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This list of Indian inventions and discoveries details the inventions, scientific discoveries and contributions made in India throughout its cultural and technological history, during which architecture, astronomy, cartography, metallurgy, logic, mathematics, metrology and mineralogy were among the branches of study pursued by its scholars. During recent times science and technology in the Republic of India has also focused on automobile engineering, information technology, communications as well as space, polar, and nuclear sciences.

Inventions

• Bangle: Bangles—made from shell, copper, bronze, gold, agate, chalcedony etc.—have been excavated from multiple archaeological sites throughout the subcontinent. A figurine of a dancing girl—wearing bangles on her left arm— has been excavated from Mohenjo-daro (2600 BCE) in what today is Pakistan. Other early examples of bangles include copper samples from the excavations at Mahurjhari—soon followed by the decorated bangles belonging to the Mauryan empire (322–185 BCE) and the gold bangle samples from the historic site of Taxila (6th century BCE), also in Pakistan. Decorated shell bangles have also been excavated from multiple Mauryan sites. Other features included copper rivets and gold-leaf inlay in some cases.

• Bhatnagar-Mathur Magnetic Interference Balance: Invented jointly by Shanti Swarup Bhatnagar and K.N. Mathur in 1928, the so-called 'Bhatnagar-Mathur Magnetic Interference Balance' was a modern instrument used for measuring various magnetic properties. The first appearance of this instrument in Europe was at a Royal Society exhibition in London, where it was later marketed by British firm Messers Adam Hilger and Co, London.

• Bow drill: The bow drill appeared in Mehrgarh in what today is Pakistan between 4th-5th millennium BCE. It was used to drill holes into lapis lazuli and cornelian and was made of green jasper. Similar drills were found in other parts of the Indus Valley Civilization in Pakistan and Iran one millennium later.

• Button, ornamental: Buttons—made from seashell—were used in the Indus Valley Civilization for ornamental purposes by 2000 BCE. Some buttons were carved into geometric shapes and had holes pieced into them so that they could attached to clothing by using a thread. Ian McNeil (1990) holds that: "The button, in fact, was originally used more as an ornament than as a fastening, the earliest known being found at Mohenjo-daro in the Indus Valley in Pakistan. It is made of a curved shell and about 5000 years old."

• Calico: Calico had originated in the subcontinent by the 11th century and found mention in Indian literature by the 12th when writer Hemacandra mentioned calico fabric prints done in a lotus design. The Indian textile merchants traded in calico with the Africans by the 15th century and calico fabrics from Gujarat appeared in Egypt. Trade with Europe followed from the 17th century onwards. Within India, calico originated in Calicut.

• Carding, devices for: Historian of science Joseph Needham ascribes the invention of bow-instruments used in textile technology to India. The earliest evidence for using bow-instruments for carding comes from India (2nd century CE). These carding devices, called kaman and dhunaki would loosen the texture of the fiber by the means of a vibrating string.

• Chaturanga and Shatranj: The precursors of chess originated in India during the Gupta dynasty (c. 280 - 550 CE). Both the Persians and Arabs ascribe the origins of the game of Chess to the Indians. The words for "chess" in Old Persian and Arabic are chatrang and shatranj respectively — terms derived from caturaṅga in Sanskrit, which literally means an army of four divisions or four corps. Chess spread throughout the world and many variants of the game soon began taking shape. This game was introduced to the Near East from India and became a part of the princely or courtly education of Persian nobility. Buddhist pilgrims, Silk Road traders and others carried it to the Far East where it was transformed and assimilated into a game often played on the intersection of the lines of the board rather than within the squares. Chaturanga reached Europe through Persia, the Byzantine empire and the expanding Arabian empire. Muslims carried Shatranj to North Africa, Sicily, and Spain by the 10th century where it took its final modern form of chess.

• Chintz: The origin of Chintz is from the printed all cotton fabric of calico in India. The origin of the word chintz itself is from the Hindi language word चित्र् (chitr) , which means a spot.

• Coherer, iron and mercury: In 1899, the Bengali physicist Jagdish Chandra Bose announced the development of an "iron-mercury-iron coherer with telephone detector" in a paper presented at the Royal Society, London. He also later received U.S. patent 755,840, "Detector for electrical disturbances" (1904), for a specific electromagnetic receiver.

• Cockfighting: Cockfighting was a pastime in the Indus Valley Civilization in what today is Pakistan by 2000 BCE. The Encyclopædia Britannica (2008)—on the origins of cockfighting—holds: "The game fowl is probably the nearest to the Indian red jungle fowl (Gallus gallus), from which all domestic chickens are believed to be descended...The sport was popular in ancient times in India, China, Persia, and other Eastern countries and was introduced into Greece in the time of Themistocles (c. 524–460 BCE). The sport spread throughout Asia Minor and Sicily. For a long time the Romans affected to despise this "Greek diversion," but they ended up adopting it so enthusiastically that the agricultural writer Columella (1st century CE) complained that its devotees often spent their whole patrimony in betting at the side of the pit."

• Corrosion-resistant iron: The first corrosion-resistant iron was used to erect the Iron pillar of Delhi, which has withstood corrosion for over 1,600 years.

• Cotton Gin: The Ajanta caves of India yield evidence of a single roller cotton gin in use by the 5th century CE. This cotton gin was used in India until innovations were made in form of foot powered gins. The cotton gin was invented in India as a mechanical device known as charkhi, more technically the "wooden-worm-worked roller". This mechanical device was, in some parts of India, driven by water power.

• Crescograph: The crescograph, a device for measuring growth in plants, was invented in the early 20th century by the Bengali scientist Jagdish Chandra Bose.

• Crucible steel: Perhaps as early as 300 BCE—although certainly by 200 CE—high quality steel was being produced in southern India also by what Europeans would later call the crucible technique. In this system, high-purity wrought iron, charcoal, and glass were mixed in a crucible and heated until the iron melted and absorbed the carbon. The first crucible steel was the wootz steel that originated in India before the beginning of the common era. Archaeological evidence suggests that this manufacturing process was already in existence in South India well before the Christian era.

