what are the contributions of aryabhatta in the field of mathematics?
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Aryabhata was both a mathematician and an astronomer.  Since your question primarily deals with mathematics, I will attempt to answer that question.\n\nAryabhata was one of the first mathematicians to theorize that the number pi was an irrational number.  Specifically, he estimated pi to be approaching the value of 62832/20000, or 3.1416.  With his writings translated, it has been assumed that his use of the word "approaching" may indicate that it is not only an approximation of the value of pi, but that pi is a non-repeating number that cannot be solved, therefore an irrational number.\n\nThe significance of this is that Aryabhata lived from approximately 476-550 AD.  The irrationality of pi was not proved until 1761 in Europe, making his insight quite substantial to the mathematical community.
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Pythagoras wasn't just a mathematician -- he was a cult leader, as well.  For more information, you could try a site like Wikipedia:
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An excellent introduction (and a broader perspective than Russell) to mathematical philosophy is "Philosophy of Mathematics : Selected Readings", eds. Paul Benacerraf and Hilary Putnam.  This will give you a good overview of the field as of the mid 80s.  After that you might find that your interest in mathematical philosophy tends more to one area than another, such as philosophy of logic (what does an "if..then..." statement really mean? [dare I say 'imply'???]), or foundations of mathematics (do we discover mathematics, or invent it?), or the nature of proof (what do we mean when we say that a theorem is proved? ). I would also recommend reading about the history of mathematics. I have no specific book recommendations here, but a quick Amazon search pops up "A History of Mathematics" by Isaac Asimov. Enjoy!
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None, Zero was invented by Indian Mathematician Aryabhata and later Brahmagupta developed its concept
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Your friend is right. Algebra originates from the ancient Babylonians of Mesopotamia (modern day Iraq), with later developments being contributed by Indian, Japanese, and Chinese mathematicians.\n\nHere's an excerpt from the Wikipedia article (see the link below for the full article):\n\nThe word algebra comes from the Arabic word "al-jabr" from the title of the book al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, meaning The book of Summary Concerning Calculating by Transposition and Reduction, a book written by Persian Muslim mathematician Muḥammad ibn Mūsā al-Ḵwārizmī in 820. The word al-jabr means "reunion". Al-Khwarizmi is often considered the "father of algebra" (though that title is also given to Diophantus), as much of his works on reduction are still in use today. Another Persian mathematician Omar Khayyam developed algebraic geometry and found the general geometric solution of the cubic equation. Indian mathematician Bhaskara and Chinese mathematician Zhu Shijie solved cubic, quartic (biquadratic) and higher-order polynomial equations.
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This theorem has an amazing number of proofs but this theorem(like many other mathematical concepts) as you said was known way before pythogorean times but only to INDIANS who didnt share it on the global scale!!
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Go to Google scearch you will find lot of papers on this.\nCopy with changes from all the papers.\nIncluding whatever Mathamatical figures you find
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Sir Isaac Newton, PRS, (4 January 1643 – 31 March 1727) [OS: 25 December 1642 – 20 March 1727] was an English physicist, mathematician, astronomer, alchemist,chemist, inventor, and natural philosopher who is generally regarded as one of the most influential scientists and mathematicians in history.\n\nNewton wrote the Philosophiae Naturalis Principia Mathematica wherein he described universal gravitation and the three laws of motion, laying the groundwork for classical mechanics. By deriving Kepler's laws of planetary motion from this system, he was the first to show that the motion of objects on Earth and of celestial bodies are governed by the same set of natural laws. The unifying and deterministic power of his laws was integral to the scientific revolution and the advancement of heliocentrism.\n\nAmong other scientific discoveries, Newton realized that the spectrum of colours observed when white light passes through a prism is inherent in the white light and not added by the prism (as Roger Bacon had claimed in the 13th century), and notably argued that light is composed of particles. He also developed a law of cooling, describing the rate of cooling of objects when exposed to air. He enunciated the principles of conservation of momentum and angular momentum. Finally, he studied the speed of sound in air, and voiced a theory of the origin of stars. Despite this renown in mainstream science, Newton spent more time working on either alchemy or chemistry, than physics.\n\nNewton played a major role in the history of calculus, sharing credit with Gottfried Leibniz. He also made contributions to other areas of mathematics, for example the generalized binomial theorem. The mathematician and mathematical physicist Joseph Louis Lagrange (1736–1813), said that "Newton was the greatest genius that ever existed and the most fortunate, for we cannot find more than once a system of the world to establish." 20\n \n\n\nBiography\nEarly years\nThe life of Isaac Newton Early life Writing Principia Later life Religious views Occult studies  \nNewton was born in Woolsthorpe-by-Colsterworth (at Woolsthorpe Manor), a hamlet in the county of Lincolnshire. Newton was born prematurely, and no one expected him to live; indeed, his mother, Hannah Ayscough Newton, is reported to have said that his body at that time could have fit inside a quart mug (Bell, 1937). His father, Isaac, had died three months before Newton's birth. When Newton was two, his mother went to live with her new husband, leaving her son in the care of his grandmother.