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Early cultures identified celestial objects with gods and spirits. They related these objects and their movements to predict things like rain, drought, seasons, and tides. The movements of Sun and Moon are used in calendars to measure the day, month and year. It is important to agricultural societies as they need to know the time to plant and harvest. Ancient societies also believed that the position of some celestial bodies have an impact on the human beings. The astronomy and the astrology of India are based upon the stars and the time it takes to make one full orbit around the Sun, relative to the stars.

The earliest references to astronomy are found in the Vedas which are dated around 3000 B.C. to 1000 B.C. By 500 AD, ancient Indian astronomy has emerged as an important part of Indian studies and its affect is also seen in several treatises of that period. In some instances, astronomical principles were borrowed to explain matters, pertaining to astrology, like casting of a horoscope. Apart from this linkage of astronomy with astrology in ancient India, science of astronomy continued to develop independently.

There are astronomical references of chronological significance in the Vedas. Some Vedic notices mark the beginning of the year and that of the vernal equinox in Orion.

Yajnavalkya (estimated 1800 BC) advanced a 95-year cycle to synchronize the motions of the sun and the moon. The Vedanga Jyotisha, a text on Vedic astrology that has been dated to 1350 BC, was written by Lagadha which describes rules for tracking the motions of the Sun and the Moon, and also develops the use of geometry and trigonometry for astronomical uses.

The sun (Surya) was one of the chief deities in the Vedas. He was recognized as the source of light (Dinkara), source of warmth (Bhaskara). In the Vedas sun is also referred to as the source of all life, the center of creation and the center of the spheres.

In Indian languages, the science of astronomy is called Khagola-shastra. The word Khagola perhaps is derived from the famous astronomical observatory at the University of Nalanda which was called Khagola. It was at Khagola that the famous 5th century Indian Astronomer Aryabhatta studied and extended the subject. In 500 AD, Aryabhata presented a mathematical system that took the earth to spin on its axis and considered the motions of the planets with respect to the sun. His book, the Aryabhatya, presented astronomical and mathematical theories in which the Earth was taken to be spinning on its axis and the periods of the planets were given with respect to the sun. Aryabhata wrote that 1,582,237,500 rotations of the Earth equal 57,753,336 lunar orbits which is an extremely accurate calculation.

The lack of a telescope hindered further advancement of ancient Indian astronomy. Though it should be admitted that with their unaided observations with crude instruments, the astronomers in ancient India were able to arrive at near perfect measurement of astronomical movements and predict eclipses. Indian astronomers also propounded the theory that the Earth was a sphere. Aryabhatta was the first one to have propounded this theory in the 5th century.

Another astronomer Varahamihira (476 A.D. – 587 A.D.) recognized that there should be a force which might be keeping bodies stuck to the Earth, and also keeping heavenly bodies in their determined places. Also recognized that this force is an attractive force. The Sanskrit term for gravity is Gurutvakarshan which is an amalgam of Guru-tva-akarshan. Akarshan means to be attracted, thus the fact that the character of this force was of attraction was also recognized. This apart, it seems that the function of attracting heavenly bodies was attributed to the sun.

Brahmagupta (598 A.D -668 A.D.) was the head of the astronomical observatory at Ujjain and during his tenure there wrote a text on astronomy, the Brahmasphutasiddhanta in 628. He was the earliest to use algebra to solve astronomical problems. He also develops methods for calculations of the motions and places of various planets, their rising and setting, conjunctions, and the calculation of eclipses of the Sun and the Moon. Brahmagupta estimated in the 7th century that the circumference of the earth was 5000 yojanas. A yojana is around 7.2 kms. Calculating on this basis we see that the estimate of 36,000 kms as the Earth's circumference comes quite close to the actual circumference known today. Brahmagupta, in the 7th century had said about gravity that ‘Bodies fall towards the Earth as it is in the nature of the Earth to attract bodies, just as it is in the nature of water to flow’.

Bhaskara (1114 A.D -1185 A.D.) was the head of the astronomical observatory at Ujjain, continuing the mathematical tradition of Brahmagupta. He wrote the Siddhantasiromani which consists of two parts: Goladhyaya (sphere) and Grahaganita (mathematics of the planets). He also calculated the time taken for the Earth to orbit the sun to 9 decimal places.

Other important astronomers from India include Madhava, Nilakantha Somayaji and Jyeshtadeva from the 14th century to the 16th century.