• Dental drill, and dental surgery: The Mehrgarh neolithic culture in Pakistan has yielded evidence of dentistry being practiced as far back as 7000 BCE. This earliest form of dentistry involved curing tooth related disorders with bow drills operated, perhaps, by skilled bead craftsmen. The reconstruction of this ancient form of dentistry showed that the methods used were reliable and effective.

• Dice: The die is attributed to India by some accounts. Some of the earliest archaeological evidence of oblong dice have been found in Harrapan sites such as Kalibangan, Lothal, Ropar, Alamgirpur, Desalpur and surrounding territories, some dating back to the third millennium BCE, which were used for gambling. The oblong or cubical dice (akṣa) is the precursor of the more primitive vibhīṣaka—small, hard nuts drawn randomly to obtain factors of a certain integer. Dicing is believed to have later spread westwards to Persia, influencing Persian board games. Early references to dicing can be found in the Ṛg Veda (c. early 2nd millennium BCE) as well as the newer Atharva Veda (c. late 2nd millennium ~ early 1st millennium BCE).

• Dike: Dikes were known to be widely used in the Indus valley civilization, which are believed to be the first dikes in the world, built as early as the 1st millennium BCE. This was the same period when the dockyard at Lothal was in operation. The use of dikes became known from then onwards.

• Dock (maritime): The world's first dock at Lothal (2400 BCE) was located away from the main current to avoid deposition of silt. Modern oceanographers have observed that the Harappans must have possessed great knowledge relating to tides in order to build such a dock on the ever-shifting course of the Sabarmati, as well as exemplary hydrography and maritime engineering. This was the earliest known dock found in the world, equipped to berth and service ships. It is speculated that Lothal engineers studied tidal movements, and their effects on brick-built structures, since the walls are of kiln-burnt bricks. This knowledge also enabled them to select Lothal's location in the first place, as the Gulf of Khambhat has the highest tidal amplitude and ships can be sluiced through flow tides in the river estuary. The engineers built a trapezoidal structure, with north-south arms of average 21.8 metres (71.5 ft), and east-west arms of 37 metres (121 ft).

• Dyeing: Early evidence of dyeing comes from India where a piece of cotton dyed with a vegetable dye has been recovered from the archaeological site at Mohenjo-daro (3rd millennium BCE). The dye used in this case was madder, which, along with other dyes—such as Indigo—was introduced to other regions through trade. Contact with Alexander the Great, who had successfully used dyeing for military camouflage, may have further helped aid the spread of dyeing from India. Within India these dyes have found consistent mention in Indian literature and in some cases have been excavated in archaeological findings. Dyes in India were a commodity of both Internal trade and exports. Indian exports of Indigo alone reached nearly 15, 097, 622 pounds in 1887-88 with the principle markets being the United Kingdom, the United States of America, France and Egypt.

• Furnace: The earliest furnace was excavated at Balakot, a site of the Indus Valley Civilization in the Mansehra District in the Hazara Province province of Pakistan, dating back to its mature phase (c. 2500-1900 BCE). The furnace was most likely used for the manufacturing of ceramic objects.

• Hospital: Brahmanic hospitals were established in what is now Sri Lanka as early as 431 BCE. The Indian emperor Ashoka (ruled from 273 BCE to 232 BCE) himself established a chain of hospitals throughout the Mauryan empire (322–185 BCE) by 230 BCE. One of the edicts of Ashoka (272—231 BCE) reads: "Everywhere King Piyadasi (Asoka) erected two kinds of hospitals, hospitals for people and hospitals for animals. Where there were no healing herbs for people and animals, he ordered that they be bought and planted."

• Incense clock: Although popularly associated with China the incense clock is believed to have originated in India, at least in its fundamental form if not function. Early incense clocks found in China between the 6th and 8th century CE—the period it appeared in China all seem to have Devanāgarī carvings on them instead of Chinese seal characters. Incense itself was introduced to China from India in the early centuries CE, along with the spread of Buddhism by travelling monks. Edward Schafer asserts that incense clocks were probably an Indian invention, transmitted to China, which explains the Devanāgarī inscriptions on early incense clocks found in China. Silvio Bedini on the other hand asserts that incense clocks were derived in part from incense seals mentioned in Tantric Buddhist scriptures, which first came to light in China after those scriptures from India were translated into Chinese, but holds that the time-telling function of the seal was incorporated by the Chinese.

• India ink, carbonaceous pigment for: The source of the carbon pigment used in India ink was India. In India, the carbon black from which India ink is produced is obtained by burning bones, tar, pitch, and other substances. Ink itself has been used in India since at least the 4th century BCE. Masi, an early ink in India was an admixture of several chemical components. Indian documents written in Kharosthi with ink have been unearthed in Xinjiang. The practice of writing with ink and a sharp pointed needle was common in ancient South India. Several Jain sutras in India were compiled in ink.

• Indian clubs: The Indian club—which appeared in Europe during the 18th century—was used long by India's native soldiery before its introduction to Europe. During the British Raj the British officers in India performed calisthenic exercises with clubs to keep in for physical conditioning. From Britain the use of club swinging spread to the rest of the world.

• Iron: Iron was developed in the Vedic period of India, around the same time as, but independently of, Anatolia and the Caucasus. Archaeological sites in India, such as Malhar, Dadupur, Raja Nala Ka Tila and Lahuradewa in present day Uttar Pradesh show iron implements in the period between 1800 BCE—1200 BCE. Early iron objects found in India can be dated to 1400 BCE by employing the method of radiocarbon dating. Spikes, knives, daggers, arrow-heads, bowls, spoons, saucepans, axes, chisels, tongs, door fittings etc. ranging from 600 BCE to 200 BCE have been discovered from several archaeological sites of India. Some scholars believe that by the early 13th century BC, iron smelting was practiced on a bigger scale in India, suggesting that the date the technology's inception may be placed earlier. In Southern India (present day Mysore) iron appeared as early as 11th to 12th centuries BC; these developments were too early for any significant close contact with the northwest of the country.

