Ancient and classical contributions

Standard weights

A precise system of weights, usually cubes of a stone called chert, regulated trade.

NCERT adds: The lower denominations were binary (1, 2, 4, 8, 16, 32) and the higher ones decimal (160, 200, 320, 640); the smaller weights were probably for jewellery and beads. 📘 NCERT Themes in Indian History I, Ch. 1 (Bricks, Beads and Bones) ↗

Scales and units of length

Objects with ruled markings that could be scales have been found at Harappan sites. Later Indian literature names units such as the angula (finger width), dhanusa and yojana, used for artefacts, architecture and town planning — and carpenters and tailors still use the angula.

Number names and fractions in the Vedas

The Yajurveda Samhita lists names for powers of ten — eka, dasha, shata, sahasra, ayuta and on up to 10¹² and beyond; the Rig Veda calls the fraction three-quarters tri-pada.

The Sulba-sutras: geometry with a rope

Geometric texts of the Vedic period on building fire altars — the earliest known Indian texts with methods to construct perpendiculars and perpendicular bisectors, using a rope as the compass. Baudhayana’s Sulbasutra (c. 800 BCE) already works with non-unit fractions.

Zero: the Bakhshali manuscript

A mathematical text with hundreds of zeros written as dots — the oldest recorded origin of the zero symbol we use today.

NCERT adds: NCERT: the first known instance of numbers written with ten digits, including 0 (then a dot), is the Bakhshali manuscript (c. 3rd century CE). 📘 NCERT Ganita Prakash, Grade 8 Part 1, Ch. 3 (A Story of Numbers) ↗

Aryabhata computes with ten digits

Aryabhata was the first mathematician to fully explain, and do elaborate scientific computations with, the Indian system of ten symbols; he also first proposed a systematic way to solve problems with a single unknown.

Brahmagupta: rules for zero

In the Brahmasphutasiddhanta he gave the rules of arithmetic with zero, negative numbers and fractions. His works were later translated into Persian and Latin.

Bhaskara I and trigonometry

Bhaskara I did pioneering work in trigonometry and wrote a lengthy commentary on the Aryabhatiya.

Brahmagupta’s rules for fractions

The Brahmasphutasiddhanta first stated in general form how to add, subtract, multiply and divide fractions — the methods still taught today. These ideas reached Europe through the Arabs.

Virahanka’s numbers

Counting the rhythms of short and long syllables in poetry, the Prakrit scholar Virahanka gave the rule for the sequence 1, 2, 3, 5, 8, 13, 21… — the first known person to write it down. It is now called the Virahanka–Fibonacci sequence.

Indian numerals reach the Arab world

Sanskrit texts of mathematics, astronomy and medicine were translated into Arabic. The Arabs adopted India’s decimal numeral system with the zero; in Europe these became known as ‘Arabic numerals’.

Al-Khwarizmi’s ‘Hindu numerals’

The Indian number system reached the Arab world by around 800 CE and was popularised there by Al-Khwarizmi’s book On the Calculation with Hindu Numerals (c. 825) and Al-Kindi’s On the Use of the Hindu Numerals (c. 830).

Mahaviracharya’s Ganita-sara-sangraha

Mahaviracharya developed the arithmetic of fractions further and, in the Ganita-sara-sangraha, named the powers of ten up to 10²³.

The Chautisa Yantra magic square

The first recorded 4 × 4 magic square, in an inscription at the Parshvanath Jain temple: every row, column and diagonal adds up to 34.

Bhaskaracharya’s Lilavati

One of India’s greatest mathematicians and astronomers: Lilavati (1150 CE) teaches mathematics through riddles, Bijaganita covers advanced algebra and Siddhantashiromani astronomical calculation. Several of his works were translated into Persian in the Mughal period.

Indian numerals reach Europe

From the Arab world the numerals reached Europe and parts of Africa by around 1100 CE; around 1200 the Italian mathematician Fibonacci made the case for Europe to adopt them. Arab scholars called them ‘Hindu numerals’.

Narayana Pandita’s Ganitakaumudi

A massive treatise of mathematics that included important original developments.

