List of Indian inventions and discoveries

This list of Indian inventions and discoveries details the inventions, scientific discoveries and contributions of India, including those from the historic

For the purpose of this list, the inventions are regarded as technological firsts developed within territory of India, as such does not include foreign technologies which India acquired through contact or any Indian origin living in foreign country doing any breakthroughs in foreign land. It also does not include technologies or discoveries developed elsewhere and later invented separately in India, nor inventions by Indian emigres in other places. Changes in minor concepts of design or style and artistic innovations do not appear in the lists.

Ancient India

• Indigo dye – Indigo, a blue pigment and a dye, was used in India, which was also the earliest major centre for its production and processing.^[2] The Indigofera tinctoria variety of Indigo was domesticated in India.^[2] 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.^[2]
• Jute cultivation – Jute has been cultivated in India since ancient times.^[3] Raw jute was exported to the western world, where it was used to make ropes and cordage.^[3] The Indian jute industry, in turn, was modernised during the British Raj in India.^[3] The region of Bengal was the major centre for Jute cultivation, and remained so before the modernisation of India's jute industry in 1855, when Kolkata became a centre for jute processing in India.^[3]
• Sugar – Sugarcane was originally from tropical South Asia and Southeast Asia,^[4] with different species originating in India, and S. edule and S. officinarum from New Guinea.^[4] The process of producing crystallised sugar from sugar cane, in India, dates to at least the beginning of the common era, with 1st century CE Greek and Roman authors writing on Indian sugar.^[5][6] The process was soon transmitted to China with travelling Buddhist monks.^[7] Chinese documents confirm at least two missions to India, initiated in 647 CE, for obtaining technology for sugar-refining.^[8] Each mission returned with results on refining sugar.^[8]

Construction, civil engineering and architecture

• Mohenjodaro and Harappa from the 3rd millennium BCE.^[9]
• Mohenjodaro in Pakistan^[10] and Dholavira in India.^[11] 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.^[10] The early centuries immediately before the common era saw the Buddhists and the Jains of India adapt the stepwells into their architecture.^[10] Both the wells and the form of ritual bathing reached other parts of the world with Buddhism.^[10] Rock-cut step wells in the subcontinent date from 200 to 400 CE.^[12] Subsequently, the wells at Dhank (550–625 CE) and stepped ponds at Bhinmal (850–950 CE) were constructed.^[12]
• Stupa – The origin of the stupa can be traced to 3rd-century BCE India.^[13] It was used as a commemorative monument associated with storing sacred relics.^[13] The stupa architecture was adopted in Southeast and East Asia, where it evolved into the pagoda, a Buddhist monument used for enshrining sacred relics.^[13]
• Residential
  Nalanda (Nālandā, pronounced [naːlən̪d̪aː]) was a renowned mahavihara (Buddhist monastic university) in ancient Magadha (modern-day Bihar), eastern India.^[14][15][16] Considered by historians to be the world's first residential university^[17] and among the greatest centres of learning in the ancient world, it was located near the city of Rajagriha (now Rajgir) and about 90 kilometres (56 mi) southeast of Pataliputra (now Patna) and operated from 427 until 1197 CE.^[18]

• Cheque/ Check – There is early evidence of using cheques/ checks. In India, during the Maurya Empire (from 321 to 185 BC), a commercial instrument called the "Adesha" was in use, which was an order on a banker desiring him to pay the money of the note to a third person (now known as or referred to as a "Negotiable Instrument").^[19]

Games

• Chola Dynasty in close relation to the martial art of kalaripayattu.^[20]
• British India^[21][22]
• Blindfold chess – Games prohibited by Buddha includes a variant of ashtapada game played on imaginary boards. Akasam astapadam was an ashtapada variant played with no board, literally "astapadam played in the sky". A correspondent in the American Chess Bulletin identifies this as likely the earliest literary mention of a blindfold chess variant.^[23]
• Patiala, India.^[25] It became very popular among the masses after World War I. State-level competitions were being held in the different states of India during the early part of the twentieth century. Serious carrom tournaments may have begun in Sri Lanka in 1935 but by 1958, both India and Sri Lanka had formed official federations of carrom clubs, sponsoring tournaments and awarding prizes.^[26]
• Arabian empire.^[36][38] Muslims carried Shatranj to North Africa, Sicily, and Spain by the 10th century where it took its final modern form of chess.^[37]
• Kabaddi – The game of kabaddi originated in India during prehistory.^[39] Suggestions on how it evolved into the modern form range from wrestling exercises, military drills, and collective self-defence but most authorities agree that the game existed in some form or the other in India during the period between 1500 and 400 BCE.^[39]
• Kalaripayattu – One of the world's oldest form of martial arts is Kalaripayattu that developed in the southwest state of Kerala in India.^[40] It is believed to be the oldest surviving martial art in India, with a history spanning over 3,000 years.^[41]
• Kho-kho – This is one of the oldest variations of tag in the world, having been played since as early as the fourth century BCE.^[42]
• Ludo – Pachisi originated in India by the 6th century.^[43] The earliest evidence of this game in India is the depiction of boards on the caves of Ajanta.^[43] A variant of this game, called Ludo, made its way to England during the British Raj.^[43]
• gymnastic postures and wrestling grips in concert with a vertical stationary or hanging wooden pole, cane, or rope.The earliest literary known mention of Mallakhamb is in the 1135 CE Sanskrit classic Manasollasa, written by Someshvara III. It has been thought to be the ancestor of Pole Dancing
  .
• Nuntaa, also known as Kutkute.^[44]
• Seven stones – An Indian subcontinent game also called Pitthu is played in rural areas has its origins in the Indus Valley Civilization.^[45]
• Snakes and ladders – Vaikunta pali Snakes and ladders originated in India as a game based on morality.^[46] During British rule of India, this game made its way to England, and was eventually introduced in the United States of America by game-pioneer Milton Bradley in 1943.^[46]
• suits game, made of painted rags, invented in Ancient India. The term kridapatram literally means "painted rags for playing."^{[47][48][49][50][51]} Paper playing cards first appeared in East Asia during the 9th century.^[47][52] The medieval Indian game of ganjifa, or playing cards, is first recorded in the 16th century.^[53]
• India around the 1860s or 1870s, who brought it back with them.^[54]
• Chalukya king Someswara III (1124–1138), although it has been conjectured to have existed since as early as the Maurya dynasty^[55][56]

• Indus Valley. It is made of a curved shell and about 5000 years old."^[58]