• Iron pillar: The first iron pillar was the Iron pillar of Delhi, erected at the times of Chandragupta II Vikramaditya (375–413 CE).

• Kabaddi: The game of kabaddi originated in India during prehistory. Suggestions on how it evolved into the modern form range from wrestling exercises, military drills, and collective self defense but most authorities agree that the game existed in some form or the other in India during the period between 1500-400 BCE.

• Ludo: Pachisi originated in India by the 6th century. The earliest evidence of this game in India is the depiction of boards on the caves of Ajanta. This game was played by the Mughal emperors of India; a notable example being that of Akbar, who played living Pachisi using girls from his harem. A variant of this game, called Ludo, made its way to England during the British Raj.

• Muslin: The fabric was named after the city where Europeans first encountered it, Mosul, in what is now Iraq, but the fabric actually originated from Dhaka in what is now Bangladesh. In the 9th century, an Arab merchant named Sulaiman makes note of the material's origin in Bengal (known as Ruhml in Arabic).

• Pajamas: Pajamas in the original form were invented in India, which was for outdoor use and was reinterpreted by the British to be sleepware. The use of this garment spread throughout the world with increasing globalization.

• Palampore: पालमपुर् (Hindi language) of Indian origin was imported to the western world—notable England and Colonial america—from India. In 17th century England these hand painted cotton fabrics influenced native crewel work design. Shipping vessels from India also took palampore to colonial America, where it was used in quilting.

• Plastic surgery: Plastic surgery was being carried out in India by 2000 BCE. The system of punishment by deforming a miscreant's body may have led to an increase in demand for this practice. The surgeon Sushruta contributed mainly to the field of Plastic and Cataract surgery. The medical works of both Sushruta and Charak were translated into Arabic language during the Abbasid Caliphate (750 CE). These translated Arabic works made their way into Europe via intermidiateries. In Italy the Branca family of Sicily and Gaspare Tagliacozzi of Bologna became familiar with the techniques of Sushruta.

• Plough, animal-drawn: The earliest archeological evidence of an animal-drawn plough dates back to 2500 BCE in the Indus Valley Civilization in Pakistan.

• Prayer flags: The Buddhist sūtras, written on cloth in India, were transmitted to other regions of the world. These sutras, written on banners, were the origin of prayer flags. Legend ascribes the origin of the prayer flag to the Shakyamuni Buddha, whose prayers were written on battle flags used by the devas against their adversaries, the asuras. The legend may have given the Indian bhikku a reason for carrying the 'heavenly' banner as a way of signyfying his commitment to ahimsa. This knowledge was carried into Tibet by 800 CE, and the actual flags were introduced no later than 1040 CE, where they were further modified. The Indian monk Atisha (980-1054 CE) introduced the Indian practice of printing on cloth prayer flags to Tibet.

• Prefabricated home and movable structure: The first prefabricated homes and movable structures were invented in 16th century Mughal India by Akbar the Great. These structures were reported by Arif Qandahari in 1579.

• Puppets and Puppetry: Evidence of puppetry comes from the excavations at the Indus Valley. Archaeologists have unearthed terracotta dolls with detachable heads capable of manipulation by a string dating to 2500 BCE. Other excavations include terracotta animals which could be manipulated up and down a stick—-archiving minimum animation in both cases. The epic Mahabharata; Tamil literature from the Sangam Era, and various literary works dating from the late centuries BCE to the early centuries of the Common Era—including Ashokan edicts—describe puppets. Works like the Natya Shastra and the Kamasutra elaborate on puppetry in some detail. The Javanese Wayang theater was influenced by Indian traditions. Europeans developed puppetry as a result of extensive contact with the Eastern World.

• Rocket artillery, iron-cased and metal-cylinder: The first iron-cased and metal-cylinder rockets were developed by Tipu Sultan, ruler of the South Indian Kingdom of Mysore, and his father Hyder Ali, in the 1780s. He successfully used these iron-cased rockets against the larger forces of the British East India Company during the Anglo-Mysore Wars. The Mysore rockets of this period were much more advanced than what the British had seen, chiefly because of the use of iron tubes for holding the propellant; this enabled higher thrust and longer range for the missile (up to 2 km range). After Tipu's eventual defeat in the Fourth Anglo-Mysore War and the capture of the Mysore iron rockets, they were influential in British rocket development, inspiring the Congreve rocket, and were soon put into use in the Napoleonic Wars.

• Ruler: Rulers made from Ivory were in use by the Indus Valley Civilization in what today is Pakistan and some parts of Western India prior to 1500 BCE. Excavations at Lothal (2400 BCE) have yielded one such ruler calibrated to about 1/16 of an inch—less than 2 millimeters. Ian Whitelaw (2007) holds that 'The Mohenjo-Daro ruler is divided into units corresponding to 1.32 inches (33.5 mm) and these are marked out in decimal subdivisions with amazing accuracy—to within 0.005 of an inch. Ancient bricks found throughout the region have dimensions that correspond to these units.' Shigeo Iwata (2008) further writes 'The minimum division of graduation found in the segment of an ivory-made linear measure excavated in Lothal was 1.79 mm (that corresponds to 1/940 of a fathom), while that of the fragment of a shell-made one from Mohenjo-daro was 6.72 mm (1/250 of a fathom), and that of bronze-made one from Harapa was 9.33 mm (1/180 of a fathom).' The weights and measures of the Indus civilization also reached Persia and Central Asia, where they were further modified.

