. We also see at-tempts to find the square root of 2 and 3 interms of continued fractions.

The Shulvasutras are a collection of textswritten between 800 BC and 200 BC, sothese could be said to belong to the latevedic and early Buddhist periods. Theoldest sutra attributed to Baudhayana isthought to be composed between 800-600B.C. These are basically the laws of mea-surement with the aid of a rope (shulva-sutra literally means “rules of the cord”),much of it meant for erecting sacrificial al-tars. In these texts, we find clear instruc-tions of how to locate the East-West lineat any place, how to construct a square,how to obtain the perpendicular bisector ofa given line, etc. They had to solve someproblems of geometry to tackle the con-struction of raised platform or vedi used inyagnas. For example, they had to constructplatforms of circular, square, and rectan-gular shapes, of the same area. The Sul-vasutras gave methods of geometric area-preserving transformations from one geo-metric shape to another, such as from asquare to a circle and vice versa, from asquare to an isosceles triangle, to a rhom-bus etc.

There is also indication that the the-orem known by the name of Pythagoraswas known to the writers of the Shulvasu-tras. Baudhayana gave the following gen-eral statement of the Pythagorus theorem:diagonal of a square produces double thearea, and for a rectangle the squares pro-duced by the length and breadth of the rect-angle together equal the area produced bythe diagonal. He also gave a set of num-bers like (3, 4, 5), (5, 12, 13), (8, 15, 17),(7, 24, 25), and (12, 35, 37) which form

“Pythagorian triads” — triplets of integersthat follow the rule x2 + y2 = z2. But noproof was given. It is now believed that peo-ple in many parts of the world, includingIndia, Egypt, and Greece, knew about thisresult and made use of it in constructionsof various sorts. Pythagoras in 6th cen-tury BC presented a rigorous mathematicalstatement and proof, which we find in Eu-clid’s writings. Baudhayana also describeda method for approximate calculation of thesquare root of 2:

√2 = 1 +

1

3+

1

3 · 4− 1

3 · 4 · 34≈ 1.4142156

It should be noted, however, that these realdevelopments have no link with what istaught nowadays in schools in some statesin the name of “Vedic Mathematics”.

In the late Vedic period agriculture wasstarted in addition to animal husbandry,and they had to formulate a calendar inorder to fix the timing of sowing, reaping,and other agricultural activities. That pro-vided the primary motivation for studyingthe motion of the objects in the sky. In ad-dition, fixing of the times of holy events likethe performance of a yagna also inducedpeople to look for auspicious events in thesky. The Vedic literature show that theycounted months on the basis of the phasesof the moon, and the year on the basis ofthe motion of the sun. Since a whole num-ber of moon-months do not make a sun-year, the extra days were counted as “mal-mas”, when no auspicious event could beheld. The year was divided into two parts:when the sun moved towards the North (ut-tarayana), and when the sun moved to-wards the South (Dakshinayana), and theycould identify the summer and winter sol-stices. In addition they named 27 starsalong the path of the sun and the moon,and could specify the positions of the sunand the moon in the background of thesestars. It is important to note that in the

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Vedic period there was no astrology—in thesense of beliefs in the influence of planetson human lives. The word Jyotisha wasused in the sense of astronomy.

The most remarkable developments hap-pened in medical science. The Atharva-Veda contains many ideas about anatomy,physiology, and medicines which, thoughnot quite correct in the light of modern sci-ence, were much advanced when comparedto the knowledge of the other societies ofthe same period. The Ayurveda was writtenin the late Vedic period in continuation ofthis tradition. It is divided in eight chap-ters: medicine, surgery, treatment of eye,ear, nose, and throat diseases, treatment ofpsychological problems, treatment of chil-dren, poisons and their effects, chemistryand preparation of medicines, and treat-ment of sexual diseases. Such attempt tosystematize the empirical knowledge of thatperiod is undoubtedly remarkable.

Even though the main content of theRigveda was chants and hymns in praiseof the gods and asking material benefits inreturn, the gods of that period were actu-ally embodiments of natural forces or deifi-cation of some Aryan leader (like Indra) suc-cessful in defeating the non-Aryans. Thatis why historians opine that the essentialcontent of the thought process of men inRigvedic times was materialistic, what an-thropologists term as the “magic phase”.That is why the Rigvedic hymns reflect ahealthy curiosity about natural phenom-ena, which was conducive to developmentof scientific enquiry.

