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Indian Mathematicians:     more detail

Ancient Indian Scientists: Ancient Indian Mathematicians, Ancient Indian Physicians, Nagarjuna, Brahmagupta, Aryabhata, Sushruta Samhita Ancient Indian Mathematicians: Brahmagupta Indian Mathematicians: Srinivasa Ramanujan, Satyendra Nath Bose, Patañjali, Subrahmanyan Chandrasekhar, Sarvadaman Chowla, Paini A critical study of Brahmagupta and his works: A most distinguished Indian astronomer and mathematician of the sixth century A.D by Satya Prakash, 1968 SOME EMINENT INDIAN MATHEMATICIANS OF THE TWENTIETH CENTURY VOLUME V by J.N. KAPUR(EDITOR), 1993 The Indian Clerk: A Novel by David Leavitt, 2007-09-04 Mathematics in Medieval India: An entry from Gale's <i>Science and Its Times</i> by Sherri Chasin Calvo, 2001

lists with details

21. A Short Note
    Brahmagupta was one of the very few early indian mathematicians, who conceptualisedthe earth as round, and not as flat and hollow. Bhaskara.  
    http://cs.annauniv.edu/~insight/insight/insight/maths/history/
    
    Extractions: Indian Mathematics - A Short Note In ancient India, mathematics or 'Ganita' was the 'Science of Calculations'. It was primarily studied in the context of numerical computation and geometric measurement. Most of the Indian mathematical work can be found as a part of 'Jyotisha' or Astronomy. This is because Astronomy, which dealt with the measurement of time using the heavenly bodies, involved high levels of sophisticated numerical computation. Mathematics in ancient India was so well developed that the body of knowledge was not restricted only to the elite scholars. It was prevalently used even by the common people in their daily activities and profession. The history of Indian mathematics dates back to the vedic period (around 1500 B.C.) The 'Sulbasutras' of this vedic age are texts on rules for altar construction. They are the oldest texts on Indian mathematics. They contain the general enunciation of the Pythagoras theorem, approximate value for square root of 2, methods of transforming one figure to another etc... Indians also used the decimal place-value system of representing the numbers. They had a representation for zero. The origin of the decimal place-value system in India was sometime around 1st century B.C. There are numerous great mathematicians who have contributed to Indian Mathematics. The subject is a synergistic effort of all of them. Since even a mention of all of them would run into pages, we are able to list the contributions of only a few of the mathematicians. The set that we have described below is only a drop in the ocean of great mathematicians who lived in India.

22. 10: Conclusions
    I wish to conclude initially by simply saying that the work of indian mathematicianshas been severely neglected by western historians, although the situation  
    http://www-groups.dcs.st-and.ac.uk/~history/Projects/Pearce/Chapters/Ch10.html
    
    Extractions: (References) I wish to conclude initially by simply saying that the work of Indian mathematicians has been severely neglected by western historians, although the situation is improving somewhat. What I primarily wished to tackle was to answer two questions, firstly, why have Indian works been neglected, that is, what appears to have been the motivations and aims of scholars who have contributed to the Eurocentric view of mathematical history. This leads to the secondary question, why should this neglect be considered a great injustice. I have attempted to answer this by providing a detailed investigation (and analysis) of many of the key contributions of the Indian subcontinent, and where possible, demonstrate how they pre-date European works (whether ancient Greek or later renaissance). I have further developed this 'answer' by providing significant evidence that a number of Indian works conversely influenced later European works, by way of Arabic transmissions. I have also included a discussion of the Indian decimal place value system which is undoubtedly the single greatest Indian contribution to the development of mathematics, and its wider applications in science, economics (and so on). Discussing my first 'question' is less easy, as within the history of mathematics we find a variety of 'stances'. If the most extreme Eurocentric model is 'followed' then all mathematics is considered European, and even less extreme stances do not give full credit to non-European contributions.