• Seamless celestial globe: Considered one of the most remarkable feats in metallurgy, it was invented in Kashmir by Ali Kashmiri ibn Luqman in between 1589 and 1590 CE, and twenty other such globes were later produced in Lahore and Kashmir during the Mughal Empire. Before they were rediscovered in the 1980s, it was believed by modern metallurgists to be technically impossible to produce metal globes without any seams, even with modern technology. These Mughal metallurgists pioneered the method of lost-wax casting in order to produce these globes.

• Sewage collection and disposal systems: Large-scale sanitary sewer systems were in place in the Indus Valley in Pakistan by 2700 BCE. The drains were 7–10 feet wide and 2 feet (0.61 m) below ground level. The sewage was then led into cesspools, built at the intersection of two drains, which had stairs leading to them for periodic cleaning. Plumbing using earthenware plumbing pipes with broad flanges for easy joining with asphalt to stop leaks was in place by 2700 BCE.

• Snakes and ladders: Snakes and ladders originated in India as a game based on morality. This game made its way to England, and was eventually introduced in the United States of America by game-pioneer Milton Bradley in 1943.

• Stepwell: Earliest clear evidence of the origins of the stepwell is found in the Indus Valley Civilization's archaeological site at Mohenjodaro in Pakistan. The three features of stepwells in the subcontinent are evident from one particular site, abandoned by 2500 BCE, which combines a bathing pool, steps leading down to water, and figures of some religious importance into one structure. The early centuries immediately before the common era saw the Buddhists and the Jains of India adapt the stepwells into their architecture. Both the wells and the form of ritual bathing reached other parts of the world with Buddhism. Rock-cut step wells in the subcontinent date from 200-400 CE. Subsequently the wells at Dhank (550-625 CE) and stepped ponds at Bhinmal (850-950 CE) were constructed.

• Stupa: The origin of the stupa can be traced to 3rd century BCE India. It was used as a commemorative monument associated with storing sacred relics. The stupa architecture was adopted in Southeast and East Asia, where it evolved into the pagoda, a Buddhist monument used for enshrining sacred relics.

• Toe stirrup: The earliest known manifestation of the stirrup, which was a toe loop that held the big toe was used in India in as early as 500 BCE or perhaps by 200 BCE according to other sources. This ancient stirrup consisted of a looped rope for the big toe which was at the bottom of a saddle made of fibre or leather. Such a configuration made it suitable for the warm climate of most of India where people used to ride horses barefoot. A pair of megalithic double bent iron bars with curvature at each end, excavated in Junapani in the central Indian state of Madhya Pradesh have been regarded as stirrups although they could as well be something else. Buddhist carvings in the temples of Sanchi, Mathura and the Bhaja caves dating back between the 1st and 2nd century BCE figure horsemen riding with elaborate saddles with feet slipped under girths. Sir John Marshall described the Sanchi relief as "the earliest example by some five centuries of the use of stirrups in any part of the world". In the 1st century CE horse riders in northern India, where winters are sometimes long and cold, were recorded to have their booted feet attached to hooked stirrups. However the form, the conception of the primitive Indian stirrup spread west and east, gradually evolving into the stirrup of today.

• Urban planning: Remains of major Indus cities (mature period c. 2600–1900 BCE) in what today is Pakistan and Western India, display distinct characteristics of urban planning such as streets crossing each other at right angles, well arranged rows of structures as well as neatly built, covered drainage and sewage lines, complete with maintenance sumps, running along backlanes. Drains in the ancient maritime city of Lothal for example, designed to be able to take out the city’s entire domestic sewage and storm-water were mostly underground, and built to high levels of uniformity, whereby the slopes never exceed 1 in 10,000. In terms of segregation, Lothal was divided into three districts: the citadel, the lower town and the dockyard, which were further divided into smaller administration centres, all having well planned infrastructure such as wide, straight roads along neatly arranged buildings to suit their purpose. Such planning is also evident from remains of Mohenjo-Daro, a city to the north-west of Lothal, which appears to have been built adhering to a complex level of city grid planning. This leads archaeologists to the conclusion that these cities were conceived entirely if not to a large extent before they were built—the earliest known manifestation of urban planning.

• Wootz steel: Wootz originated in India before the beginning of the common era. Wootz steel was widely exported and traded throughout ancient Europe, China, the Arab world, and became particularly famous in the Middle East, where it became known as Damascus steel. Archaeological evidence suggests that this manufacturing process was already in existence in South India well before the Christian era.

Discoveries

Agriculture

• Cashmere wool: The fiber is also known as pashm or pashmina for its use in the handmade shawls of Kashmir, India. The woolen shawls made from wool in Kashmir region of India find written mention between 3rd century BCE and the 11th century CE. However, the founder of the cashmere wool industry is traditionally held to be the 15th century ruler of Kashmir, Zayn-ul-Abidin, who employed weavers from Central Asia.

• Cotton: Cotton was cultivated by the inhabitants of the Indus Valley Civilization by the 5th millennium BCE - 4th millennium BCE. The Indus cotton industry was well developed and some methods used in cotton spinning and fabrication continued to be practiced till the modern Industrialization of India. Well before the Common Era, the use of cotton textiles had spread from India to the Mediterranean and beyond.

• Diamond Gemstones: Early diamonds used as gemstones originated in India. Golconda served as an important center for diamonds in central India. Diamonds then were exported to other parts of the world, including Europe. Early references to diamonds in India come from Sanskrit texts. India remained the only major source of diamonds in the world until the discovery of diamonds in Brazil. The Arthashastra of Kautilya mentions diamond trade in India. Buddhist works dating from the 4th century BCE mention it as a well-known and precious stone but don't mention the details of diamond cutting. Another Indian description written at the beginning of the 3rd century describes strength, regularity, brilliance, ability to scratch metals, and good refractive properties as the desirable qualities of a diamond. A Chinese work from the 3rd century BCE mentions: "Foreigners wear it in the belief that it can ward off evil influences". The Chinese, who did not find diamonds in their country, initially did not use diamond as a jewel but used as a "jade cutting knife".