Madhava and the Kerala School

Madhava gave the series expansion for trigonometric functions — a world first — and an exact value of π as an infinite series. He and his followers are known as the Kerala School of Astronomy and Mathematics.

Shadow clocks and water clocks

The earliest reference to measuring time by shadows is in Kautilya’s Arthasastra, which also describes a water clock with water flowing out.

Aryabhata and the Aryabhatiya

A short treatise of mathematics and astronomy. Aryabhata proposed that the Earth spins on its axis, gave the length of the year within minutes of the modern value, estimated the size of the Earth and correctly explained solar and lunar eclipses. His value for one rotation of the Earth is about 23 hours 56 minutes 4.1 seconds.

The Ghatika-yantra (sinking-bowl water clock)

Because outflow clocks slowed as the water dropped, a sinking-bowl water clock was developed — first mentioned by Aryabhata. It kept time at monasteries, palaces and town squares, where each sinking of the bowl was announced; the day was divided into 60 ghatis.

Varahamihira’s Brihat Samhita

An encyclopedic work covering astronomy and astrology, weather forecasting, architecture, town planning and even farming.

Time from a stick’s shadow

Varahamihira gave an accurate expression for time in terms of the shadow of a vertical stick.

Al-Biruni studies Indian science

Al-Biruni learnt Sanskrit and wrote an encyclopaedic survey of India, compiling in mathematics and astronomy what he could gather from the works of Aryabhata, Varahamihira and Brahmagupta.

Watching the sky in bowls of water

More than 800 years ago, astronomers looked at stars and planets reflected in shallow bowls of water, through tubes set at the right angles, to measure their positions.

Nilakantha Somayaji’s planetary model

A scholar of the Kerala School worked out a planetary model in which Mercury and Venus went round the Sun.

Jantar Mantar observatory

Some 20 giant masonry instruments for observing the sky with the naked eye.

The earliest dentistry

Eleven molar teeth from nine adults were drilled — with flint tips — while the people were alive.

Charaka and Sushruta Samhitas

Works on medicine in Sanskrit. Ayurveda has much older roots, but these texts — which deal with cataloguing and diagnosing diseases, among other topics — were compiled and given their final shape during the Gupta period.

Stone hand-axes at Attirampakkam

Acheulian hand-axes and cleavers — some of the oldest tools made by early humans in South Asia.

Smaller, finer stone tools

A Middle Palaeolithic culture of prepared-core tools, far earlier than once thought.

Early cotton

Cotton fibres preserved inside a copper bead — the first evidence of cotton at Neolithic Mehrgarh.

Copper and bronze metallurgy

The Harappan civilisation mastered copper and bronze metallurgy — a technology that made its cities possible.

Lost-wax bronze casting

The ‘lost-wax’ (cire-perdu) casting process was learnt as long ago as the Indus Valley Culture; the ‘Dancing Girl’ from Mohenjodaro is perhaps the earliest bronze sculpture, datable to 2500 BCE. Tribal craftspeople still use the process today.

Drilling hard stone beads

Beads of carnelian and other stones were shaped, ground, polished and drilled; specialised drills have been found at Chanhudaro, Lothal and Dholavira.

Iron working in the Ganga plain

Iron artefacts, furnaces, tuyeres and slag in layers radiocarbon-dated between 1800 and 1000 BCE.

Wootz steel

The famed 'wootz': high-carbon steel made in crucibles in South India.

NCERT adds: Wootz steel was among the Indian goods highly sought after in the Mediterranean world. 📘 NCERT Exploring Society: India and Beyond, Grade 8 Part 1, Ch. 4 ↗

The rust-resistant iron pillar

An ancient iron pillar that has resisted corrosion for centuries — a puzzle explained by metallurgists.

NCERT adds: Over 1,600 years old, about 8 metres high and more than 6,000 kg, it has barely any rust; its inscription speaks of a king ‘Chandra’, identified with Chandragupta II. 📘 NCERT Exploring Society: India and Beyond, Grade 7 Part 1, Ch. 7 (The Gupta Era) ↗

Pure zinc by distillation

The production of pure zinc reached its peak, with a special distillation process used for the first time in the world.