\n\nAccording to E.T. Bell (1937, Simon and Schuster) and H. Eves:\n\nNewton began his schooling in the village schools and was later sent to The Kings Grammar School (Grantham) where he became the top boy in the school. At Kings he lodged with the local apothecary, William Clarke and eventually became engaged to the apothecary's stepdaughter, Anne Storer, before he went off to Cambridge University at the age of 19. As Newton became engrossed in his studies, the romance cooled and Miss Storer married someone else. It is said he kept a warm memory of this love, but Newton had no other recorded 'sweethearts' and never married. \nHowever, William Stukeley and Mrs Vincent, the source which Bell and Eves have embroidered so unhelpfully, merely say that Newton entertained 'a passion' for her while he lodged at the Clarke house. Mrs Vincent's maiden name was Katherine Storer, not Anne.\n\n \nEngraving after Enoch Seeman's 1726 portrait of NewtonFrom the age of about twelve until he was seventeen, Newton was educated at The King's School in Grantham (where his signature can still be seen upon a library window sill). He was removed from school and by Oct 1659 he was to be found at Woolsthorpe where his mother attempted to make a farmer of him. He was, by later reports of his contemporaries, thoroughly unhappy with the work. It appears to be Henry Stokes, master at the Ki
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this may be somewhat subjective, eh?\n\n1) Euclid's work\n2) Isaac Newton's calculus\n3) ___________________ (open for discussion) The Pythagoreans? Archimedes? The development of Algebra from al-jah-bra...dang - i'm anxious to see the other answers
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No no solution since n>2\n\nPierre de Fermat died in 1665. Today we think of Fermat as a number theorist, in fact as perhaps the most famous number theorist who ever lived. It is therefore surprising to find that Fermat was in fact a lawyer and only an amateur mathematician. Also surprising is the fact that he published only one mathematical paper in his life, and that was an anonymous article written as an appendix to a colleague's book.\n\nThere is a statue of Fermat and his muse in his home town of Toulouse:\n(Click it to see a larger version)\n\n\nBecause Fermat refused to publish his work, his friends feared that it would soon be forgotten unless something was done about it. His son, Samuel undertook the task of collecting Fermat's letters and other mathematical papers, comments written in books, etc. with the object of publishing his father's mathematical ideas. In this way the famous 'Last theorem' came to be published. It was found by Samuel written as a marginal note in his father's copy of Diophantus's Arithmetica. \n\nFermat's Last Theorem states that \n\nxn + yn = zn \n\nhas no non-zero integer solutions for x, y and z when n > 2. Fermat wrote \n\nI have discovered a truly remarkable proof which this margin is too small to contain.
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my advice is to look for a history book, but also you can check wikipedia:\n\nGreek mathematics studied before the Hellenistic period refers only to the mathematics of Greece. Greek mathematics studied from the time of the Hellenistic period (from 323 BC) refers to all mathematics of those who wrote in the Greek language, since Greek mathematics was now not only written by Greeks but also non-Greek scholars throughout the Hellenistic world, which was spread across the Eastern end of the Mediterranean. Greek mathematics from this point merged with Egyptian and Babylonian mathematics to give rise to Hellenistic mathematics. Most mathematical texts written in Greek were found in Greece, Egypt, Mesopotamia, Asia Minor, Sicily and Southern Italy.\n\nAlthough the earliest found Greek texts on mathematics were written after the Hellenistic period, many of these are considered to be copies of works written during and before the Hellenistic period. Nevertheless, the dates of Greek mathematics are more certain than the dates of earlier mathematical writing, since a large number of chronologies exist that, overlapping, record events year by year up to the present day. Even so, many dates are uncertain; but the doubt is a matter of decades rather than centuries.\n\nGreek mathematics is thought to have begun with Thales (c. 624—c.546 BC) and Pythagoras (c. 582—c. 507 BC). Although the extent of the influence is disputed, they were probably influenced by the ideas of Egypt, Mesopotamia and less likely[citation needed], India. Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. According to Proclus' commentary on Euclid, Pythagoras stated the Pythagorean theorem and constructed Pythagorean triples algebraically. It is generally conceded that Greek mathematics differed from that of its neighbors in its insistence on axiomatic proofs.[8]\n\nGreek and Hellenistic mathematicians were the first to give a proof for irrational numbers (due to the Pythagoreans), and the first to develop Eudoxus's method of exhaustion, and the Sieve of Eratosthenes for uncovering prime numbers. They took the ad hoc methods of constructing a circle or an ellipse and developed a comprehensive theory of conics; they took many various formulas for areas and volumes and deduced methods to separate the correct from the incorrect and generate general formulas. The first recorded abstract proofs are in Greek, and all extant studies of logic proceed from the methods set down by Aristotle. Euclid, in the Elements, wrote a book that would be used as a mathematics textbook throughout Europe, the Near East and North Africa for almost two thousand years. In addition to the familiar theorems of geometry, such as the Pythagorean theorem, The Elements includes a proof that the square root of two is irrational and that there are infinitely many prime numbers.\n\nSome say the greatest of Greek mathematicians, if not of all time, was Archimedes (287—212 BC) of Syracuse. According to Plutarch, at the age of 75, while drawing mathematical formulas in the dust, he was run through with a spear by a Roman soldier. Roman society has left little evidence of an interest in pure mathematics.\n\n\nEuropean Renaissance mathematics (c. 1200—1600)\n\nIn Europe at the dawn of the Renaissance, most of what is now called school mathematics -- addition, subtraction, multiplication, division, and geometry -- was known to educated people, though the notation was cumbersome: Roman numerals and words were used, but no symbols: no plus sign, no equal sign, and no use of x as an unknown. Most of the mathematics now taught at universities was either known only to the mathematical community in India or had yet to be investigated and developed in Europe.\n\nThrough Latin translations of Arabic texts, knowledge of the Hindu-Arabic numerals and other important developments of Islamic and Indian mathematics were brought to Europ
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Aryabhatta, the Indian mathematician who invented 0.