• Indigo dye: Indigo, a blue pigment and a dye, was used in India, which was also the earliest major center for its production and processing. The Indigofera tinctoria variety of Indigo was domesticated in India. Indigo, used as a dye, made its way to the Greeks and the Romans via various trade routes, and was valued as a luxury product.

• Jute: Jute has been cultivated in India since ancient times. Raw jute was exported to the western world, where it was used to make ropes and cordage. The Indian jute industry, in turn, was modernized during the British Raj in India. The region of Bengal was the major center for Jute cultivation, and remained so before the modernization of India's jute industry in 1855, when Kolkata became a center for jute processing in India.

• Sugar: Sugarcane was originally from tropical South Asia and Southeast Asia. Different species likely originated in different locations with S. barberi originating in India and S. edule and S. officinarum coming from New Guinea. Crystallized sugar was discovered by the time of the Imperial Guptas, and the earliest reference of candied sugar comes from India. The process was soon transmitted to China with traveling Buddhist monks. Chinese documents confirm at least two missions to India, initiated in 647 CE, for obtaining technology for sugar-refining. Each mission returned with results on refining sugar.

Mathematics

• 0: The concept of zero as a number, and not merely a symbol for separation is attributed to India. In India, practical calculations were carried out using zero, which was treated like any other number by the 9th century CE, even in case of division.

• AKS primality test: The AKS primality test is a deterministic primality-proving algorithm created and published by three Indian Institute of Technology Kanpur computer scientists, Manindra Agrawal, Neeraj Kayal, and Nitin Saxena on August 6, 2002 in a paper titled PRIMES is in P. Commenting on the impact of this discovery, Paul Leyland noted: "One reason for the excitement within the mathematical community is not only does this algorithm settle a long-standing problem, it also does so in a brilliantly simple manner. Everyone is now wondering what else has been similarly overlooked".

• Algebraic abbreviations: The mathematician Brahmagupta had begun using abbreviations for unknowns by the 7th century. He employed abbreviations for multiple unknowns occurring in one complex problem. Brahmagupta also used abbreviations for square roots and cube roots.

• Analysis, classical: Madhava of Sangamagrama is considered the founder of classical analysis, for developing the first Taylor series expansions of trigonometric functions and for first making use of an intuitive notion of a limit to compute his results in infintie series.

• Basu's theorem: The Basu's theorem, a result of Debabrata Basu (1955) states that any complete sufficient statistic is independent of any ancillary statistic.

• Binary numbers: The modern system of binary numerals appears in the works of German polymath Gottfried Leibnitz during the 17th century. However, the first description of binary numbers is found in the chandaḥ-śāstra treatise of the Indian mathematician Pingala.

• Binomial coefficients: The Indian mathematician Pingala, by 300 BCE, had also managed to work with Binomial coefficients.

• Brahmagupta–Fibonacci identity, Brahmagupta formula, Brahmagupta interpolation formula Brahmagupta matrix, and Brahmagupta theorem: Discovered by the Indian mathematician, Brahmagupta (598–668 CE).

• Calculus textbook: The Yuktibhāṣā, written by Jyesthadeva of the Kerala school of astronomy and mathematics in circa 1530, is widely considered to be the first textbook on calculus.

• Chakravala method: The Chakravala method, a cyclic algorithm to solve indeterminate quadratic equations is commonly attributed to Bhāskara II, (c. 1114–1185 CE) although some attribute it to Jayadeva (c. 950 ~ 1000 CE). Jayadeva pointed out that Brahmagupta’s approach to solving equations of this type would yield infinitely large number of solutions, to which he then described a general method of solving such equations. Jayadeva's method was later refined by Bhāskara II in his Bijaganita treatise to be known as the Chakravala method, chakra (derived from cakraṃ चक्रं) meaning 'wheel' in Sanskrit, relevant to the cyclic nature of the algorithm. With reference to the Chakravala method, E. O. Selenuis held that no European performances at the time of Bhāskara, nor much later, came up to its marvellous height of mathematical complexity.

• Derivative and differential: In the 12th century, Bhāskara II developed the concept of a derivative and a differential representing infinitesimal change.

• Differential equation: In 499, the Indian mathematician Aryabhata used a notion of infinitesimals and expressed an astronomical problem in the form of a basic differential equation. Manjula, in the 10th century, elaborated on this differential equation in a commentary. This equation was eventually solved by Bhāskara II in the 12th century.

• Diophantine equation and Indeterminate equation: The Śulba Sūtras (literally, "Aphorisms of the Chords" in Vedic Sanskrit) (c. 700-400 BCE) list rules for the construction of sacrificial fire altars. Certain Diophantine equations, particularly the case of finding the generation of Pythagorean triples, so one square integer equals the of the other two, are also found.

• Fibonacci numbers: The Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci. Fibonacci's 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been previously described in Indian mathematics. The so-called Fibonacci numbers were also known to the Indian mathematician Pingala by 300 BCE.

• Hindu-Arabic numeral system: The Hindu-Arabic numeral system originated in India. Graham Flegg (2002) dates the history of the Hindu-Arabic system to the Indus valley civilization. The inscriptions on the edicts of Ashoka (1st millennium BCE) display this number system being used by the Imperial Mauryas. This system was later transmitted to Europe by the Arabs.

• Large numbers: The religious texts of the Vedic Period provide evidence for the use of large numbers. By the time of the last Veda, the Yajurvedasaṃhitā (1200-900 BCE), numbers as high as ${\displaystyle 10^{12}}$ were being included in the texts. For example, the mantra (sacrificial formula) at the end of the annahoma ("food-oblation rite") performed during the aśvamedha ("horse sacrifice"), and uttered just before-, during-, and just after sunrise, invokes powers of ten from a hundred to a trillion.

• Limit: The mathematicians of the Kerala school of astronomy and mathematics were the first to make use of an intuitive notion of a limit to compute their results in infinite series.