• Calico – Calico had originated in the subcontinent by the 11th century and found mention in Indian literature, by the 12th-century writer Hemachandra. He has mentioned calico fabric prints done in a lotus design.^[59] The Indian textile merchants traded in calico with the Africans by the 15th century and calico fabrics from Gujarat appeared in Egypt.^[59] Trade with Europe followed from the 17th century onward.^[59] Within India, calico originated in Kozhikode.^[59]
• Carding devices – Historian of science Joseph Needham ascribes the invention of bow-instruments used in textile technology to India.^[60] The earliest evidence for using bow-instruments for carding comes from India (2nd century CE).^[60] These carding devices, called kaman and dhunaki would loosen the texture of the fibre by the means of a vibrating string.^[60]
• Cashmere – The fibre cashmere fibre also known as pashm or pashmina for its use in the handmade shawls of Kashmir, India.^[61] The woolen shawls made from wool in Indian administered Kashmir find written mention between the 3rd century BCE and the 11th century CE.^[62]
• Charkha (Spinning wheel): invented in India, between 500 and 1000 CE.^[63]
• Hindi language word चित्र् (chitr), which means an image.^[64][65]
• Mediterranean and beyond.^[68]
• Single roller cotton gin – The Ajanta Caves of India yield evidence of a single roller cotton gin in use by the 5th century.^[69] This cotton gin was used in India until innovations were made in form of foot powered gins.^[70] 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.^[60]
• Worm drive cotton gin – The worm drive later appeared in the Indian subcontinent, for use in roller cotton gins, during the Delhi Sultanate in the thirteenth or fourteenth centuries.^[71]
• Cotton Gin – The incorporation of the crank handle in the cotton gin, first appeared in either the late Delhi Sultanate or the early Mughal Empire.^[72]
• Colonial America—from India.^[74][75] In 17th-century England these hand painted cotton fabrics influenced native crewel work design.^[74] Shipping vessels from India also took palampore to colonial America, where it was used in quilting.^[75]
• Atisha (980–1054 CE) introduced the Indian practice of printing on cloth prayer flags to Tibet.^[77]
• sandals. Tanning was being carried out by the inhabitants of Mehrgarh in Ancient India between 7000 and 3300 BCE.^[79]
• Roller
  worm gearing, by the 17th century.^[80]

• 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.^[81] During the British Raj the British officers in India performed calisthenic exercises with clubs to keep in physical condition.^[81] From Britain the use of club swinging spread to the rest of the world.^[81]
• Guru of Sikhism, made references to soapberry tree and soap in 16th century.^[90] Washing of hair and body massage (champu) during a daily strip wash was an indulgence of early colonial traders in India. When they returned to Europe, they introduced their newly learnt habits, including the hair treatment they called shampoo.^[91]
• ancient India.^[92]

• Angina pectoris – The condition was named "hritshoola" in ancient India and was described by Sushruta (6th century BCE).^[93]
• complementary and alternative medicine. In village settings, away from urban centres, it is simply "medicine." The Sanskrit word आयुर्वेदः (āyur-vedaḥ) means "knowledge (veda) for longevity (āyur)".^[95] Siddha medicine is mostly prevalent in South India, and is transmitted in Tamil, not Sanskrit, texts. Herbs and minerals are basic raw materials of the Siddha therapeutic system whose origins may be dated to the early centuries CE.^[96][97]
• Atharva-veda (1500–1200 BCE), written before the Sushruta Samhita.^[99]
• Lithiasis treatment – The earliest operation for treating lithiasis, or the formations of stones in the body, is also given in the Sushruta Samhita (6th century BCE).^[100] The operation involved exposure and going up through the floor of the bladder.^[100]
• kala azar) and a new disease, post-kalaazar dermal leishmanoid.'^[101] Brahmachari's cure for Visceral leishmaniasis was the urea salt of para-amino-phenyl stibnic acid which he called Urea Stibamine.^[102] Following the discovery of Urea Stibamine, Visceral leishmaniasis was largely eradicated from the world, except for some underdeveloped regions.^[102]
• Ganja was used as herb for ayurverdic medicine development for last 2,000 years. The Sushruta Samhita, an ancient medical treatise, recommends cannabis plant extract for treating respiratory ailments and diarrhoea.
• Shalihotra Samhita
  is the first text to talk about cures for elephants and equines.
• Gentleman's Magazine reported the practice of rhinoplasty, as described in the Sushruta Samhita. Moreover, two centuries later, contemporary practices of otoplastic praxis were derived from the techniques and procedures developed and established in antiquity by Sushruta.^[103][104]
• BCE
• Mauryan Samrat (emperor) of India, accidentally consumed poison and died when she was close to delivering him. Chanakya, Chandragupta's teacher and adviser, made up his mind that the baby should survive. He cut open the belly of the queen and took out the baby, thus saving the baby's life.^[107]

• 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.^{[112][113][114]} 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".^[114] 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.^[109] However the form, the conception of the primitive Indian stirrup spread west and east, gradually evolving into the stirrup of today.^[110][113]