Many people carry a misconception thatspiritualism is the only characteristic fea-ture of the Vedic times. Actually manydifferent philosophical currents were verymuch alive during this period. One of thesephilosophical currents is called Lokayata(sometimes also called Charvaka). It didnot believe in the existence of atma or soul,

refused to accept anything on the basisof belief, and theorized that everything inthe world is made of four constituents orchaturbhuta: earth, water, air, and fire (afifth one, sky, was added later). It believedthat when a man dies, his body returnsto these four constituents, and does notgo to heaven or hell. Whether the ideaslike chaturbhuta were correct in the lightof modern science is not of our concern.What really matters is the fact that it soughtto explain the world through material pro-cesses and phenomena. Other philosoph-ical lines of thought like Nyaya-Vaiseshikaand Samkhya also existed. Notwithstand-ing the differences between these lines ofthought, at the basic level they were alsomaterialistic philosophies. Under the influ-ence of these philosophical currents, therewas a healthy curiosity about the materialworld, and we see steady progress in man’sunderstanding of it.

But the later Vedas laid too much em-phasis on ritualistic practices like yagnas,homas, chants, and on prescribing whatto do and what not to do. Such an en-vironment hampered the natural enquir-ing mind of men, and so the scientific en-quiries subsided. When the “end” of theVedas or Vedanta came, it sought to createan alienation of the individual from the ma-terial world. Seeking nirvana away from lifeand society became the ideal for the learnedpeople. This created a condition detrimen-tal to scientific enquiry, and as a result, wedo not see much development of science inthe late Vedic period.

Post-Vedic period

This condition began to change in the 6thcentury BC when a group of people, dis-enchanted by the suffocating intellectualatmosphere dominated by ritualistic prac-tices, started looking for alternative philo-sophical ideas. Jainism and Buddhism

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The method of “squaring a circle” in Boudhayana Shulvashutra

“If you wish to square a circle, divide its diameter into eight parts; then divide one part intotwenty-nine parts and leave out twenty-eight of these; and also the sixth part (of the precedingsub-division) less the eighth part (of the last).”According to this prescription, the side of the square will be

a =7d

8+d

8

(1− 28

29+{1

6

[1− 1

8

]})= 0.87868× d

Now we know that the area of the square is a2 and that of the circle is πr2 = πd2/4. As per moderncalculation, the value of a should be 0.8862×d, and thus their prescription was reasonably good.

were born in this period. Even though wemainly hear of these two religions, histori-ans have shown that the materialist philo-sophical thoughts like Charvaka, Samkhya,etc., that were born during the Vedic periodfound resurgence in this period throughman’s attempts to find alternate ways tointerpret the world. Even Buddha did notbelieve in the existence of god. The pres-ence of such rich array of philosophical cur-rents and the clash of ideas created an in-tellectual atmosphere that aided scientificenquiries. That is why we see a resurgenceof science starting from the 6th century BC.But this period can no longer be called the“Vedic” period.

The materialistic line of thinking wasalive in India for a long time, and slowlydied out after about 9th-10th century AD(we’ll talk in detail about it later). And this1600-year period from 6th century BC toabout 10th century AD was the golden ageof ancient Indian science. We shall discussthis era with reference to the different areasof human endeavour.

Medical Science

After Atharvaveda and Ayurveda, medicalscience reached an altogether different di-mension since the 6th century BC in thehands of a few eminent medical practi-tioners like Athreya and Susruta (6th cen-tury BC), Jivaka (566-486 BC) and Charaka

(time controversial). The unusual aspect ofthis development is the practice of surgerywhich was unequalled in the world beforethe initiation of modern methods of surgeryafter the European renaissance. SusrutaSamhita mentions 121 kinds of surgical in-struments, and has detailed instruction onhow to run the knife and other instrumentson different organs, how to sew the woundwith plant-fibre after a surgical procedure,what to do in case of broken bones, etc.

The most unusual aspect of these is theprocedure to rejoin severed noses and ears.In those times a common punishment wasto cut off the culprit’s nose and ears. Afterthis was carried out, if the King learned thatthe punished person is not really the crim-inal, then the doctor would receive instruc-tion to rejoin the nose and ears. The de-tailed account of the procedure in the writ-ings of both Susruta and Charaka indicatesthat they succeeded in some cases. How-ever, there is no description or instructionon how to place the head of an elephant ona human torso, as claimed by Prime Minis-ter Narendra Modi.

Chemistry

Everywhere the primary motivation in thestudy of chemistry came from three di-rections. Medical practice demanded oneto know the properties of different kindsof substances and mixtures that could be

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used for medical purposes. For that rea-son, wherever medical science had ad-vanced, knowledge about the properties ofthe substances that have some medicinaluse also advanced hand-in-hand. Second,the demands of metallurgy have inducedman to experiment with different metalsand their alloys in an attempt to obtainharder and non-brittle material. Third,the belief that it is possible to transformother substances into gold by chemical pro-cesses also prompted man to try out vari-ous things. In India the studies in chem-istry were initiated from all these angles.Since medical science and metallurgy sig-nificantly advanced in this country, it isexpected that knowledge of chemistry alsomust have advanced in step. That is whathad actually happened.