• Leibniz formula for pi The Leibniz formula for pi was derived in the early part of the 15th century by Madhava of Sangamagrama (c. 1340-1425 CE), an Indian mathematician and founder of the Kerala school of astronomy and mathematics over 200 years before Leibniz.

• Mean value theorem: An early version of this calculus theorem was first described by Parameshvara (1370–1460) from the Kerala school of astronomy and mathematics in his commentaries on Govindasvāmi and Bhāskara II.

• Negative numbers: The use of negative numbers was known in ancient India and their role in mathematical problems of debt and directions between points on a straight line was understood. Mostly consistent and correct rules for working with these numbers were formulated. The diffusion of this concept led the Arab intermediaries to pass it on to Europe.

• Pascal triangle: The so-called Pascal triangle was solved by the Indian mathematician Pingala by 300 BCE.

• Pell's equation, integral solution for: About a thousand years before Pell's time, Indian scholar Brahmagupta (598–668 CE) was able to find integral solutions to vargaprakṛiti (Pell's equation): ${\displaystyle \ x^{2}-Ny^{2}=1,}$ where N is a nonsquare integer, in his Brâhma-sphuṭa-siddhânta treatise.

• Pi, infinite series: The infinite series for π is attributed to Madhava of Sangamagrama (c. 1340-1425) and his Kerala school of astronomy and mathematics. He made use of the series expansion of ${\displaystyle \arctan x}$ to obtain an infinite series expression, now known as the Madhava-Gregory series, for π. Their rational approximation of the error for the finite sum of their series are of particular interest. They manipulated the error term to derive a faster converging series for π. They used the improved series to derive a rational expression,${\displaystyle 104348/33215}$ for π correct up to eleven decimal places, i.e. ${\displaystyle 3.14159265359}$.

• Ramanujan theta function, Ramanujan prime, Ramanujan summation, Ramanujan graph and Ramanujan's sum: Discovered by the Indian mathematician Srinivasa Ramanujan in the early 20th century.

• Rolle's theorem: The calculus theorem now known as "Rolle's theorem" was first stated by the Indian mathematician, Bhāskara II, in the 12th century.

• Sign convention: Symbols, signs and mathematical notation were employed in an early form in India by the 6th century when the mathematician-astronomer Aryabhata recommended the use of letters to represent unknown quantities. By the 7th century Brahmagupta had already begun using abbreviations for unknowns, even for multiple unknowns occurring in one complex problem. Brahmagupta also managed to use abbreviations for square roots and cube roots. By the 7th century fractions were written in a manner similar to the modern times, except for the bar separating the numerator and the denominator. A dot symbol for negative numbers was also employed. The Bakhshali Manuscript displays a cross, much like the modern '+' sign, except that it symbolized subtraction when written just after the number affected. The '=' sign for equality did not exist. Indian mathematics was transmitted to the Islamic world where this notation was seldom accepted initially and the scribes continued to write mathematics in full and without symbols.

• Taylor-Maclaurin series: In the 14th century, the earliest examples of the Taylor-Maclaurin series were first given by Madhava of Sangamagrama and his successors at the Kerala school of astronomy and mathematics. They found a number of special cases of the Taylor series, including those for the trigonometric functions of sine, cosine, tangent, and arctangent. They also found the second-order Taylor approximations for these functions, and the third-order Taylor approximation for sine.

• Trigonometric functions: The trigonometric functions sine and versine were discovered by the Indian mathematician, Aryabhata, in the late 5th century.

Medicine

• Cataract surgery: Cataract surgery was known to the Indian physician Sushruta (6th century BCE). In India, cataract surgery was performed with a special tool called the Jabamukhi Salaka, a curved needle used to loosen the lens and push the cataract out of the field of vision. The eye would later be soaked with warm butter and then bandaged. Though this method was successful, Susruta cautioned that cataract surgery should only be performed when absolutely necessary. Greek philosophers and scientists traveled to India where these surgeries were performed by physicians. The removal of cataract by surgery was also introduced into China from India.

• Inoculation and Variolation: The earliest record of inoculation and variolation for smallpox is found in 8th century India, when Madhav wrote the Nidāna, a 79-chapter book which lists diseases along with their causes, symptoms, and complications. He included a special chapter on smallpox (masūrikā) and described the method of inoculation to protect against smallpox.

• Leprosy: Kearns & Nash (2008) state that the first mention of leprosy is described in the Indian medical treatise Sushruta Samhita (6th century BCE). However, The Oxford Illustrated Companion to Medicine holds that the mention of leprosy, as well as ritualistic cures for it, were described in the Atharva-veda (1500–1200 BCE), written before the Sushruta Samhita.

• Stones: The earliest operation for curing stone is also given in the Sushruta Samhita (6th century BCE). The operation involved exposure and going up through the floor of the bladder.

• Veterinary medicine: The Egyptian Papyrus of Kahun (1900 BCE) and literature of the Vedic period in India offer the first written records of veterinary medicine. One of the edicts of Ashoka (272 - 231 BCE) reads: "Everywhere King Piyadasi (Asoka) erected two kinds of hospitals, hospitals for people and hospitals for animals. Where there were no healing herbs for people and animals, he ordered that they be bought and planted."

• Visceral leishmaniasis, treatment of: The Indian (Bengali) medical practitioner Upendra Nath Brahmachari (December 19, 1873 - February 6, 1946) was nominated for the Nobel Prize in Physiology or Medicine in 1929 for his discovery of 'ureastibamine (antimonial compound for treatment of kala azar) and a new disease, post-kalaazar dermal leishmanoid.' Brahmachari's cure for Visceral leishmaniasis was the urea salt of para-amino-phenyl stibnic acid which he called Urea Stibamine. Following the discovery of Urea Stibamine, Visceral leishmaniasis was largely eradicated from the world, except for some underdeveloped regions.