• Southern India (present day Mysore) iron appeared as early as 11th to 12th centuries BCE; these developments were too early for any significant close contact with the northwest of the country.^[117] In the time of Chandragupta II Vikramaditya (375–413 CE), corrosion-resistant iron was used to erect the Iron pillar of Delhi, which has withstood corrosion for over 1,600 years.^[118]
• Crucible steel – Perhaps as early as 300 BCE—although certainly by 200 BCE—high quality steel was being produced in southern India, by what Europeans would later call the crucible technique.^[119] 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.^[119]
• Dockyard
  – The world's earliest enclosed dockyard was built in the Harappan port city of Lothal circa 2600 BC in Gujarat, India.
• Diamond drills – in the 12th century BCE or 7th century BCE, Indians not only innovated use of diamond tipped drills but also invented double diamond tipped drills for bead manufacturing.^[120]
• Diamond cutting and polishing – The technology of cutting and polishing diamonds was invented in India, Ratnapariksha, a text dated to 6th century talks about diamond cutting and Al-Beruni speaks about the method of using lead plate for diamond polishing in the 11th century CE.^[121]
• Draw bar – The draw bar was applied to sugar-milling, with evidence of its use at Delhi in the Mughal Empire by 1540, but possibly dating back several centuries earlier to the Delhi Sultanate.^[122]
• Etched carnelian beads – are a type of ancient decorative beads made from carnelian with an etched design in white. They were made according to a technique of alkaline-etching developed by the Harappans during the 3rd millennium BCE and were widely disperced from China in the east to Greece in the west.^{[123][124][125]}
• Glassblowing – Rudimentary form of glass blowing from Indian subcontinent is attested earlier than Western Asian counterparts(where it is attested not earlier than 1st century BCE) in the form of Indo-Pacific beads which uses glass blowing to make cavity before being subjected to tube drawn technique for bead making dated more than 2500 BP.^[126][127] Beads are made by attaching molten glass gather to the end of a blowpipe, a bubble is then blown into the gather.^[128] The glass blown vessels were rarely attested and were imported commodity in 1st millennium CE though.
• Iron pillar of Delhi – The world's first iron pillar was the Iron pillar of Delhi—erected at the time of Chandragupta II Vikramaditya (375–413).^[129] The pillar has attracted attention of archaeologists and materials scientists and has been called "a testament to the skill of ancient Indian blacksmiths" because of its high resistance to corrosion.^[130]
• Harappan period (c. 3300–1300 BC).^[131][132] Other examples include the buffalo, bull and dog found at Mohenjodaro and Harappa,^{[133][132][134]} two copper figures found at the Harappan site Lothal in the district of Ahmedabad of Gujarat,^[131] and likely a covered cart with wheels missing and a complete cart with a driver found at Chanhudaro.^[133][134]
• Seamless celestial globe – Considered one of the most remarkable feats in metallurgy, it was invented in India in between 1589 and 1590 CE.^[135][136] 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.^[136]
• Stoneware – Earliest stonewares, predecessors of porcelain have been recorded at Indus Valley Civilization sites of Harappa and Mohenjo Daro, they were used for making stoneware bangles.^{[137][138][139]}
• Tube drawn technology: Indians used tube drawn technology for glass bead manufacturing which was first developed in the 2nd century BCE.^{[140][141][128]}
• Tumble polishing – Indians innvoted polishing method in the 10th century BCE for mass production of polished stone beads.^{[142][120][143][144]}
• Chera dynasty and called Seric Iron in Rome, and later known as Damascus steel in Europe.^{[146][147][148][149]} Reproduction research is undertaken by scientists Dr. Oleg Sherby and Dr. Jeff Wadsworth and the Lawrence Livermore National Laboratory have all attempted to create steels with characteristics similar to Wootz, but without success. J.D Verhoeven and Al Pendray attained some success in the reconstruction methods of production, proved the role of impurities of ore in the pattern creation, and reproduced Wootz steel with patterns microscopically and visually identical to one of the ancient blade patterns.^[150]
• Bhāskara's wheel – A hypothetical perpetual-motion machine design created around 1150 CE by the Indian mathematician Bhāskara II. The wheel consisted of curved or tilted spokes partially filled with mercury.^[151] Once in motion, the mercury would flow from one side of the spoke to another, thus forcing the wheel to continue motion, in constant dynamic equilibrium.
• Rain gauge – People living in India began to record rainfall in 400 BCE.^[152] The readings were correlated against expected growth. In the Arthashastra, used for example in Magadha, precise standards were set as to grain production. Each state storehouse was equipped with a rain gauge to classify land for taxation purposes.^[153]
• Harappa period of the Indus Valley civilization ca. 2600–1900 BC for testing the purity of soft metals.^[154]

• 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.^[156]
• Persia and Central Asia, where they were further modified.^[161]

A total of 558 weights were excavated from Mohenjodaro, Harappa, and

binary and decimal systems. 83% of the weights which were excavated from the above three cities were cubic, and 68% were made of chert.^[162]

• Persia and Central Asia, where they were further modified.^[161]

• Seamless
  metallurgists to be technically impossible to produce metal globes without any seams.^[164]
• 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.^[165]
• Scythed chariot – Invented by Ajatashatru in Magadha, India.^[166]

Indigenisation and improvements

• Jain sutras in India were compiled in ink.^[173]

• Catuskoti (Tetralemma) – The four-cornered system of logical argumentation with a suite of four distinct functions that refers to a logical proposition P, with four possibilities that can arise. The tetralemma has many logico-epistemological applications and has been made ample use of by the Indian philosopher Nāgarjuna in the Madhyamaka school. The tetralemma also features prominently in the Greek skepticist school of Pyrrhonism, the teachings of which are based on Buddhism. According to Christopher I. Beckwith ,the founder of the Pyrrhonist school lived in India for 18 months and likely learned the language, which allowed him to carry these teachings to Greece.^[174] However, other scholars, such as Stephen Batchelor^[175] and Charles Goodman^[176] question Beckwith's conclusions about the degree of Buddhist influence on Pyrrho
• Trairūpya – Trairūpya is a logical argument that contains three constituents which a logical ‘sign’ or ‘mark’ (linga) must fulfill to be 'valid source of knowledge' (pramana):

1. It should be present in the case or object under consideration, the ‘subject-locus' (pakṣa)
2. It should be present in a ‘similar case’ or a homologue (sapakṣa)
3. It should not be present in any ‘dissimilar case’ or heterologue (vipakṣa)

When a ‘sign’ or ‘mark’ (linga) is identified, there are three possibilities: the sign may be present in all, some, or none of the sapakṣas. Likewise, the sign may be present in all, some or none of the vipakṣas. To identify a sign, we have to assume that it is present in the pakṣa, however; that is the first condition is already satisfied. Combining these, Dignaga constructed his ‘Wheel of Reason’ (Sanskrit: Hetucakra).^[177]

• Jaina seven-valued logic – The Saptabhangivada, the seven predicate theory may be summarized as follows:^[178]

The seven predicate theory consists in the use of seven claims about sentences, each preceded by "arguably" or "conditionally" (syat), concerning a single object and its particular properties, composed of assertions and denials, either simultaneously or successively, and without contradiction. These seven claims are the following.

1. Arguably, it (that is, some object) exists (syad asty eva).
2. Arguably, it does not exist (syan nasty eva).
3. Arguably, it exists; arguably, it doesn't exist (syad asty eva syan nasty eva).
4. Arguably, it is non-assertible (syad avaktavyam eva).
5. Arguably, it exists; arguably, it is non-assertible (syad asty eva syad avaktavyam eva).
6. Arguably, it doesn't exist; arguably, it is non-assertible (syan nasty eva syad avaktavyam eva).
7. Arguably, it exists; arguably, it doesn't exist; arguably it is non-assertible (syad asty eva syan nasty eva syad avaktavyam eva).