Susruta Samhita and Charaka Samhitadescribe the properties of six metals (iron,tin, lead, copper, gold, and silver), fivetypes of salts (depending on their sourcerather than their composition), and a fewalkalis. They also give elaborate proce-dures for preparing mild and strong al-kaline substances (potassium carbonateand sodium carbonate) which were usedto treat wounds. Books written in thelater periods also mention the use of mer-cury, zinc, and sulphur. A process called“killing” metals is described in some books,which is nothing but reactions that pro-duce substances whose properties are dif-ferent from those of the original metal. Adetailed account of this knowledge can befound in Acharya Prafulla Chandra Ray’sfamous book “The History of Hindu Chem-istry”. Quite a few books on chemistry, likeRasa-ratnakara, Rasa-hridaya, Rasarnava,Rasendra-churamani, Rasakalpa, etc. werewritten between 11th and 14th century AD.But by then chemistry had become a partof mystic practices or tantravidya. That iswhy modern chemistry could not take birth

from that.

Experiments in metallurgy have a veryrich tradition in India. The extraction ofmetals from ores and the mixing of differ-ent metals to obtain brass and steel of therequired strength demanded people to ex-periment with various ingredients and pro-cesses. Since all weapons are made ofmetals, this pursuit had patronage of thekings. That is why, even though the cul-tivation of knowledge subsided in India af-ter the 10th century, the art of metallurgycould advance more or less unhindered fora long time. In many archaeological sites wesee instances of specific metals prepared forspecific purposes.

Out of these the famous iron pillar ofQutub Minar in Delhi demands specialmention. The 24 foot tall pillar built in the4th century AD has not rusted as yet. Thepreparation of the specific kind of metal andthe technology of fashioning such a hugepillar are truly examples of technical excel-lence reached during the Gupta dynasty.But the Hindutva proponents go a bit far inclaiming that modern science has not ad-vanced enough to produce rust-less steelsimilar to that produced by the ancients.This is however not a fact. Scientists haveexamined the composition of that iron andhave found that it has excessive quanti-ties of phosphorous. This is not surpris-ing, since phosphorous is naturally presentin the iron ore and gets mixed with iron inthe process of its extraction. Even thoughphosphorus prevents rusting, this phos-phorus is removed by reacting with oxygenin the modern steel-making process, be-cause phosphorus makes steel brittle. Butfor such a large pillar, it does not matterif the material is brittle, because the bulkholds it together. The iron for the pillarwas prepared without removing the phos-phorus, and that is why it does not rust.But the same material cannot be used to

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make swords, for which they adopted a dif-ferent technique.

The technology of producing Wootz steelwhich was renowned for making swordswith exceptional sharpness and toughnessoriginated in India. This was exported toEurope and the Middle East where it wasknown as Damascus steel. Another im-portant Indian contribution to metallurgywas in the isolation, distillation and use ofzinc. There is evidence of zinc ore mining atZawar in Rajasthan from the fifth centuryBC, The earliest confirmed evidence of zincsmelting by distillation is dated back to 9thcentury from Zawar.

Linguistics

It is known that Sanskrit was not a spo-ken language. It is a language created by“purifying” the spoken languages like Pali,Prakrit etc. Such purification itself is a featin linguistics. But in the early stage, whenthe Vedas were initially composed, therewas no standardization in its form. The featof standardizing the language by extract-ing the rules of its grammar was performedby Panini (4th century BC), considered thegreatest grammarian of antiquity. Becauseof this contribution, Sanskrit became easierto learn and post-Panini Sanskrit becamethe common medium of discourse and ex-change among the learned section of thepeople of the entire subcontinent. The de-velopment of this common medium of ex-change played a great role in further devel-opment of ideas in this multi-lingual region.

Another remarkable achievement of thisperiod is to arrange the consonants in a5× 5 matrix depending on which part of themouth is touched by the tongue and howmuch air is exhaled while pronouncing analphabet. This highly scientific way of ar-ranging the alphabets is not found in anyother language in the world.

Mathematics and astronomy

In ancient India, astronomy and mathe-matics progressed hand in hand, as theastronomers also practised mathematicsand mathematicians cultivated astronomy.That is why these two subjects, where an-cient Indians had made major contribution,will have to be discussed together.

We have already discussed the advancesin these two subjects during the Vedic age,which are found in texts like Shulvasutra,the Brahmana literature, and the VedangaJyotisha. In the post-Vedic period, the Jainmathematicians (between 400 BC and 200BC) initiated the process of freeing mathe-matics from religious and ritualistic motiva-tions, and made it stand on its own ground.They were particularly interested in verylarge numbers, and could conceive infin-ity. In the writings of the mathematicianPingala (3rd century BC) we see importantworks on number theory including whatare now known as Pascal’s triangle and Fi-bonacci numbers. Important mathematicalworks of this period are Surya Prajnapti,Vaishali Ganit, Sthananga Sutra, Anoyo-gdwar Sutra, and the Satkhandagama.