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Here you go:\nhttp://en.wikipedia.org/wiki/Ajanta
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Bertrand Russell addressed the rigorous formal definition of one, zero, addition and other fundamental concepts in "The Principles of Mathematics" (1903).\n\nSee: http://en.wikipedia.org/wiki/Bertrand_Russell#Logic_and_philosophy_of_mathematics
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Mathematics makes significant contributions to IT, supporting the development of both hardware and software systems. Some examples of maths that have specific application to IT (in a digital as opposed to analogue computer) are:\n\nBoolean logic:\n\nThis is a system of mathematics based around the binary states True and False (represented typically as non zero and zero). A number of basic logical operations are defined from which infinitely more complex logical rules can be built. These operations are defined in terms of inputs and outputs, and the effects can be shown by truth tables. The basic logical operations are:\n    NOT (negation)\n         Input    Output\n             T          F\n             F          T\n     OR (either or both inputs may be True)\n         Input1  Input2   Output\n             T           F          T\n             F           T          T\n             T           T          T\n             F           F          F\n     AND (both inputs must be true)\n         Input1  Input2   Output\n             T          T           T\n             T          F           F\n             F          T           F\n             F          F           F\n     XOR (one and only one input is true)\n          Input1  Input2   Output\n             T          T           F\n             T          F           T\n             F          T           T\n             F          F           F\n\nThe application of this to IT may not be immediately apparent, but this system of logic underpins both the design of the microprocessor in modern personal computers and the means to implement decision making in programming. Rules such as the following can be constructed:\n\nIf (AuthorAlive = True) AND (AuthorNotPaidEnough = True) Then GiveAuthorPayRise\n\nBinary representation:\n\nBinary is a system of mathematics based around the presence of only 2 numbers, 0 and 1. Where we have a tens column in decimal, this becomes a twos column in binary, the hundreds column becomes a fours column, the thousands column and eights column, and so on. Both processing and data storage devices in a digital computer work on a binary system at the lowest level and this has important ramifications for the capabilities of the computer.\n\nWe frequently refer to a single binary digit as a bit. Ultimately all bandwidth and data storage capacities are measured in bits, because this is the fundamental unit a computer works on. The internal limitations of a computer are derived from properties of binary mathematics.\n\nThe reason that a digital computer is built on base 2 representation is that it is much easier to construct systems with 2 stable states as opposed to more. This can correspond to the presence or absence of voltage, a north versus south pole magnetic field, a True or False boolean value in a logic gate and so on.\n\nAdditionally:\n\nThere are a lot of mathematical problems or modelling that are represented using computers. The very early origins of the computer were heavily driven by their application as calculating machines (to calculate the trajectory of artillery shells, for instance).\n\nAlso, as with any modern engineering, the field of mathematics heavily underpins IT at the physical level, through physics. We could not design a modern computer without the application of a lot of physics and therefore Maths.\n\nTherefore, this really is a very open wide ranging question.
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Leibniz discovered the product rules of Differentiation.\nNewton helped to shape the quotient rule, and was a major mathematician in the field of Calculus.\nI'm not sure about the chain rule.
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well, we cannot count Fermat, he is not a mathematician,its been said that Fermat is the greatest mathematician who wasn't a mathematician...Fermat was a Judge by profession and did mathematics to take his mind off of his cases.\n\nI would say that one of the greatest Mathematicians who had something to do with probability is Blaise Pascal