23. 8 IV. Mathematics Over The Next 400 Years (700AD-1100AD)
    Ellipse Only Indian mathematician to refer to the ellipse, indeed indian mathematiciansdid not study conic sections or anything along these lines.  
    http://www-groups.dcs.st-and.ac.uk/~history/Projects/Pearce/Chapters/Ch8_4.html
    
    Extractions: (8 V. Bhaskaracharya II) Mahavira (or Mahaviracharya), a Jain by religion, is the most celebrated Indian mathematician of the 9 th century. His major work Ganitasar Sangraha was written around 850 AD and is considered 'brilliant'. It was widely known in the South of India and written in Sanskrit due to his Jaina 'faith'. In the 11 th century its influence was still being felt when it was translated into Telegu (a regional language of the south). Mahavira was aware of the works of Jaina mathematicians and also the works of Aryabhata (and commentators) and Brahmagupta , and refined and improved much of their work. What makes Mahavira unique is that he was not an astronomer, his work was confined solely to mathematics and he stands almost entirely alone in the history of Indian mathematics (at least up to the 14 th century) in this respect. He was a member of the mathematical school at Mysore in the south of India and his major contributions to mathematics include: Arithmetic:

24. Recognition For A Mathematician
    EXCELLENCE. Recognition for a mathematician. MS Raghunathan joins the select bandof indian mathematicians elected Fellows of the Royal Society, London. SG DANI.  
    http://www.frontlineonnet.com/fl1726/17261130.htm
    
    Extractions: ON JULY 14, 2000, one more Indian mathematician affixed his signature to the Register of the Royal Society, London, a parchment book which also bears the signatures of Sir Isaac Newton and many other eminent names in science: Professor M.S. Raghunathan, of the Tata Institute of Fundamental Research (TIFR), Mumbai. Elected a Fellow of the Royal Society this year, he joins the rank of distinguished Indian mathematicians, the legendary Srinivasa Ramanujan, Harish-Chandra, C.S. Seshadri, M.S. Narasimhan and S.R.S. Varadhan, who have received this coveted recognition. Professor M.S. Raghunathan signing in as a Fellow of the Royal Society in London. A rather unique book, A Panorama of Pure Mathematics , was published by French mathematician Jean Dieudonne in 1977 (the English translation of the original French version appeared in 1982), recounting important results from various areas of pure m athematics, based on the choice of the well-known Bourbaki group in France, in just about 300 pages. Raghunathan was one of the few Indian mathematicians named in the book for having made substantial contributions, though he was still in his mid-thirties when the book was published. Personally, however, what Raghunathan finds most gratifying is a reference in an interview given by eminent physicist and Nobel laureate, Professor S. Chandrasekhar, which he noticed most unexpectedly, in

25. I Love Maths -A Complete, Indian Site On Maths
    Maths Club has lots of fun, humor (humour), jokes, puzzles, a Maths quotient test(do try it!), a section on ancient indian mathematicians (like Aryabhata  
    http://www.geocities.com/madanlalaggarwal/ilovemaths.htm
    
    Extractions: www.ilovemaths.com - A complete, Indian site on school math. Covers cbse, icse, isc. Fun, humor, jokes and puzzles, vedic maths, ancient India famous mathematicians. Mathclubs. Lesson plans, questions, problems, exercises, worksheets in mathematics. Maths Club has lots of fun, humor (humour), jokes, puzzles, a Maths quotient test (do try it!), a section on ancient Indian Mathematicians (like Aryabhata, Bhaskara, Ramanujan etc.), some real gems from Leelavati, history of mathematics and so on. "We Recommend" section has many useful links to sites related to Math. There is a collection of interesting articles like different kinds of numbers (prime numbers, square numbers, palindromes etc), story of zero, story of pi( Faculty Room is where teachers from all corners of the country can exchange views, articles, research papers etc. Contributions will be put on our site (free of cost) and will be acknowledged clearly on site. Keep yourself up to date with latest happenings in the field! Professor Theta is a multi featured question answering service. Anybody can post a question (mainly from 6th to 12th standard level) and anybody can reply. If nobody replies, professor Theta will attempt it. Homework help (helper) is at hand! This section is open only to registered users. Registration is FREE at the moment. (Hurry!)