Mathematics

• Zero – Zero and its operation are first defined by (Hindu astronomer and mathematician) Brahmagupta in 628.^[179] The Babylonians used a space, and later a zero glyph, in their written Sexagesimal system, to signify the 'absent',^[180] the Olmecs used a positional zero glyph in their Vigesimal system, the Greeks, from Ptolemy's Almagest, in a Sexagesimal system. The Chinese used a blank, in the written form of their decimal Counting rods system. A dot, rather than a blank, was first seen to denote zero, in a decimal system, in the Bakhshali manuscript.^[181] The usage of the zero in the Bakhshali manuscript was dated from between 3rd and 4th centuries, making it the earliest known usage of a written zero, in a decimal place value system.^[182]
• Arabic numeral system. It was developed in the Indian subcontinent between the 1st and 6th centuries CE.^[183][184]
• Law of signs in multiplication – The earliest use of notation for negative numbers, as
  subtrahend, is credited by scholars to the Chinese, dating back to the 2nd century BCE.^[185] Like the Chinese, the Indians used negative numbers as subtrahend, but were the first to establish the "law of signs" with regards to the multiplication of positive and negative numbers, which did not appear in Chinese texts until 1299.^[185] Indian mathematicians were aware of negative numbers by the 7th century,^[185] and their role in mathematical problems of debt was understood.^[186] Mostly consistent and correct rules for working with negative numbers were formulated,^[187] and the diffusion of these rules led the Arab intermediaries to pass it on to Europe.,^[186]
  for example (+)×(-)=(-),(-)×(-)=(+) etc.
• Bakhshali Manuscript displays a cross, much like the modern '+' sign, except that it symbolised subtraction when written just after the number affected.^[188] The '=' sign for equality did not exist.^[188] 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.^[189]
• Modern elementary arithmetic – Modum indorum or the method of the Indians for arithmetic operations was popularised by Al-Khwarizmi and Al-Kindi by means of their respective works such as in Al-Khwarizmi's on the Calculation with Hindu Numerals (ca. 825), On the Use of the Indian Numerals (ca. 830)^[190] as early as the 8th and 9th centuries.They, amongst other works, contributed to the diffusion of the Indian system of arithmetic in the Middle-East and the West.The significance of the development of the positional number system is described by the French mathematician Pierre Simon Laplace (1749–1827) who wrote:

"It is India that gave us the ingenuous method of expressing all numbers by the means of ten symbols, each symbol receiving a value of position, as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit, but its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions, and we shall appreciate the grandeur of this achievement when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest minds produced by antiquity."

• Chakravala method – The Chakravala method, a cyclic algorithm to solve indeterminate quadratic equations is commonly attributed to Bhāskara II, (c. 1114 – 1185 CE)^{[191][192][193]} although some attribute it to Jayadeva (c. 950~1000 CE).^[194] 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.^[195] 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.^[195][196] 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.^{[191][195][197]}
• Varahamihira discovered a few basic trigonometric formulas and identities, such as sin^2(x) + cos^2(x) = 1.^[200]
• Kerala School of Astronomy and Mathematics in India, in his commentaries on Govindasvāmi and Bhāskara II.^[201]
• Bhāskara I's sine approximation formula
• arctangent is now attributed to Madhava of Sangamagrama (c. 1340 – 1425) and his Kerala school of astronomy and mathematics.^[202][203]
  He made use of the series expansion of ${\displaystyle \arctan x}$ to obtain an infinite series expression for π.[202] 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.^[204] They used the improved series to derive a rational expression,^[204]${\displaystyle 104348/33215}$ for π correct up to eleven decimal places, i.e. ${\displaystyle 3.1415926539214}$.^[205][206] Madhava of Sangamagrama and his successors at the Kerala school of astronomy and mathematics used geometric methods to derive large sum approximations for sine, cosine, and arctangent. They found a number of special cases of series later derived by Brook Taylor series. They also found the second-order Taylor approximations for these functions, and the third-order Taylor approximation for sine.^{[207][208][209]}
• Power series – The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, Kerala, India. Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series). However, they did not formulate a systematic theory of differentiation and integration.^[210]
• Finite difference interpolation – The Indian mathematician Brahmagupta presented what is possibly the first instance^[211][212] of finite difference interpolation around 665 CE.^[213]
• cube roots.^[188]
• Narayana Pandita in 14th century India, and has been rediscovered frequently.^[214]
• Discovered by the Indian mathematician, Brahmagupta (598–668 CE):[215]^{[216][217][218]}
  • Brahmagupta–Fibonacci identity
  • Brahmagupta formula
  • Brahmagupta theorem
• Combinatorics – the Bhagavati Sutra had the first mention of a combinatorics problem; the problem asked how many possible combinations of tastes were possible from selecting tastes in ones, twos, threes, etc. from a selection of six different tastes (sweet, pungent, astringent, sour, salt, and bitter). The Bhagavati is also the first text to mention the choose function.^[219] In the second century BC, Pingala included an enumeration problem in the Chanda Sutra (also Chandahsutra) which asked how many ways a six-syllable metre could be made from short and long notes.^[220][221] Pingala found the number of metres that had ${\displaystyle n}$ long notes and ${\displaystyle k}$ short notes; this is equivalent to finding the
  binomial coefficients
  .
• Jain texts define five different types of
  Satkhandagama
• Fibonacci numbers – This sequence was first described by Virahanka (c. 700 CE), Gopāla (c. 1135), and Hemachandra (c. 1150),^[223] as an outgrowth of the earlier writings on Sanskrit prosody by Pingala
  (c. 200 BCE).
• Madhava's correction terms – Madhava's correction term is a mathematical expression attributed to Madhava of Sangamagrama (c. 1340 – c. 1425), the founder of the Kerala school of astronomy and mathematics, that can be used to give a better approximation to the value of the mathematical constant π (pi) than the partial sum approximation obtained by truncating the Madhava-Leibniz infinite series
  for π. The Madhava-Leibniz infinite series for π.
• Varahamihira^[200] and in the 10th century by Halayudha,^[224] commenting on an obscure reference by Pingala
  (the author of an earlier work on prosody) to the "Meru-prastaara", or the "Staircase of Mount Meru", in relation to binomial coefficients. (It was also independently discovered in the 10th or 11th century in Persia and China.)
• Integral solution to Pell's equation – 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):^[225][226] ${\displaystyle \ x^{2}-Ny^{2}=1,}$ where N is a non-square integer, in his
  Brâhma-sphuṭa-siddhânta treatise.^[227]
• Ardhacheda – Earlier than
  2-adic order rather than the logarithm.^[229]
• Kuṭṭaka – The Kuṭṭaka algorithm has much similarity with and can be considered as a precursor of the modern day extended Euclidean algorithm. The latter algorithm is a procedure for finding integers x and y satisfying the condition ax + by = gcd(a, b).^[230]
• bhaskaracharya^[231]

• Backus-Naur form, used to describe the syntax of programming languages, applies similar concepts.^[233]

• Kautilya mentions diamond trade in India.^[240] 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.^[234] 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.^[234] A Chinese work from the 3rd century BCE mentions: "Foreigners wear it [diamond] in the belief that it can ward off evil influences".^[234] The Chinese, who did not find diamonds in their country, initially used diamonds as a "jade cutting knife" instead of as a jewel.^[234]
• 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.^[246][247]
  India was to melt the first derived from a long experience of the old alchemy zinc by the distillation process, an advanced technique. The ancient Persians had also tried to reduce zinc oxide in an open stove, but had failed. Zawar in Tiri valley of Rajasthan is the first known old zinc smelting site in the world. The distillation technique of zinc production dates back to the 12th century CE and is an important contribution of India in the world of science.