In the late Vedic era(9th–6th century BC), the astronomer Yajnavalkya, in his Shatapatha Brahmana, referred to an early concept of heliocentrism with the Earth being round and the Sun being the "centre of spheres". He measured the distances of the Moon and the Sun from the Earth as 108 times the diameters of these heavenly bodies, which were close to the modern values of 110.6 for the Moon and 107.6 for the Sun.

In 499 A.D., the mathematician-astronomer Aryabhata propounded a detailed model of the heliocentric solar system of gravitation, where the planets rotate on their axes causing day & night and follow elliptical orbits around the Sun causing year, and where the planets and the Moon do not have their own light but reflect the light of the Sun. Aryabhata also correctly explained the causes of the solar and lunar eclipses and predicted their times, gave the radii of planetary orbits around the Sun, and accurately measured the lengths of the day, year, and the Earth's diameter and circumference. Brahmagupta, in his Brahma Sputa Siddhanta in 628 A.D., recognized gravity as a force of attraction and understood the law of gravitation.

Harappan civilization (2400 B.C) used shell objects served as compasses to measure the angles of the 8–12 fold divisions of the horizon and sky in multiples of 40–360 degrees, and the positions of stars.

The Samkhya and Vaisheshika schools developed theories on light from the 6th–5th century BC. According to the Samkhya School, light is one of the five fundamental "subtle" elements out of which emerge the gross elements, which were taken to be continuous. The Vaisheshika School defined motion in terms of the non-instantaneous movement of the physical atoms. Light rays were taken to be a stream of high velocity fire atoms, which can exhibit different characteristics depending on the speed and the arrangements of these particles. The Buddhists Dignāga (5th century) and Dharmakirti (7th century) developed a theory of light being composed of energy particles, similar to the modern concept of photons.

Ayurveda as a science of medicine owes its origins in ancient India. The literal meaning of the Sanskrit word Ayurveda is the science of life or longevity. Ayurveda constitutes ideas about ailments and diseases, their symptoms, diagnosis and cure, and relies heavily on herbal medicines, including extracts of several plants of medicinal values. Ayurveda was formally organized into eight sections or branches called Astanga (eight-armed) Ayurveda. They are Kayachikitsa Tantra(Internal Medicine), Shalya Tantra(Surgery) - Shalakya Tantra(Ears, eyes, nose and throat), Kaumarabhritya Tantra (Pediatrics ), Agada Tantra(Toxicology), Bajikarana Tantra(Purification of the genetic organs), Rasayana Tantra(Health and Longevity), and Bhuta Vidya(Spiritual Healing).

Ancient scholars of India like Atreya, and Agnivesa have dealt with principles of Ayurveda as long back as 800 BC. Their works and other developments were consolidated by Charaka who compiled a compendium of Ayurvedic principles and practices in his treatise Charaka-Samahita, which remained like a standard textbook almost for 2000 years and was translated into many languages, including Arabic and Latin. 'Charaka-Samahita' deals with a variety of matters covering physiology, etiology and embryology, concepts of digestion, metabolism, and immunity.

The oldest treatise dealing with surgery is the Shushruta Samahita. Shusruta was one of the first to study the human anatomy. In the Shusruta Samahita he has described in detail the study of anatomy with the aid of a dead body. Shusruta's specialty was rhinoplasty (Plastic surgery) and ophthalmology (ejection of cataracts). Shushruta has described surgery under eight heads Chedya (excision), Lekhya (scarification), Vedhya (puncturing), Esya (exploration), Ahrya (extraction), Vsraya (evacuation) and Sivya (Suturing).

Around 500 AD, Vagbhatt compiled the third major treatise on Ayurveda, Astanga Hridaya. From 500 AD to 1900 AD, sixteen major Nighantus or supplementary texts on Ayurveda like Dhanvantari Bhavaprakasha, Raja and Shaligram among others were written incorporating new drugs, expansion in applications, discarding of old drugs and identification of substitutes. These texts mention about 1814 varieties of plants in vogue.

Yoga is a system of exercise for physical and mental nourishment. Since Vedic times, the principles and practice of yoga have crystallized. But, it was only around 200 BC that all the fundamentals of yoga were collected by Patanjali in his treatise, named Yogasutra, that is, Yoga-Aphorisms. Patanjali says that through the practice of yoga, the energy latent within the human body may be made live and released, which has a salubrious affect on the body and the mind.