26. Hindu1
    More importantly, indian mathematicians knew algebra at least as early as the 5thcentury AD Known as Bijaganitam, algebra (a corruption of the Arabic word Al  
    http://www.geocities.com/avarangal/hindu1.html
    
    Extractions: the future.' J D Bernal, Science in History As we hurtle into a new millennium, we would do well to reflect where all those s came from. The greatness that was Greece and the grandeur that was Rome started their numeral systems at one. The Arabs brought the modern numerals, including zero, to Europe centuries ago. But while , are commonly and mistakenly referred to as the "Arabic" numerals, they actually originated in India, and are but one of many achievements that became treasures lost to the oblivion of history. India is the epitome of diversity in all respects, geographically and culturally. From such diversity has bloomed the myriad blossoms of science and mathematics. Indian science flowered long before the

27. Indo-French Cooperation In Mathematics
    two french mathematicians to visit Pondicherry University and give lectures there,and two or three indian mathematicians to visit France for one month each.  
    http://www.math.tifr.res.in/mirrors/iml.univ-mrs.fr/infrcoop/agreement.html
    
    Extractions: agreement A tripartite cooperation agreement has been signed between the Universities of Pondicherry Poitiers and Paris VI in november 1993. Each year a support from the french Minstry of Foreign Affairs is provided, which enables two french mathematicians to visit Pondicherry University and give lectures there, and two or three indian mathematicians to visit France for one month each. A report on this programm has been written by Professor P. Jothilingam Under this programm Mrs Gayatri came to France to prepare a thesis under the supervision of In the following visits took place: In the other direction

28. Indo-French Cooperation In Mathematics
    NBHM will make available funds to support the travel expenses of upto 4indian mathematicians to enable them to visit institutions in India.  
    http://www.math.tifr.res.in/mirrors/iml.univ-mrs.fr/infrcoop/agreement2.html
    
    Extractions: Here is the letter from NBHM Indo French Cooperation in Mathematics has been very fruitful and vigorous over the past 5 decades. NBHM would like to develop this cooperative effort at promoting Mathematical Research further in the framework of a programme of exchange of visits of mathematicians. This letter of intent sets out the programme that NBHM will implement on its side. The collaboration programme will be in the general area of Mathematics with emphasis on Algebra and Geometry. The aims of the programme is to organise mutual visits of mathematicians from India and France to each others' countries for carrying out collaborative studies and research. The programme will be managed on the Indian side by two nominees of NBHM : Professor R.Balasubramanian and Professor M.S. Raghunathan NBHM will make available funds to support the travel expenses of upto 4 Indian mathematicians to enable them to visit institutions in India. It will also provide funding to cover local expenses upto 4 visitors from France to India for a total period not exceeding 8 months. The French visitors are expected to have their travel expenses as also their health insurance cover met by French sources. The programme will operate until March 31, 2001. It may be renewed by mutual agreement for definite periods after that

29. Math: Evolution Of Roman Numerals From India
    Medieval indian mathematicians, such as Brahmagupta (seventh century), Mahavira (ninthcentury), and Bhaskara (twelfth century), made several discoveries which  
    http://www.gosai.com/chaitanya/saranagati/html/vishnu_mjs/math/math_4.html
    
    Extractions: Evolution of Arabic (Roman) Numerals from India A close investigation of the Vedic system of mathematics shows that it was much more advanced than the mathematical systems of the civilizations of the Nile or the Euphrates. The Vedic mathematicians had developed the decimal system of tens, hundreds, thousands, etc. where the remainder from one column of numbers is carried over to the next. The advantage of this system of nine number signs and a zero is that it allows for calculations to be easily made. Further, it has been said that the introduction of zero, or sunya as the Indians called it, in an operational sense as a definite part of a number system, marks one of the most important developments in the entire history of mathematics. The earliest preserved examples of the number system which is still in use today are found on several stone columns erected in India by King Ashoka in about 250 B.C.E. Similar inscriptions are found in caves near Poona (100 B.C.E.) and Nasik (200 C.E.). These earliest Indian numerals appear in a script called brahmi After 700 C.E. another notation, called by the name "Indian numerals," which is said to have evolved from the brahmi numerals, assumed common usage, spreading to Arabia and from there around the world. When Arabic numerals (the name they had then become known by) came into common use throughout the Arabian empire, which extended from India to Spain, Europeans called them "Arabic notations," because they received them from the Arabians. However, the Arabians themselves called them "Indian figures" (Al-Arqan-Al-Hindu) and mathematics itself was called "the Indian art" (hindisat).