• Hindu cosmological time cycles explained in the Surya Siddhanta (c.600 CE), give the average length of the sidereal year (the length of the Earth's revolution around the Sun) as 365.2563627 days, which is only a negligible 1.4 seconds longer than the modern value of 365.256363004 days.^[248]
• Preliminary concept of gravity – Although concept of gravity was already known to Greek philosophers, it was Brahmagupta who described gravity as an attractive force, using the term gurutvākarṣaṇa in which heavier objects attract towards the earth.^{[249][250][251]}
• Bhattotpala listed the names and estimated periods of certain comets, but it is unfortunately not known how these figures were calculated or how accurate they were.^[252]
• Tychonic system – A similar model was implicitly mentioned in the Hindu astronomical treatise Tantrasamgraha (c. 1500 CE) by Nilakantha Somayaji of the Kerala school of astronomy and mathematics.^[253][254]
• Reduction of the ecliptic: Achyutha Pisharadi discovered the techniques
• World's Largest
  Jai Singh II at his then-new capital of Jaipur
  , India between 1727 and 1733. The larger equatorial bow is called the Samrat Yantra (The Supreme Instrument); standing at 27 meters, its shadow moves visibly at 1 mm per second, or roughly a hand's breadth (6 cm) every minute.

• Hookah or water pipe: according to Cyril Elgood (PP.41, 110), the physician Irfan Shaikh, at the court of the Mughal emperor Akbar I (1542–1605) invented the Hookah or water pipe used most commonly for smoking tobacco.^{[257][258][259][260]}

Modern India

Medicine

• kala-azar
  (visceral leishmaniasis).
• post-kala-azar dermal leishmaniasis – n 1922, Brahmachari also discovered a new, deadly form of leishmaniasis. He called it dermal leishmanoid, marked by the appearance of sudden eruptions on the face of the patients without fever or other complaints. He observed it as a disease in partially cured cases of kala-azar, along with those who had no history of the disease at all.^[261] It has since been termed as post-kala-azar dermal leishmaniasis.
• Cholera toxin – Cholera toxin was discovered in 1959 by Indian microbiologist Sambhu Nath De.^[262]
• better source needed
  ]
• Bombay in 1955.^[266] In 1963, Shirodkar traveled to NYC to perform the procedure at the New York Hospital of Special Surgery; the procedure was successful, and the baby lived to adulthood.^{[citation needed}
  ]

• Horn antenna or microwave horn, One of the first horn antennas was constructed by Jagadish Chandra Bose in 1897.^[267][268]
• Microwave communication – The first public demonstration of microwave transmission was made by Jagadish Chandra Bose, in Calcutta, in 1895, two years before a similar demonstration by Marconi in England, and just a year after Oliver Lodge's commemorative lecture on Radio communication, following Hertz's death. Bose's revolutionary demonstration forms the foundation of the technology used in mobile telephony, radars, satellite communication, radios, television broadcast, WiFi, remote controls and countless other applications.^[269][270]
• Low Mobility Large cell (LMLC), is a feature of 5G and is designed to enhance the signal transmission range of a basestation several times, helping service providers cost-effectively expand coverage in rural areas.^[271]
• millimetre wavelengths using waveguides, and in 1897 described to the Royal Institution in London his research carried out in Kolkata.^[272]

• Hyderabad-based Microsoft India Development Center at HITEC City in India.^[273][274]
• Julia is a high-level, dynamic programming language. Its features are well suited for numerical analysis and computational science. Viral B. Shah an Indian computer scientist contributed to the development of the language in Bangalore while also actively involved in the initial design of the Aadhaar project in India using India Stack.^[275]
• Kojo – A programming language and integrated development environment (IDE) for computer programming and learning. Kojo is an open-source software. It was created, and is actively developed, by Lalit Pant, a computer programmer and teacher living in Dehradun, India.^[276][277]
• RISC-V ISA (microprocessor) implementations (a US standard, not from India, but some implementations are such as those below):
  • SHAKTI – Open Source, Bluespec System Verilog definitions, for FinFET implementations of the ISA, have been created at IIT Madras, and are hosted on GitLab.^[278]
  • C-DAC.^[279]
• File Transfer Protocol (FTP) – A standard communication protocol used for the transfer of computer files from a server to a client on a computer network. FTP is built on a client–server model architecture using separate control and data connections between the client and the server. Abhay Bhushan is the author of the File Transfer Protocol (which he started working on while he was a student at IIT-Kanpur) and the early versions of email protocols^[280]
• Beckn Protocol – An open and interoperable protocol for decentralised digital commerce. The first of its kind across the globe and developed by Nandan Nilekani, Pramod Varma and Sujith Nair, Beckn Gateways provide anonymised aggregated data generated from the network. The interoperability achieved by unbundling packet transmission layer from experience layer, so that the core of commercial transactions such as discovery, order booking, payment, delivery and fulfillment can happen in a standardised manner.^[281]