Planned drainage

A planned drainage system in Harappan cities — evidence of town planning.

NCERT adds: House drains first emptied into a sump where solid matter settled, while waste water flowed on into street drains; the drains were covered with loose bricks that could be removed for cleaning. 📘 NCERT Themes in Indian History I, Ch. 1 (Bricks, Beads and Bones) ↗

Bricks of a standard ratio

Sun-dried or baked, Harappan bricks kept one ratio — length four times and breadth twice the height — and were used at all Harappan settlements, a sign the towns were planned first and then built.

The wheel: terracotta carts

Terracotta models of wheeled carts show wheeled transport in Harappan times.

The dockyard at Lothal

A huge brick basin at the Harappan settlement of Lothal, which NCERT presents as a dockyard linked to trade.

Water management at Dholavira

A sophisticated water-management system let a walled city thrive on an arid island.

NCERT adds: NCERT shows a large reservoir cut into the rock at Dholavira, 33 metres long. 📘 NCERT Exploring Society: India and Beyond, Grade 6, Ch. 6 (The Beginnings of Indian Civilisation) ↗

The Kallanai (Grand Anicut)

A complex water-diversion system built by the Chola king Karikala just downstream of Srirangam island, sending Kaveri waters to the central and southern delta so that more land could be irrigated.

Sudarshana lake, a reservoir

An artificial reservoir known from a Sanskrit rock inscription recording the achievements of the Shaka ruler Rudradaman, who rebuilt it.

Stepwells: Rani-ki-Vav

Stepwells stored underground water in India since the 3rd millennium BCE; this one is a masterpiece of the craft.

NCERT adds: In classical times a tradition of stepwells (vavs or baoris) developed in Gujarat and Rajasthan — many of them engineering marvels as well as works of art. 📘 NCERT Exploring Society: India and Beyond, Grade 8 Part 2, Ch. 3 (A Journey through Indian Architecture) ↗

Jaipur, a planned city

Vidyadhar Bhattacharya, appointed by Sawai Jai Singh II, designed the new city on a grid of rectangular blocks, aligned to the cardinal directions, with wide streets, gardens and nine public squares.

Farming begins at Mehrgarh

One of the earliest farming villages of the subcontinent, excavated and dated by French archaeologists.

A ploughed field and terracotta ploughs

A field with two sets of furrows at right angles — two crops grown together; terracotta plough models were found in Cholistan and at Banawali.

Paddy transplantation

Transplanting rice seedlings spread in the Ganga valley, alongside the growth of towns.

Surapala’s Vrikshayurveda

A text of plant science: which plants suit which soils, seed collection and treatment, irrigation by species and season, and natural pest control.

The Harappan script

Short inscriptions on seals — some 375 to 400 signs, the longest about 26 signs long. It is still undeciphered.

Panini’s Ashtadhyayi

The Ashtadhyayi of Panini, a work on Sanskrit grammar.

Takshashila, a centre of learning

According to Buddhist texts, Kautilya — author of the Arthashastra, ‘the science of governance and economics’ — was a teacher at the world-renowned Takshashila university.

Brahmi: Ashoka's inscriptions

Edicts carved in the Brahmi script — deciphered by James Prinsep only in 1838.

Nalanda Mahavihara

The most ancient university of the Indian subcontinent, teaching without a break for some 800 years.

NCERT adds: The Palas, like Harsha before them, continued to patronise Nalanda; large monasteries like it were, in effect, the universities of the time. 📘 NCERT Exploring Society: India and Beyond, Grade 7 Part 2, Ch. 3 ↗

Vikramashila university

Founded by the Pala king Dharmapala, it remained a great centre of learning for more than four centuries, with six colleges, a vast library and nearly 3,000 scholars. Each college had a ‘scholar gatekeeper’ who set the admission test.

The first printing press

Set up by Jesuit missionaries at the Colegio de São Paulo — the first printing press in India.