In astronomy, we do not see any majorwork in the late Vedic period, and the firstsigns of resurgence in the post-Vedic periodare visible in the texts written between 100and 500 AD, which are collectively namedas Siddhanta-Jyotisha, and the first ma-jor advancement in mathematics, after theShulvasutras, can be found in the writingsof Aryabhata (end of 5th century AD).

The Siddhanta Jyotisha is not onebook. It is actually a common namegiven to a large number of books (likeSurya-siddhanta, Pitamaha-siddhanta,Vashista-siddanta, etc.) of similar con-tent. Out of these some books like theRomaka-siddhanta, Poulish-siddhanta,Yavana-siddhanta contain ideas culledfrom Greek and Roman astronomy of the

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post-Alexander period. These resulted fromthe opening of trade routes between Indiaand Europe following Alexander’s invasion,and the cultural exchanges resulting fromthat. It is in these books that astrology ap-pears for the first time in Indian literature;so the superstition seems to have beenimported from the West.

One important aspect of the Siddhanta-Jyotisha books is the attempt to find theperiodicities of the motion of the sun, themoon, and the planets. But their wayof expressing it was different. Today weknow the period of revolution of the Eartharound the sun is 365.24219 days (the daymeasured in terms of the earth’s rotationaround its own axis), and that of the moonaround the earth is 27.3216 days. But inthe time of Siddhanta-Jyotisha it was notknown that Earth moves around the sunor that it spins around its own axis. Peo-ple saw the sun going around the earth,but they noticed that it does not return toexactly the same position at sunrise everyday. After every 365 days it comes to moreor less the same position, and according tothat the year was counted. But they hadnoticed that the position after 365 days wasalso not exactly the same. By noticing theshift after every year, they calculated theperiod after which it would return to exactlythe same position. This “periodicity” of thesun’s motion was called a Mahayuga. Ac-cording to many Siddhanta-Jyotisha books,a Mahayuga contains 4,320,000 years. Ifone calculates the period of revolution ofthe earth around the sun from this fig-ure, the length of the year becomes 365.258days, which is very close to the modern es-timate. Similarly they had calculated theperiods of the moon and the planets —the period within which the object revolvesa whole number of times. These cometo be very large numbers, and historianswere surprised to see the mention of such

large numbers in astronomical literature ofthat time. Actually, before the invention ofthe place-value system of writing numbers,there was no way of expressing the periodic-ity of these bodies other than in whole num-bers. That is why this ingenuous way wasadopted.

Since Indian kingdoms of that timehad trade relations with the kingdoms inGreece, Rome, and Arabia, there was ex-change of knowledge between the schol-ars of these regions. Through these ex-changes the knowledge created in Indiapercolated to Greece, Rome, and Per-sia, and ideas from knowledge-centres likeBaghdad, Athens and Alexandria reachedIndia and became integrated into its bodyof knowledge. We know that the Greekphilosopher Eratosthenes of Alexandria(276-194 BC) measured the diameter of theEarth by observing the shadows of verti-cal sticks in two different places. We seethe mention of exactly the same methodin Siddhanta-Jyotisha. The motions of theplanets as seen from the Earth are not uni-form. Sometimes they are fast, sometimesslow, and sometimes they even move in thereverse direction. To explain such peculiarmotion, the Greek astronomer Ptolemy (90-168 AD) had proposed that these do notmove around the Earth in circles, ratherthere are circles over circles — called epicy-cles (see the 2nd instalment on this essay).In Aryabhata we see a similar explanationof planetary motion, based on two epicycles.

It is however remarkable that Aryabhatawas the first to talk about the spin of theEarth about its own axis. This means hewas the first to guess that the sun is notreally moving around the Earth; rather wesee it moving because the Earth itself isspinning about its own axis. But this ideawas not accepted by other eminent scholarslike Brahmagupta and Varahamihira, whocriticised Aryabhata for infusing fanciful

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The Bakhshali manuscript

The Bakhshali Manuscript is a mathemat-ical text written on birch bark which wasfound near the village of Bakhshali in Pak-istan in 1881. Only about 70 pages havesurvived, and are now kept in the Univer-sity of Oxford.The manuscript is written in an earlierform of Sarada script which was mainly inuse from the 8th to the 12th century AD. Itis a handbook of rules and illustrative ex-amples together with their solutions. It isdevoted mainly to arithmetic and algebra,with just a few problems on geometry andmensuration.

ideas into astronomy. Even though Aryab-hata talked about the diurnal motion of theEarth, he did not reach the same conclu-sion as Copernicus, as he described plan-etary motion in the same way as Ptolemy.He, however, gave the correct scientific ex-planation for the solar and lunar eclipses.