Construction, civil engineering and architecture

• CO₂-treated-C&D, researchers at the Centre for Sustainable Technologies (CST), IISc, are exploring ways to store carbon dioxide from industrial flue gas in excavated soil in Construction and Demolition (C&D) waste. the effect of injecting carbon dioxide gas into clayey soil—typically excavated from construction sites. This resulted in better stabilization of clay by cement and lime, and reduced the surface area, pore volume and lime reactivity of clay in soil, thereby improving the bulk engineering performance of the material.^[282][283]
• Rib & spine/Spine & Wing technique, NHAI has developed a flyover design which allows to save cost, time, minimum material usage and allows light under the flyover using the same technique.
• Dedicated freight corridors, is a new kind of railway lines that solely serve high-speed electric freight trains, thus making the freight service in India faster and more efficient.
• Genome Valley is world's first organized cluster for Life Sciences R&D and Clean Manufacturing activities, with Industrial / Knowledge Parks, Special Economic Zones (SEZs), Multi-tenanted dry and wet laboratories and incubation facilities.
• (I)-TM Tunneling technique:(I)-TM as Himalayan tunnelling method for tunnelling through the Himalayan geology to build tunnels in Jammu and Kashmir. Engineers decided to provide rigid supports using 'ISHB' as against the lattice girder method used in the New Austrian Tunnelling Method.ISHB uses nine-metre pipes in the mountains. It is called pipe roofing. Engineers made an umbrella using these perforated poles and filled them with PU grout.^{[284][285][286]}
• KOLOS – KOLOS is a wave-dissipating concrete block intended to protect coastal structures like seawalls and breakwaters from the ocean waves. These blocks were first developed in India by Navayuga Engineering Company(NEC)^[287] and were first adopted for the breakwaters of the Krishnapatnam Port
• supergrid
  to connect the middle east, south asia and southeast asia which will be powered by renewable sources instead of carbon based fossil fuels.
• plastic waste within the asphalt as an aggregate. Plastic roads first developed by Rajagopalan Vasudevan in 2001^{[288][289][290]}
• elevated transit system, which can provide connectivity to long distances(60km to 80kms) in a short time for large megapolis
  . RRTS provides semi-high speeds which ranges from 100 km/hr to 160km/hr.
• Chenab Bridge is world's highest rail bridge and world's first blast-proof steel bridge. The bridge is built using 63 millimetre-thick special blast-proof steel.^[291]

Finance and banking

• Direct Benefit Transfer – This programme aims to transfer subsidies directly to the people through their bank accounts. It is hoped that crediting subsidies into bank accounts will reduce leakages, delays, etc.
• Payments bank is an Indian new model of banks conceptualised by the Reserve Bank of India (RBI) without issuing credit.
• Small finance bank are a type of niche banks in India. Banks with a small finance bank (SFB) licence can provide basic banking service of acceptance of deposits and lending. The aim behind these is to provide financial inclusion to sections of the economy not being served by other banks.
• Payment Soundbox comes with a portable speaker that gives you an instant audio confirmation on receiving digital payments in your preferred regional language. This ensures that you do not miss even a single payment during peak times at work.
• Micro-finance institutions (MFI) is an organization that offers financial services to low income populations.

Genetics

• Amrapali mango – A named mango cultivar introduced in 1971 by Dr. Pijush Kanti Majumdar at the Indian Agriculture Research Institute in Delhi.
• Mynvax – The world's first "warm" COVID-19 vaccine, developed by IISc, capable of withstanding 37 °C (99 °F) for a month and neutralise all coronavirus variants of concern.^[292]
• ZyCoV-D vaccine – The world's first DNA-based COVID-19 vaccine.^[293]

Metallurgy, manufacturing, and industry

• 2G-Ethanol technology – A process for producing ethanol from agricultural residue feedstock, which has the potential to significantly reduce emissions from the transportation and agricultural sectors in India. The IP belongs to Praj Industries.
• Carbon nitride solar reactor – In September 2021, A team from the Institute of Nano Science and Technology (INST), Mohali, has fabricated a prototype reactor which operates under natural sunlight to produce hydrogen at a scale of around 6.1 litres in eight hours. They have used an earth-abundant chemical called carbon nitrides as a catalyst for the purpose.^[294][295]
• High ash coal gasification (coal to methanol) – The central government gave the country world's first 'coal to methanol' (CTM) plant built by the Bharat Heavy Electricals Limited (BHEL). The plant was inaugurated in BHEL's Hyderabad unit, The pilot project is the first that uses the gasification method for converting high-ash coal into methanol. Handling of high ash and heat required to melt this high amount of ash is a challenge in the case of Indian coal, which generally has high ash content. Bharat Heavy Electricals Limited has developed the fluidized bed gasification technology suitable for high ash Indian coals to produce syngas and then convert syngas to methanol with 99% purity.^[296]
• CBM in blast furnace – Tata Steel has initiated the trial for continuous injection of Coal Bed Methane (CBM) gas in one of the Blast Furnaces at its Jamshedpur Works, making it the first such instance in the world where a steel company has used CBM as injectant. This process is expected to reduce coke rate by 10 kg/thm, which will be equivalent to reducing 33 kg of CO₂ per tonne of crude steel.^[297]
• Automated Coating Control Using Regression Approach Towards Enterprise 5.0 (ACCURATE 5.0), 2 officers from SAIL conceived an entirely new system for zinc coating, achieving an astounding more than 99% accuracy.^[298]The Coating Prediction System project is an innovative system designed to predict, monitor, and control zinc coating weight in continuous galvanizing lines using Machine Learning, IoT, and Cloud Computing technologies.The system uses a dataset of 30,000+ tuples to perform Multivariate Polynomial Regression Analysis and dynamically arrive at an equation for predicted coating weight.^[299]
• Controlled shunt reactor – In 2002, Bharat Heavy Electricals Limited has successfully developed a first-of-its-kind in the world device for improving power transfer capability and reducing transmission losses in the country's highest rating (400 kV) transmission lines.The device is called Controlled Shunt Reactor.^[300][301]
• DMR grade steel – For several high-technology applications, such as military hardware and aerospace, need to possess ultrahigh strength (UHS; minimum yield strength of 1380 MPa (200 ksi)) coupled with high fracture toughness in order to meet the requirement of minimum weight while ensuring high reliability.
• JD-1 alloy – A special lightweight alloy developed by Jindal Defence with a minimum guaranteed hardness of 500 HB. It can be used in aerospace, small arms, and engineering solutions. It is mainly used in armoured jacket.
• Fortified Cabin – A car designing technique by TATA Motors such that the high-strength steel structure absorbs impact energy and protects the passenger during an unfortunate collision.Tata Nexon has the fortified cabin design for achieving full 5 star safety ratings.
• HIsarna – A new process for production of steel, one it says "results in enormous efficiency gains" and reduces energy use and carbon dioxide emissions by a fifth of that in the conventional blast furnace route.It's IP belongs to TATA Steel.
• Sorption-enhanced steam methane reforming (SESMR) – In April 2022, the scientists from CSIR-Indian Institute of Chemical Technology (CSIR-IICT), Hyderabad developed a fluidized bed reactor (FBR) facility in Hyderabad to perform sorption enhanced steam methane reforming (SESMR) to achieve clean hydrogen in its purest form. The team of scientists have designed a hybrid material to simulate capturing carbon dioxide in-situ (onsite) and converting it into clean hydrogen from non-fuel grade bioethanol.^[302]
• Spray-drying buffalo milk – The collective consensus of dairy experts worldwide was that buffalo milk could not be spray-dried due to its high fat content. Harichand Megha Dalaya & his invention of the spray dry equipment, led to the world's first buffalo milk spray-dryer, at Amul Dairy in Gujarat.
• Jackal steel – An advanced grade high-strength, low-alloy steel. The technology of Jackal steel has been passed on to Steel Authority of India Limited (SAIL) and MIDHANI for its bulk production.
• High-Rise Pantograph – The new-design world record pantograph, developed completely in-house for use in DFC & other freight routes with height of 7.5 metres (25 ft).^[303]
• 1200 kV UHDVC Transformer – The world's first ultra-high voltage AC 1200 kV transformer through in-house R&D by BHEL in 2011.^[304]
• Commercial CCU plant: Tuticorin Alkali Chemicals and Fertilizers Limited (TFL) partnered with Carbon Clean to create the world’s first fully commercial CCU plant. The 10 MW facility captures coal-fired boiler flue gas and uses it to deliver industrial quality CO₂. The 10 MW facility captures coal-fired boiler flue gas and uses it to deliver industrial quality CO₂.^[305] The technology has been developed by Carbon Clean Solutions, headquartered in London – a start-up by two Indian engineers focusing on carbon dioxide separation technology.There are many chemicals exported out of India where CO₂ is the raw material.^[306]
• Triple-stack container freight train^[307][308] – In order to ensure new streams of traffic and commodities and to bring about a modal shift, the DFC is undertaking trials for running smaller than usual containers, known as dwarf containers (where the container height is lower by 660 mm than normal containers), in triple-stack formation to further improve the profitability of train operations. It may be possible to run these as double-stack on conventional routes and triple-stack on routes with high-rise OHE, once the trials are successfully completed.^[309]