30. Math: Equations And Symbols
    Outside of the religioastronomical sphere, only the problems of day to day life(such as purchasing and bartering) interested the indian mathematicians. next.  
    http://www.gosai.com/chaitanya/saranagati/html/vishnu_mjs/math/math_5.html
    
    Extractions: Equations and Symbols B.B. Dutta writes: "The use of symbols-letters of the alphabet to denote unknowns, and equations are the foundations of the science of algebra. The Hindus were the first to make systematic use of the letters of the alphabet to denote unknowns. They were also the first to classify and make a detailed study of equations. Thus they may be said to have given birth to the modern science of algebra." The great Indian mathematician Bhaskaracharya (1150 C.E.) produced extensive treatises on both plane and spherical trigonometry and algebra, and his works contain remarkable solutions of problems which were not discovered in Europe until the seventeenth and eighteenth centuries. He preceded Newton by over 500 years in the discovery of the principles of differential calculus. A.L. Basham writes further, "The mathematical implications of zero (sunya) and infinity, never more than vaguely realized by classical authorities, were fully understood in medieval India. Earlier mathematicians had taught that X/0 = X, but Bhaskara proved the contrary. He also established mathematically what had been recognized in Indian theology at least a millennium earlier: that infinity, however divided, remains infinite, represented by the equation oo /X = oo." In the 14th century, Madhava , isolated in South India, developed a power series for the arc tangent function, apparently without the use of calculus, allowing the calculation of pi to any number of decimal places (since arctan 1 = pi/4). Whether he accomplished this by inventing a system as good as calculus or without the aid of calculus; either way it is astonishing.

31. | International School Of Photonics | ISP Knowledge Portal | Great Indian Scient
    replication in laboratory, is a step towards the creation of life artificially.indian mathematicians. Top of the pageTop of the page 2.  
    http://www.photonics.cusat.edu/Indian_scientists2.html

32. The Arab-Indian Contribution.
    the inheritance of the Egyptian and Babylonian cultures merged with the texts ofclassic Greek geometry and the innovations of indian mathematicians, the Arabs  
    http://www.math.unifi.it/archimede/archimede_inglese/trigonometria/trigonometria
    
    Extractions: of trigonometry The Roman conquest didn't contribute in any way to the development of the mathematical sciences but neither did it hinder its continuation, especially around the school of Alexandria that continued on well beyond the Roman conquest of Egypt in the first century B.C. After the fall of the Western Roman Empire, and cultural retreat of the Eastern one, the natural successors of the Greek geometers - at least from the IX century - were the Arabs. Placed at the crossroads of a mathematical tradition in which the inheritance of the Egyptian and Babylonian cultures merged with the texts of classic Greek geometry and the innovations of Indian mathematicians, the Arabs quickly assimilated most of these different traditions. This they incorporated into an original method, that a few centuries later, they bequeathed to the scholars of an emerging Europe. Some fundamental discoveries, both technological and on paper, reached the West through Arab influence, and were to be crucial in the diffusion of culture and the development of science. These are both scientific, like the use of the numeric characters commonly called Arab (which would more accurately be called Indian), and the positional notation. The first innovation related to Alexandrine trigonometry came from India: the use of the sine instead of the chord. The first work containing the table of the sines, which dates from the IV or V century of our era, is known by the name of

33. ThinkQuest Library Of Entries
    They also used decimal system. indian mathematicians thought aboutthe negative numbers for the first time and they made it a rule.  
    http://library.thinkquest.org/22584/emh1300.htm
    
    Extractions: The web site you have requested, Mathematics History , is one of over 4000 student created entries in our Library. Before using our Library, please be sure that you have read and agreed to our To learn more about ThinkQuest. You can browse other ThinkQuest Library Entries To proceed to Mathematics History click here Back to the Previous Page The Site you have Requested ... click here to view this site Click image for the Site Languages : Site Desciption An extensive history of mathematics is at your fingertips, from Babylonian cuneiforms to advances in Egyptian geometry, from Mayan numbers to contemporary theories of axiomatical mathematics. You will find it all here. Biographical information about a number of important mathematicians is included at this excellent site.

34. Science & Technology In India
    AD. indian mathematicians and astronomers have contributed immenselyto the fundamental concept of celestial science. The discovery  
    http://www.meadev.nic.in/science/intro.htm
    