In his book Aryabhatiya written in 499AD, we see many contributions in math-ematics, including square root and cuberoots of numbers, arithmetic progression,solution of simultaneous equations, etc. Wealso see treatments of infinite series includ-ing formulae like

12 + 22 + · · ·+ n2 =n(n+ 1)(2n+ 1)

6

After Aryabhata, the cultivation of astron-omy and mathematics gained momentum,and continued unhindered for many cen-turies. In this period it was enriched in dif-ferent directions by eminent scholars likeVarahamihira (6th century), Brahmagupta(7th century), Mahavira (9th century), Mun-jal (9th century), Sripati (10th century),Sridhara (11th century) and Bhaskara(12th century). But before going into thisglorious phase of Indian science, we have to

understand the greatest contribution of In-dia in the world of knowledge — the discov-ery of zero and the invention of the place-value system of writing numbers.

Writing of numbers requires a basis. Indifferent parts of the world, different baseswere used to write numbers. The Babyloni-ans used base 60, the Mayans used base20. In India, Arabia, and in many otherparts of the world, the number system hadbase 10 since antiquity. This means thatthere were 10 number-symbols (1 to 10) towrite numbers up to 19 (19 = 10+9). An-other symbol representing 20 would be re-quired for writing numbers from 20 to 29,and then it would require another symbol,so on and so forth. Thus, such a num-ber system would require a large numberof symbols to write big numbers. This wasthe problem with the Brahmi and Kharosthinumbers found in stone tablets of Ashoka’stime. The same was the problem of the Ro-man number system. If you try to writea number like 3905 in Roman script, youwould realize the difficulty.

But today we write arbitrarily big num-bers with ease, with only 10 number sym-bols. This has been possible due to two ma-

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jor discoveries that happened in India. Thefirst was the realization that the absence ofsomething, or zero, is also a number. Thesecond was the invention of the place valuesystem. In the modern decimal system ofwriting numbers when we write 3905, weactually construct it as

3× 103 + 9× 102 + 0× 101 + 5× 100

Here a digit assumes a “value”, a powerof 10, depending on the position where thedigit is written. This system of writing num-bers was developed in India. The literatureof that time shows that this way of writingnumbers was started sometime between the1st and 3rd centuries AD. Zero may havebeen discovered a century or two beforethat, because the place value system is notpossible without the use of zero. We see theuse of the place value system in Aryabhataand the later mathematicians like Brah-magupta and Varahamihira. Their writingswere translated into Arabic, through whichthe Arabs came to know of this system.The Arab world was very fast in adoptingit. Through them, it reached Europe. Thatis why the English numerals are still calledthe “Arabic” numbers, even though the sys-tem was invented in India.

With the introduction of a new numbersystem, society faced a new problem. Noneof the old methods of adding, subtracting,multiplying and dividing numbers wouldbe applicable to the new number system.So one had to freshly develop the methodsof arithmetic suitable for this new numbersystem. At that time many techniques wereinvented, some of which have come to beadopted universally — the ones that stu-dents learn in school today.

In mathematics another area in which In-dia made big contribution is algebra. Thecontribution of the ancient Greeks in math-ematics is restricted to geometry. Theycould not advance much in arithmetic and

algebra because they could not invent zeroand the place value system. In contrast,the Indian mathematicians did not havethis handicap, and so could progress sig-nificantly in these directions. The unknownquantity (x in modern algebra) used to bewritten in Devnagri script using the alpha-bet “ya”, or if two unknown quantities wereinvolved, using the first letters of Sanskritwords for different colours. They used towrite equations using these notations, andproceeded to solve many of these equations.Much of the Indian contribution to alge-bra concerns linear and quadratic equa-tions. Brahmagupta (628 A.D.) gave thefirst explicit solution of the quadratic equa-tions. Later it was systematized by SridharAcharya in the eleventh century.

Another important contribution was inthe field of indeterminate equations. Whenan equation has two unknowns, it is notpossible to obtain the values of the un-known quantities. But Brahmagupta, Sri-pati and Bhaskara showed that in particu-lar situations, such as when the quantitiesto be found are whole numbers, it is pos-sible to find solutions. Brahmagupta gavea general solution to the linear Diophantineequation ax + by = c, where a, b, and c areintegers. The solution of second order inde-terminate equations of the form

x2 −Ny2 = 1

(called Pell’s equation) using whole num-bers is considered one of the greatest con-tributions in number theory. Bhaskaradeveloped an algorithm called Chakravalafor solving indeterminate equations like thePell’s equation in a systematic way.