Metrology

• Crescograph – The crescograph, a device for measuring growth in plants, was invented in the early 20th century by the Bengali scientist Sir Jagadish Chandra Bose.^[310][311]
• Shearing Interferometer utilises a laser source for measuring refractive index.^[312][313]

• Bipyrazole Organic Crystals, the piezoelectric molecules developed by IISER scientists recombine following mechanical fracture without any external intervention, autonomously self-healing in milliseconds with crystallographic precision.^[314]
• Single-crystalline Scandium Nitride, that has the ability to convert infrared light into energy, Scientists based in Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Bengaluru have discovered a novel material that can emit, detect, and modulate infrared light with high efficiency making it useful for solar and thermal energy harvesting and for optical communication devices.^[315][316]
• e-mode HEMT, In 2019 scientists from Bangalore have developed a highly reliable, High Electron Mobility Transistor (HEMTs) that is a normally OFF device and can switch currents up to 4A and operates at 600V. This first-ever indigenous HEMT device made from gallium nitride (GaN). Such transistors are called e-mode or enhancement mode transistors.^[317][318]
• Nano Urea, the size of one nano urea liquid particle is 30 nanometre and compared to the conventional granular urea it has about 10,000 times more surface area to volume size. Due to the ultra-small size and surface properties, the nano urea liquid gets absorbed by plants more effectively when sprayed on their leaves.Ramesh Raliya of IFFCO is the inventor of nano urea.
• Locomotive with regenerative braking, BHEL has developed world's first ever DC electric locomotive with a regenerative braking system through its in-house R&D centre, First proposed by the Railway Ministry, the concept involving the energy-efficient regeneration system was put into shape by BHEL in a 5,000 HP WAG-7 electric locomotive.^[319]
• In2Se3 transistor developed by the Centre for Nano Science and Engineering (CeNSE), a ferroelectric channel semiconductor FET, i.e., FeS-FET, whose gate-triggered and polarization-induced resistive switching is then exploited to mimic an artificial synapse.
• Indian Ocean Dipole is an unusual pattern in the ocean-atmosphere system of the equatorial Indian Ocean that influences the monsoon and can offset the adverse impact of El Nino. It is typically characterized by cooler than normal eastern equatorial Indian Ocean and warmer than normal west and unusual equatorial easterly winds. It was discovered in Centre for Atmospheric And Oceanic Sciences, IISc. team led by NH Saji in 1999.^[320]
• Wireless Railway Signaling System: Nokia partnered with Alstom to implement the 4.9G/LTE private wireless network to support the ETCS L2 signalling in Regional Rapid Transit System. This is a “world-first application” of an LTE network that is being used along with ETCS Level 2 signaling to provide high-speed, high-reliability commuter service. In addition, ETCS Level 2-based system allows trains to report their precise location in real-time.^[321]
• Solution combustion synthesis (SCS) was accidentally discovered in 1988 at Indian Institute of Science (IISc), Bengaluru, India. SCS involves an exothermic redox chemical reaction between an oxidizer like metal nitrate and a fuel in an aqueous medium.^[322]
• Three-stage nuclear power programme was formulated by Homi Bhabha, the well-known physicist, in the 1950s to secure the country's long term energy independence, through the use of uranium and thorium reserves found in the monazite sands of coastal regions of South India.
• Electrically Excited Synchronous Motor (EESM) or Rare earth free motor: In 2021 deep-tech startup Chara Technologies has built scalable, cloud-controlled electric vehicle motors free of toxic rare-earth metals, thus cutting a massive dependency on imports to accelerate electric mobility in India.^[323][324]
• Radium belt for animals or cattle: To save animals in many parts of india, people have adopted radium belt for cattle and animals for identification as well as prevention of accidents on highways or roads.^[325][326]