The first appearance of evidence of the use of mathematics in the Indian subcontinent was in the Indus Valley Civilization, which dates back to around 3300 BC. Excavations at Harappa, Mohenjo-daro and the surrounding area of the Indus River, have uncovered much evidence of the use of basic mathematics. The mathematics used by this early Harappan civilization was very much for practical means, and was primarily concerned with weights and measuring scales.

By 1800 BC, Indian mathematicians were discussing the idea of infinity, pointing out that "if you remove a part from infinity or add a part to infinity, what remains is still infinity." By about 400 BC, Indian mathematicians were doing more work on the idea of infinity. The Surya Prajinapti defines five kinds of infinity: an infinite line beginning from an endpoint, an infinite line going directions, an infinite plane, an infinite universe, and the infinity of time.

Lot of progress was made in geometry as a result of interest in astronomy, and by 1300 BC the Indian astronomer Lagadha used geometry to write a book of rules for the apparent movement of the sun and moon.

Around 300 BC, Indian mathematicians began working on the mathematical idea of combinations. This is the study of how many combinations you can make out of the same group of things. They were working on how you could figure that out, and published their ideas in a book called the Bhagabati Sutra. Around the same time, Indian mathematicians worked out the first beginnings of our modern number system. By 100 AD, people in India were writing the numbers.

Indian mathematician’s biggest invention was the use of zero as a placeholder, to make it easier to add and multiply numbers. Our word "zero" comes from the Sanskrit word meaning "nothing." In 458 AD, Indian mathematicians wrote a book, the Lokavibhaaga, that uses zero in this way. In 628 AD, Brahmagupta wrote a book explaining how zero worked, with rules like "The sum of zero and zero is zero" and "The sum of a positive and a negative is their difference; or, if they are equal, zero.”

Algebraic theories, as also other mathematical concepts, which were in circulation in ancient India, were collected and further developed by Aryabhatta, an Indian mathematician, who lived in the 5th century. He has referred to Algebra as Bijaganitam in his treatise on mathematics named Aryabhattiya, composed in A.D. 499. He was first to treat Mathematics as a distinct subject and he dealt with evolution and involution, area and volume, progressions and algebraic identities, and intermediate equations of the first degree. He also arrived at a remarkably accurate value of PI ( 3.1416). Aryabhatta was also the first to hold that the earth was a sphere and rotated on its axis. He says, to a person traveling in a boat trees on the shore appear to move in opposite direction, similarly because earth is rotating on its axis towards east it appears to us as if the sun moves from east to west. He also explained that the eclipses were caused by the shadow of the earth falling on the moon. One of the most important features of Aryabhatta's mathematical system is his unique system of notation. It is based on the decimal place value system, now in use throughout the civilized world.

Another mathematician of the 12th century, Bhaskaracharya also authored several treatises on the subject ­ one of them, named Siddantha Shiromani has a chapter on algebra. He is known to have given a basic idea of the Rolle's theorum and was the first to conceive of differential calculus Bhaskaracharya's Leelavati translated to English in 1816 by James Taylor.

The 14th century Indian mathematician Madhava of Sangamagrama along with other mathematician’s of the Kerala School studied infinite series, convergence, differentiation, and iterative methods for solution of non-linear equations. Jyestadeva of the Kerala School wrote the first calculus text, the Yuktibhasa, which explores methods and ideas of calculus repeated only in seventeenth century Europe.

The credit for fine-tuning and internationalizing these mathematical concepts originated in India ­ goes to the Arabs and Persians. Al-Khawarizmi, a Persian mathematician, developed a technique of calculation that became known as "algorism." This was the seed from which modern arithmetic algorithms have developed. Al-Khwarizmi¹s work was translated into Latin under the title Algoritmi de numero Indorum, meaning The System of Indian Numerals. A mathematician in Arabic is called Hindsa which means from India. With the formation of the Islamic in 16 the century, the use of Indian Mathematics spread quickly from India to West Asia and Africa (by the 800's), and then more slowly to Christian Europe.

Will Durant, American historian, said that India was the mother of our philosophy of much of our mathematics. A. L. Basham, an Australian, writes in his book, "The Wonder That was India" says the world owes most to India in the realm of mathematics, which was developed in the Gupta period to a stage more advanced than that reached by any other nation of antiquity. Albert Einstein says, “We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made.”