However, the Indian contribution in ge-ometry is meagre, mostly confined to men-suration. We see rules of finding the ar-eas of rectangles and triangles in the writ-ings of Aryabhata and Brahmagupta. Brah-magupta also gave a formula for the area

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The spread of the Indian numeral system

It is worth quoting from a speech delivered by the Nobel Prize winning Pakistani physicist Dr.Abdus Salam [5]:

“Almost twelve hundred years ago, Abdullah Al Mansur, the second Abbasid Caliph, celebratedthe founding of his new Capital, Baghdad, by inaugurating an international scientific confer-ence. To this conference were invited Greek, Nestorian, Byzantine, Jewish, as well as Hinduscholars. From this conference, the first international conference in an Arab country, datesthe systematic renaissance of science associated with Islam. The theme of the conference wasobservational astronomy. Al Mansur was interested in more accurate astronomical tables thanavailable then. He wanted, and he ordered at the conference, a better determination of the cir-cumference of the Earth. No one realized it then, but there was read at the conference a paperdestined to change the whole course of mathematical thinking. This was a paper read by theHindu astronomer, Kankah, on Hindu numerals, then unknown to anyone outside India.”

of a cyclic quadrilateral (whose diagonalsare perpendicular to each other). Eventhough the value of π is stated as

√10

in some Siddhanta Jyotisha manuscripts,people like Aryabhata succeeded in obtain-ing it in much greater accuracy (3.1416).

In trigonometry also we see significantadvancement. Aryabhata introduced anumber of trigonometric functions. Vara-hamihira gave a table of the sines andcosines (he called jya and kojya) in hisbook Panchasiddahntika. From his writ-ings we see that many trigonometric rela-tions taught at school today were known inhis time. Bhaskara obtained the sines andcosines of even smaller angles, for examplehe gives sin 1◦ = 10/573, cos 1◦ = 6565/6569.Note, however, that the Greek astronomerHipparchus (2nd century BC) was the firstto prepare a sine table and to use it for as-tronomical calculations.

Bhaskara’s astronomical work of the 12thcentury covers topics such as latitudesand longitudes of planets, lunar and solareclipses, the moon’s crescent, conjunctionof the planets with each other, conjunctionof the planets with fixed stars, etc.

The Kerala school of mathematics and as-tronomy (14th to 16th century) made sig-

nificant advances in astronomy and espe-cially mathematics, including fields suchas trigonometry and analysis. They madeimportant contributions to the field of infi-nite series and provided the first exampleof power series. Rudiments of calculus arealso present in their works, but they did notformulate a systematic theory of differenti-ation and integration.

The centres of learning

In the Vedic age the way of imparting ed-ucation was personal. A learned personor sage would teach a handful studentsin his own home. The students lived fora few years with the teacher, gave servicein the teacher’s home and field, looked af-ter the cattle, and in return got an educa-tion. But in the Buddhist period, the Stu-pas and Mutts started emerging as centresof learning, where a large number of monksand bhikkhus lived together and exchangedknowledge.

This model slowly caught on, and anumber of specialized centres of learningemerged where a large number of teach-ers and students lived in a compound, andthe teachers could teach a larger number

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of students. The oldest of these is situ-ated in Takshashila, the capital of Gand-hara (present Kandahar province in EastAfghanistan) which started developing froma time slightly before Buddha, but reachedglory during the Buddhist period. Later, inthe 5th century AD, another centre of learn-ing was established in Nalanda with the pa-tronage of the Magadh kings. Even thoughthese two were the most famous, manymore relatively smaller centres of learninghave been found, like Pushpagiri in Odisha,Odantapuri and Vikramshila in Bihar, Ja-gaddal in Bengal, Balavi in Gujarat, etc.Some of these were so famous that studentscame from far-away places like China.

In these centres of learning, educationwas imparted in an organized mannersomewhat like the Buddhist monasteries.However, the form and content of educationwere personal in nature. The residentialfacilities and class-rooms in these centresof learning enabled a teacher to teach 20-30 students at a time depending on one’sability and fame, and facilitated exchangeof ideas among many scholars. These cen-tres of learning were undoubtedly great ini-tiatives in ancient India that helped knowl-edge to be consolidated and expanded.

The decline of science in India

In spite of such a rich tradition in the cul-tivation of science and technology, after the9th-10th century it subsided, and then wascompletely extinguished. Bhaskara can besaid to be the last spark of light before itbecame dark. After him for more than 800years, there was practically no contributionto science coming from India.

What was the reason behind the declineand fall of Indian science? The famous 19thcentury chemist Acharya Prafulla ChandraRay investigated this issue in his book “TheHistory of Hindu Chemistry”. According tohim, three factors were responsible for this

decline in the cultivation of science.

The first was the introduction of the castesystem in a rigid form. According to him,the interaction and exchange of ideas be-tween the doers and the thinkers is an es-sential precondition of the cultivation of sci-ence, and casteism blocked this process.“The arts being thus relegated to the lowcastes and the professions made heredi-tary, a certain degree of fineness, delicacyand deftness in manipulation was no doubtsecured, but this was done at a terriblecost. The intellectual portion of the com-munity being thus withdrawn from activeparticipation in the arts, the how and whyof phenomena—the coordination of causeand effect—were lost sight of—the spirit ofenquiry gradually died out among a nationnaturally prone to speculation and meta-physical subtleties and India for once badeadieu to experimental and inductive sci-ences. Her soil was rendered mortally un-fit for the birth of a Boyle, a DesCartes ora Newton and her very name was all butexpunged from the map of the scientificworld.”