    Extractions: S tarting with the Indus Valley civilization around 2500 BC, India has been the site for significant historical and philosophical developments intermeshed with several facets of scientific and technological activities. Recent excavations at Kalibangan (Rajasthan) and Lothal (Gujarat) have underlined the singular achievements of this period in history, especially in the spheres of town planning and building of houses using standard burnt bricks, interlinked drainage system, wheel - turned ceramics, solid wheel carts and the use of copper and bronze in various products. ISRO, French agency sign accord November 21, 1999 Statement by Dr R Chidambaram, Chairman, Atomic Energy Commission and Leader of the Indian delegation at the 43rd General Conference of the International Atomic Energy Agency - 27 September - 01 October 99 PM's letter to President Clinton - July 19, 1999 I have a long way to go, says Indian Hero of Planet Indian touch to US space laboratory ISRO hits escape velocity Indigenous technologies released to mark Pokhran II anniversary May 11, 1999 Agni-II test-fired successfully April 11, 1999

35. Links Ancient India's Mathematics - Elaborates And Explains
    indian mathematicians Comprehensive list of indian mathematiciansfrom ancient times. Exhaustive details of their life and work.  
    http://www.vigyan.org.in/mathlinks.html

36. Numbersystem, Some Clarification: Interact Inn All India Mailing List
    English. Yes, it is a fact that indian mathematicians developed thenumber system in the pre Greek/Roman era. The conceptualisation  
    http://manaskriti.com/InteractInn/10119801.html

37. Math(s) Reviews -- Teachers @ Work - Mark Teadwell
    Ancient indian mathematicianscontributed much to our modern understanding of mathematics today. ID 23554 Title Ancient Indian Mathematics  
    http://www.teachers.work.co.nz/reviews/math.asp

38. Mathematics
    It is without doubt that mathematics today owes a huge debt to the outstandingcontributions made by indian mathematicians over many hundreds of years.  
    http://hem.passagen.se/samband/maths.html
    
    Extractions: Professors J J O'Connor and E F Robertson in their article An overview of Indian mathematics begin with the following passage: It is without doubt that mathematics today owes a huge debt to the outstanding contributions made by Indian mathematicians over many hundreds of years. What is quite surprising is that there has been a reluctance to recognise this and one has to conclude that many famous historians of mathematics found what they expected to find, or perhaps even what they hoped to find, rather than to realise what was so clear in front of them. Needless to say that the contribution of the Indian Mathematicians is not recognised to the extend it should have been for one reason or other. But never mind. We present here some articles by the gentlemen above which give somewhat fairer account of the situation. Negative numbers which are so obvious to us now (who does not have a debt of this or that amount), were nonexistent in ancient mathematics. The concept of zero which is so obvious and useful now took several hundred years to evolve in the minds of mathematicians. Read more about it.

39. Indian Association
    objectives in mind. For instance in mathematics you would find linksabout vedic mathematics and about famous indian mathematicians.  
    http://hem.passagen.se/samband/main.html
    
    Extractions: Welcome to the Indian Association of Stockholm This site will serve the cause of Indian community in Stockholm and worldwide by Links below are chosen by keeping above objectives in mind. For instance in mathematics you would find links about vedic mathematics and about famous indian mathematicians. Teach your self Other indian sites This site is under construction, so some of the links above may not be active or complete, please have some patience and visit us again.

40. Fibonacci's Roots
    Meanwhile, indian mathematicians had long before started their longtradition of fine mathematical thought. In the early parts of  
    http://www.fuzzygalore.biz/articles/fibonacci.shtml
    
    Extractions: FUZZY GALORE knit spin weave ... home Leonardo Pisano Bonacci, better known as Fibonacci (standardized in the 19th century from Fillius Bonacci), played a major role in the advancement of mathematics in the daily lives of Europeans, particularly with the publication of his Liber Abaci 800 years ago in 1202. He explained the practicality of using a 10-base notation rather than Roman numerals, which effectively ended their use. He also contributed his own mathematical gems, particularly in Enclidian geometry and number theory. His engaging use of examples such as the reproduction of rabbits made everyone notice the use of his sequence in many natural phenomena, something which we are still discovering, and we're still using it in many designs. The only biographical details we know about him are that he was born in Pisa and that his father was a customs official in North Africa. It's this later fact that led young Leonardo to be educated in Arabic mathematics and accounting methods, and to be able to popularize these concepts among Northern Europeans. The Roman numerals in use in medieval Europe were a clumsy affair at best, barely allowing one to add and substract. A torturous method had been devised for multiplication and division, and the tool of choice was an abacus for practical use, after which results were translated and recorded in Roman numerals. The ealiest known example of this device is dated from about 3000 BC and originated in Babylonia, where no doubt it contributed to its inventors' domination of their neighbors by giving them better architectural, astronomical (and therefore navigational) and financial tools.

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