Weapon systems

• ASMI – Indian submachine gun which means "pride, self respect and hard work", was first showcased in January 2021, and developed over the course of four months by Lieutenant Colonel Prasad Bansod. 3D printing was utilized to make parts of the gun^[327][328]
• ATAGS – Bharat Forge and the DRDO has developed world's first electric artillery gun^[329]
• Rifle-rated ballistic helmet, MKU has developed what it bills as "a first-of-its-kind rifle-rated ballistic helmet", MKU states that the Kavro Doma 360 is "the first anti-rifle helmet in the world that does not have bolts or any metal parts"^[330]
• Critical Situation Response Vehicle (CSRV) – The Central Reserve Police Force (CRPF) has made and inducted a bomb/bulletproof armoured vehicle. The latest all-terrain highly sophisticated vehicle 'CSRV' has given a shot in the arm to the Central Reserve Police Force engaged in counter-terror operations.
• E-bomb – The Defence Research and Development Organisation (DRDO) has been developing an e-bomb which will emit electromagnetic shock waves that destroy electronic circuits and communication networks of enemy force.^[331] The tow bodies in Lakshya-2 Weapon Delivery Configuration carry High Energy Weapon Payload.^[332]
• Phosphoric Acid Fuel Cell air-independent propulsion (PAFC AIP) is a 270 kilowatt phosphoric acid fuel cell (PAFC) air-independent propulsion (AIP) system to power the Kalvari-class submarines is developed by the
  DRDO. It's application is considered to be wide and it can also power ships in future.^[333]

• CNG car/vehicle – Bajaj Auto
  launched the first 'commercial' lot of its CNG (Compressed Natural Gas) autorickshaws in Delhi on 29 May 2000.
• Digital rupee (e₹) or eINR or e-rupee is a tokenised digital version of the Indian rupee, to be issued by the Reserve Bank of India (RBI) as a central bank digital currency (CBDC). Digital Rupee is using blockchain distributed-ledger technology. Digital rupee users to hit 50,000 by Jan-end on better acceptance.^[334]
• MD-15 is a fuel grade in which Methanol is blended with diesel. Research Design and Standards Organisation (RDSO), in collaboration with the Indian Oil Corporation Ltd (IOCL), has developed a special cost-effective fuel that would not only minimize IR’s dependency on diesel, but will also be emit fewer pollutants. IOCL developed the composition, adding 14% additives (developed indigenously by IOCL) along with 71% mineral diesel, 15% methanol. MD-15 fuelled engine has shown superior performance, emission and combustion characteristics than the mineral diesel fuelled engine.^[335][336]
• Electrified Flex-fuel – The world's first electrified flex-fuel vehicle was unveiled by Toyota in India, an electrified flex-fuel vehicle has both a flex-fuel engine as well as an electric powertrain, thereby offering higher use of ethanol combined with better fuel efficiencies.^[337]
• Unified Payments Interface – An instant real-time payment system developed by National Payments Corporation of India (NPCI) facilitating person-to-merchant (P2M) transactions through inter-bank peer-to-peer (P2P) mechanism. UPI doesn't need an internet connection for financial transactions, and cardless ATM transactions can also occur using UPI. UPI is not an alternative to a wallet, but more of a solution to the money printing problem.

Mathematics

• Indian Institute of Technology Kanpur computer scientists, Manindra Agrawal, Neeraj Kayal, and Nitin Saxena on 6 August 2002 in a paper titled PRIMES is in P.^[338][339] 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".^[339][340]
• Seshadri constant – In algebraic geometry, a Seshadri constant is an invariant of an ample line bundle L at a point P on an algebraic variety.The name is in honour of the Indian mathematician C. S. Seshadri.
• 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.^[341][342]
• orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. Stochastic processes given by infinite series of this form were first^[343] considered by Damodar Dharmananda Kosambi.^[344]
• Magical Indian Math discovery: Numbers 495 and 6174. The Indian mathematician Dattaraya Ramchandra Kaprekar discovered the number 6174 is reached after repeatedly subtracting the smallest number from the largest number that can be formed from any four digits not all the same. The number 495 is similarly reached for three digits number.
• Kosaraju's algorithm is a linear time algorithm to find the strongly connected components of a directed graph. Aho, Hopcroft and Ullman credit it to S. Rao Kosaraju and Micha Sharir. Kosaraju suggested it in 1978.
• 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.^[345]
• Shrikhande graph – Graph invented by the Indian mathematician S.S. Shrikhande in 1959.

Sciences

• Prafulla Chandra Roy synthesised NH₄NO₂ in its pure form, and became the first scientist to have done so.^[346] 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.^[346]
• gauge field and its complementary variable. Ashtekar variables are the key building block of loop quantum gravity
  .
• 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.^[347] 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.^[347]
• Proceedings of the Royal Society, Series A, in which he performed the first calculation to determine the cross section of electron-positron scattering.^[348] Electron-positron scattering was later named Bhabha scattering, in honour of his contributions in the field.^[348]
• photons.^[349][350] 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.^[349][350] Einstein later applied Bose's principles on particles with mass and quickly predicted the Bose-Einstein condensate.^[350][351]
• Boson – The name boson was coined by Paul Dirac^[352] to commemorate the contribution of the Indian physicist Satyendra Nath Bose.^[353][354] In quantum mechanics, a boson^[355][356]) is a particle that follows Bose–Einstein statistics. Bosons make up one of the two classes of particles, the other being fermions.^[357]
• Braunstein-Ghosh-Severini Entropy – This modelling of entropy using network theory is used in the analysis of quantum gravity and is named after Sibasish Ghosh and his teammates, Samuel L. Braunstein
  and Simone Severini.
• ultraviolet light.^[358] In 1904 Bose patented the use of Galena Detector which he called Point Contact Diode using Galena.^[359]
• Mahalanobis distance – Introduced in 1936 by the Indian (Bengali) statistician Prasanta Chandra Mahalanobis (29 June 1893 – 28 June 1972), this distance measure, based upon the correlation between variables, is used to identify and analyze differing pattern with respect to one base.^[360]
• Journal of the Asiatic Society of Bengal.^[346] The discovery contributed as a base for significant future research in the field of chemistry.^[346]
• 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.^[361]
• 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."^[362]
• Penrose-Hawking singularity theorems of general relativity.^[363]
• Periodicity in Nuclear Properties: A sharp pattern is discovered by an Indian researcher regarding the nuclear properties of chemical elements. The remarkable deviations are noticed near the magic numbers.[364]
• Process of formation of the E layer of the ionosphere and night sky luminiscence: Discovered by the Indian physicist, Sisir Kumar Mitra.^[365]

Space

• Lunar water – Although the presence of water ice on the Moon has been conjectured by various scientists since the 1960s, inconclusive evidence of free water ice had also been identified. The first incontrovertible evidence of water on the Moon was provided by the payload Chace carried by the Moon Impact Probe released by Chandrayaan-1 in 2009,^{[366][367][368]} confirmed and established by NASA.^[369]
• ionisations in context of stellar atmospheres.^[370]
• quasi-normal modes of black holes.^[371]
  These modes of black hole vibrations are one of the main targets of observation using the gravitational wave detector.

• Timeline of Indian innovation
• History of science and technology in India
• Timeline of historic inventions

References