The second reason was the introductionof the “shastras” or moral code books thatspecified what can and cannot be done.“The drift of Manu and of the later Puranasis in the direction of glorifying the priestlyclass, which set up most arrogant and out-rageous pretensions. According to Susruta,the dissection of dead bodies is a sine quanon to the student of surgery and his highauthority lays particular stress on knowl-edge gained from experiment and observa-tion. But Manu would have none of it. Thevery touch of a corpse, according to Manu,is enough to bring contamination to the sa-cred person of a Brahmin. Thus we findthat shortly after the time of Vagbhata, thehandling of a lancet was discouraged andAnatomy and Surgery fell into disuse andbecame to all intents and purposes lost sci-

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ences to the Hindus.”The third reason was the influence of the

Vedanta philosophy, which taught peopleto see the material world as maya or il-lusion, on the learned section of the peo-ple. “The Vadanta philosophy, as modifiedand expanded by Samkara, which teachesthe unreality of the material world, is alsoto a large extent responsible for bringingthe study of physical science into disrepute.Samkara is unsparing in his strictures onKanada and his system. One or two ex-tracts from Samkara’s commentary on theVedanta Sutras, will make the point clear.”Thus, according to Acharya P. C. Ray, ascientist’s queries are directed at the ma-terial world, its processes, phenomena andevents. If one sees the material world asmaya or illusion, one cannot do any sci-ence. The spread and intellectual domi-nance of the Vedanta philosophy as prop-agated by its powerful exponent Samkara(8th century AD), was responsible for theelimination of the materialistic philosophieslike Lokayata, and for the death of sciencein India.

The unscientific claims

In recent times various claims are be-ing made—mainly by the Hindutvaprotagonists—by mixing science withmysticism, and history with mythology,in order to create an imaginary pictureof India’s past glory based on religiouschauvinism. It is not possible to go intoan in-depth analysis of such claims in thisarticle. But I shall briefly deal with someof them, to enable the reader judge forthemselves the veracity of the claims.

Claim 1: Indus Valley civilization was apart of the Vedic era

On this issue, we need to understand why,soon after the discovery of the Harappansites, historians and archaeologists had

come to the conclusion that this was a pre-Vedic civilization. They had found four im-portant clues.

1. The Harappan people knew how to makebricks, but the Vedic people did not. Nota single brick has been found in the onethousand year span of the Vedic age.After the Indus Valley civilization, thefirst brick-built building was found inthe Buddhist period, during the reign ofthe Maurya dynasty.

2. The horse is the main animal in theVedic literature. But no horse bone hasbeen found in any of the Indus Valleycities. The main animal depicted in theIndus Valley art, sculpture and seals, isthe bull. Not a single picture of a horsehas been found. This implies that thisanimal—the horse—was not known tothe Harappan people, but was very com-mon in the Vedic age.

3. The Harappan people had a written lan-guage, though scientists have not suc-ceeded in deciphering the script becauseit has no resemblance with any of themodern languages. In contrast, theVedic people did not have a written lan-guage in the early part of the Vedic age.That is why the Rigveda was communi-cated through sruti (to listen) and smriti(to memorize), and was written up muchlater.

4. No description of the Harappan cities arefound anywhere in the literature of theVedic age. There are no references tostructures built on platforms, or the gridpattern of streets and the careful con-struction of drainage systems, to gra-naries, warehouses and areas of inten-sive craft production, to seals and theirfunction, etc. “If the two societies wereidentical” writes the eminent HistorianRomila Thapar, “the two systems wouldat least have to be similar.”

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There have been attempts by the Hin-dutva protagonists to contradict thesepointers. In the year 2000 a book titled“The Deciphered Indus Script” was pub-lished by N. S. Rajaram and N. Jha whichclaimed that the scripts are actually wor-ship of river Saraswati, in Sanskrit. Theyalso claimed to have found the image ofa horse in a Harappan seal. The claimswere soon debunked by archaeologists whoshowed that the translation was a completepiece of imagination. There are linguisticrules that have to be observed in any de-cipherment, which make it necessary for aclaim to stand the test of linguistic analy-ses. No such scientific process was followedin the claim of Rajaram and Jha. Moreover,the broken seal was photographed by shin-ing light from one side so that the shadowlooks like the image of a horse. For detailssee the article by the Harvard IndologistMichael Witzel and historian Steve Farmerin Frontline (September 30, 2000).

Claim 2: Vedic Aryans were originalresidents of India

Today Hindutva theorists are claiming thatthe Aryans did not come from outside theland. Some of them change the antiquity ofthe Vedic culture — some say it is 10000years old, some say 50000 years. That iswhy it is necessary to understand on whatbasis the scientists have come to the con-clusion about the antiquity of the Vedic age.