Mining

• Diamond: Diamonds were first recognized and mined in central India, where significant alluvial deposits of the stone could then be found along the rivers Penner, Krishna and Godavari. It is unclear when diamonds were first mined in India, although estimated to be at least 5,000 years ago. India remained the world's only source of diamonds until the 18th century.

• Zinc: Zinc was first recognised as a metal in India.Zinc metal extraction was one of the most difficult extractions but not for Indians. Zinc mines of Zawar, near Udaipur, Rajasthan, were active during 400 BCE. There are references of medicinal uses of zinc in the Charaka Samhita (300 BCE). The Rasaratna Samuccaya which dates back to the Tantric period (c. 5th - 13th century CE) explains the existence of two types of ores for zinc metal, one of which is ideal for metal extraction while the other is used for medicinal purpose. The metal extraction was then stolen by the Chinese and then used by William Champion for his metallurgy of zinc.

Science

• Atomism: The earliest references to the concept of atoms date back to India in the 6th century BCE. The Nyaya and Vaisheshika schools developed elaborate theories of how atoms combined into more complex objects (first in pairs, then trios of pairs). The references to atoms in the West emerged a century later from Leucippus whose student, Democritus, systematized his views. In approximately 450 BCE, Democritus coined the term átomos (Template:Lang-el), which means "uncuttable" or "the smallest indivisible particle of matter", i.e., something that cannot be divided. Although the Indian and Greek concepts of the atom were based purely on philosophy, modern science has retained the name coined by Democritus.

• Ammonium nitrite, synthesis in pure form: Prafulla Chandra Roy managed to synthesize NH₄NO₂ in its pure form, and became the first scientist to have done so. Prior to Ray’s synthesis of Ammonium nitrite it was thought that the compound undergoes rapid thermal decomposition releasing nitrogen and water in the process.

• Bhabha scattering: In 1935, Indian nuclear physicist Homi J. Bhabha published a paper in the Proceedings of the Royal Society, Series A, in which he performed the first calculation to determine the cross section of electron-positron scattering. Electron-positron scattering was later named Bhabha scattering, in honor of his contributions in the field.

• Bose–Einstein statistics, condensate and Boson: On June 4, 1924 the Bengali professor of Physics Satyendra Nath Bose mailed a short manuscript to Albert Einstein entitled Planck's Law and the Light Quantum Hypothesis seeking Einstein's influence to get it published after it was rejected by the prestigious journal Philosophical Magazine. The paper introduced what is today called Bose statistics, which showed how it could be used to derive the Planck blackbody spectrum from the assumption that light was made of photons. Einstein, recognizing the importance of the paper translated it into German himself and submitted it on Bose's behalf to the prestigious Zeitschrift für Physik. Einstein later applied Bose's principles on particles with mass and quickly predicted the Bose-Einstein condensate.

• Chandrasekhar limit and Chandrasekhar number: Discovered by and named after Subrahmanyan Chandrasekhar, who received the Nobel Prize in Physics in 1983 for his work on stellar structure and stellar evolution.

• Cosmic ray showers, theoretical explanation of: In 1936, physicist Homi Jehangir Bhabha collaborated with Walter Heitler to formulate a theory on cosmic ray showers. They conjectured that the showers were formed by the cascade production of gamma rays and positive and negative electron pairs. In this process, high energy electrons passing through matter would turn into high energy photons by means of the bremsstrahlung process. The photons then produced a positive and negative electron pair, which then led to additional production of photons. This process continued until the energy of the particles went below a critical value.

• Formal language and formal grammar: The 4th century BCE Indian scholar Pāṇini is regarded as the forerunner to these modern linguistic fields.

• Galena, applied use in electronics of: Bengali scientist Jagadish Chandra Bose effectively used Galena crystals for constructing radio receivers. The Galena receivers of Bose were used to receive signals comprising of shortwave, white light and ultraviolet light. In 1904 Bose patented the use of Galena Detector which he called Point Contact Diode using Galena.

• Linguistics: The study of linguistics in India dates back at least two and one-half millennia. During the 5th century BCE, the Indian scholar Pāṇini had made several discoveries in the fields of phonetics, phonology, and morphology.

• Mahalanobis distance: Introduced in 1936 by the Indian (Bengali) statistician Prasanta Chandra Mahalanobis (June 29, 1893–June 28, 1972), this distance measure, based upon the correlation between variables, is used to identify and analyze differing pattern with respect to one base.

• Mercurous Nitrite: The compound mercurous nitrite was discovered in 1896 by the Bengali chemist Prafulla Chandra Roy, who published his findings in the Journal of Asiatic Society of Bengal. The discovery contributed as a base for significant future research in the field of chemistry.

• Metrology: The inhabitants of the Indus valley developed a sophisticated system of standardization, using weights and measures, evident by the excavations made at the Indus valley sites. This technical standardization enabled gauging devices to be effectively used in angular measurement and measurement for construction. Calibration was also found in measuring devices along with multiple subdivisions in case of some devices.

• Molecular biophysics: Gopalasamudram Narayana Iyer Ramachandran is considered one of the founders of the rapidly developing field of molecular biophysics, for bringing together different components such as peptide synthesis, X-ray crystallography, NMR and other optical studies, and physico-chemical experimentation, together into the one field of molecular biophysics. He founded the first Molecular Biophysics Unit in 1970.

• Panini-Backus Form: Pāṇini's grammar rules have significant similarities to the Backus–Naur Form or BNF grammars used to describe modern programming languages, hence the notation is sometimes referred to as the Panini–Backus Form.

• Ramachandran plot, Ramachandran map, and Ramachandran angles: The Ramachandran plot and Ramachandran map were developed by Gopalasamudram Narayana Iyer Ramachandran, who published his results in the Journal of Molecular Biology in 1963. He also developed the Ramachandran angles, which serve as a convenient tool for communication, representation, and various kinds of data analysis.