1. The first evidence is linguistic: It hasbeen found that the languages spokenin Europe and in India have a commonroot. These languages are classified un-der a group, called the Indo-Europeanfamily of languages. That is why it isbelieved that this language group hasradiated along with human migrations,starting from a common birthplace. Lin-guistic evidence suggests that the Indo-Aryans split off from the Indo-Iranians

around 1800-1500 BC.

2. The second evidence is zoological: Thehorse is the prime animal in all Vedicliterature, but this animal is not nativeto the Indian subcontinent. There is nowild horse in any of the Indian forests.Wild horses are found in Asia Minor.Signs of the existence of horses in largenumbers are found in India only after acertain time. That is why scientists havecome to the conclusion that the horse-riding Aryans entered India around thattime.

Nowadays there are attempts to disprovethis theory by showing that there werehorse fossils in Harappan sites, but theclaims have not gone beyond newspaper ar-ticles as professional archaeologists did notfind scientific merit in such claims. Thereare also attempts to show that the geneticmake-up of Indians has not changed in mil-lennia; hence the Aryan migration did nothappen. This is sheer nonsense as manyinvading populations like Kushans, Huns,Mongols, Pathans, Portuguese, and Englishhave settled in India and their genes havebecome integral part of the Indian genepool. But the most important point is that,out of the various classifications on the ba-sis of physical characteristics, “Aryan” wasnever identified as a “race”. The idea ofan “Aryan race” was originated by the Ger-man fascists, which has been debunkedlong since. Scientifically it is a languagegroup, and those who spoke that group oflanguages are called Aryans.

Claim 3: Vedic Mathematics

Nowadays we see attempts to introduce cer-tain calculation techniques into school cur-riculum in the name of “Vedic Mathemat-ics”. It should be clear from the abovediscussion that the discovery of zero hap-pened much after the Vedic age, in the

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Buddhist period. The techniques in theseVedic Mathematics books include the use ofmodern decimal number system, and hencethese cannot be Vedic in origin. The pro-ponents are basically counting on the factthat he average Indian considers anythingwritten in Sanskrit as “vedic”.

The way Latin was the common languageof academic discourse all over Europe be-fore the advent of modern languages likeEnglish, German, etc., in a similar waySanskrit was the common link language ofthe educated people of India from antiquityall the way up to the medieval period. Thatis why, anything written in Sanskrit is not“Vedic”.

But the most worrisome aspect of these“Vedic Mathematics” books is that most oftheir content is not obtained from ancientliterature at all and are creations of peo-ple in the modern times, written in San-skrit. Sometimes text written in moderntimes are inserted into ancient literature(Prof. Narlikar calls these as prakshipta orinserted [5]), and then the whole shloka iscited as pointer to certain calculation tech-nique invented by the vedic people. Some-times the text in the shlokas are just cryp-tic phrases from which any meaning canbe extracted. The techniques given in theVedic mathematics books are at best someshortcuts for number crunching that do nothelp the young minds to grasp the beauty ofmathematical logic at all.

Conclusion

Thus we see that there was significant cul-tivation of science in India in the ancienttime, but a lion’s share of it was done in theperiod from 6th century BC to about 10thcentury AD. The contribution of India to theworld of knowledge in this period is truly

something to be proud of. But this period isnot the Vedic period, and the impact of theLokayata and Buddhist philosophies wasprincipally responsible for the developmentof science in this period. We also have tokeep in mind that the glorious tradition ofcultivation of science was halted and finallyterminated in India, due to the impositionof a rigid caste system, and due to the sas-tras that dictate what to do and what notto do, and due to the revival of the Vedantaphilosophy.

The preposterous claims about the sci-ence in ancient India — like the claims ofaircraft that flew from one planet to an-other, of surgery to place an elephant’shead on a human body, of in-vitro fertiliza-tion for giving birth to Karna — will onlymake Indian science a laughing stock be-fore the rest of the world, and will under-mine the actual contributions of India tothe world of knowledge. Any right-mindedperson should defend the actual historyand be proud of it, and should debunk theludicrous claims. 2

References:

1. A People’s History of India 3: The VedicAge —Irfan Habib and Vijay Kumar Thakur, Tulikabooks, 2003.

2. Science in History — J D Bernal, MIT Press1971

3. History of Hindu Chemistry — Acharya P.C.Ray, Indian Chemical Society, 1956; andCosmo Publications, 2010. Note that thechapter on decline and fall of Indian sciencewas edited out in the later versions of thebook.

4. Vigyaner Itihas (Bengali) — SamarendraNath Sen, Shaibya Publishers, 1955

5. The Scientific Edge — Jayant Narlikar, Pen-guin Books, 2003

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