• Raman effect: The Encyclopædia Britannica (2008) reports: "change in the wavelength of light that occurs when a light beam is deflected by molecules. The phenomenon is named for Sir Chandrasekhara Venkata Raman, who discovered it in 1928. When a beam of light traverses a dust-free, transparent sample of a chemical compound, a small fraction of the light emerges in directions other than that of the incident (incoming) beam. Most of this scattered light is of unchanged wavelength. A small part, however, has wavelengths different from that of the incident light; its presence is a result of the Raman effect."

• Raychaudhuri equation: Discovered by the Bengali physicist Amal Kumar Raychaudhuri in 1954. This was a key ingredient of the Penrose-Hawking singularity theorems of general relativity.

• Saha ionization equation: The Saha equation, derived by the Bengali scientist Meghnad Saha (October 6, 1893 – February 16, 1956) in 1920, conceptualizes ionizations in context of stellar atmospheres.

• Universe: The earliest known philosophical models of the universe are found in the Vedas, the earliest texts on Indian philosophy and Hindu philosophy dating back to the late 2nd millennium BC. They describe ancient Hindu cosmology, in which the universe goes through repeated cycles of creation, destruction and rebirth, with each cycle lasting 4,320,000 years. Hindu and Buddhist philosophers also developed a theory of five classical elements: Vayu (air), Ap (water), Agni (fire), Prithvi/Bhumi (earth) and Akasha (aether). In the 6th century BCE, Kanada, founder of the Vaisheshika school, developed a theory of atomism and proposed that light and heat were varieties of the same substance. In the 5th century CE, the Buddhist atomist philosopher Dignāga proposed atoms to be point-sized, durationless, and made of energy. They denied the existence of substantial matter and proposed that movement consisted of momentary flashes of a stream of energy.

Innovations

• Bhatnagar-Gross-Krook: The operator is named after Prabhu Lal Bhatnagar, E. P. Gross, and Max Krook, the three scientists who introduced it in a paper in Physical Review in 1954.

• BCH code: The BCH error detecting codes were discovered by Hocquenghem, Bose & Ray-Chaudhuri by 1960, and are named after their inventors.

• Pati-Salam model: A mainstream Grand Unification Theory proposed by Jogesh Pati in collaboration with Abdus Salam in 1974.

• Ivory: The use of ivory in India dates to the Indus Valley Civilization (2300-1750 BCE). Archaeological excavations have yielded combs, buttons, and other material made from Ivory. The use of ivory for making figurines in India continued into the 6th century BCE. Banglapedia (2008) holds that: "Stone inscriptions found at the ruins of Sanchi Stupa speak of trading in ivory crafts at Bidisha in the 1st century BC. During the Sung rule (1st century BCE) ivory craftsmen were engaged to work on the gates of the stupas at Bharhut, Buddhgaya and Sanchi. Ivory artefacts dating from the Sung period meant for cosmetic use have also been found at Chandraketu Garh in West Bengal. Ivory crafts were also popular during the Kushan period, as suggested by the abundance of ivory artefacts found at Taxila and Begram.".

• Public bathing: According to John Keay the Great Bath of Mohenjo Daro was the size of 'a modest municipal swimming pool', complete with stairs leading down to the water at each one of its ends. The bath is housed inside a larger—more elaborate—building and was used for public bathing.

• Radio: In 1894, the Bengali physicist, Jagdish Chandra Bose, demonstrated publicly the use of radio waves in Calcutta, but he was not interested in patenting his work. He also ignited gunpowder and rang a bell at a distance using electromagnetic waves, showing independently that communication signals can be sent without using wires. In 1896, the Daily Chronicle of England reported on his UHF experiments: "The inventor (J.C. Bose) has transmitted signals to a distance of nearly a mile and herein lies the first and obvious and exceedingly valuable application of this new theoretical marvel." The 1895 public demonstration by Bose in Calcutta was before Marconi's wireless signalling experiment on Salisbury Plain in England in May 1897.

• Same language subtitling: Same Language Subtitling (SLS) refers to the idea of subtitling in the same language as the audio, converse to the original idea of subtitling, which was to present a different language. This idea was struck upon by Brij Kothari, who believed that SLS makes reading practice an incidental, automatic, and subconscious part of popular TV entertainment, at a low per-person cost to shore up literacy rates in India. His idea was well received by the Government of India who now uses SLS on several national channels. For his idea, Kothari was adjudged a winner at the Development Marketplace— the World Bank’s Innovation Award which gave him enough funds to implement this programme nationally. The innovation has been recognised by the Institute for Social Inventions, UK and the Tech Museum of Innovations, San Jose, USA.

• Simputer: The Simputer (acronym for "simple, inexpensive and multilingual people's computer") is a self-contained, open hardware handheld computer, designed for use in environments where computing devices such as personal computers are deemed inappropriate. It was developed in 1999 by 7 scientists of the Indian Institute of Science, Bangalore, led by Dr. Swami Manohar in collaboration with Encore India, a company based in Bangalore. Originally envisaged to bring internet to the masses of India, the Simputer and its derivatives are today widely utilized by governments of several Indian states as part of their e-governance drive, the Indian Army, as well as by other public and private organizations.

• Wilson-Bappu effect: In a paper published in 1957, American astronomer Olin Chaddock Wilson and Manali Kallat Vainu Bappu had described what would later be known as the Wilson-Bappu effect. The effect as described by L.V. Kuhi is: 'The width of the Ca II emission in normal, nonvariable, G, K, and M stars is correlated with the visual absolute magnitude in the sense that the brighter the star the wider the emission.' The paper opened up the field of stellar chromospheres for research.

Footnotes

1. The term "India" in this article refers to the Indian Sub-continent.

See also

• History of science and technology in Indiahi
• Inventions of the Islamic Golden Age
• List of Chinese inventions
• List of Japanese inventions
• List of Korean inventions
• Timeline of historic inventions

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External links

• Essays on Indian Science and Technology.

• Science and technology in India
• Indian inventions
• Lists of inventions or discoveries