61. Astronomy And Mathematics In Ancient India As argued by James Q. Jacobs, Aryabhata, an Indian Mathematician (c. Later indian mathematicians had names for zero, but no symbol for it. http://www.cerc.utexas.edu/~jay/anc.html

Astronomy, Computer Science and Mathematics in Ancient India Astronomy Earliest known precise celestial calculations: As argued by James Q. Jacobs, Aryabhata, an Indian Mathematician (c. 500AD) accurately calculated celestial constants like earth's rotation per solar orbit, days per solar orbit, days per lunar orbit. In fact, to the best of my knowledge, no source from prior to the 18th century had more accurate results on the values of these constants! Click here for details. Aryabhata's 499 AD computation of pi as 3.1416 (real value 3.1415926...) and the length of a solar year as 365.358 days were also extremely accurate by the standards of the next thousand years. Astronomical time spans: The notion of of time spans that are truly gigantic by modern standards are rarely found in ancient civilizations as the notion of large number is rare commodity. Apart from the peoples of the Mayan civilization, the ancient Hindus appear to be the only people who even thought beyond a few thousand years. In the famed book Cosmos , physicist-astronomer-teacher Carl Sagan writes "... The dates on Mayan inscriptions also range deep into the past and occasionally far into the future. One inscription refers to a time more than a million years ago and another perhaps refers to events of 400 million years ago, ... The events memorialized may be mythical, but the time scales are pridigious".

62. Development Of Philosophical Thought And Scientific Method In Ancient India indian mathematicians were also the first to invent the concept of abstractinfinite numbers numbers that can only be represented through abstract http://www.positiveatheism.org/india/science.htm

South Asian History Development of Philosophical Thought and Scientific Method in Ancient India Return to India Index Home to Positive Atheism Mirrored from: South Asian History Contrary to the popular perception that Indian civilization has been largely concerned with the affairs of the spirit and "after-life", India's historical record suggests that some of the greatest Indian minds were much more concerned with developing philosophical paradigms that were grounded in reality. The premise that Indian philosophy is founded solely on mysticism and renunciation emanates from a colonial and orientalist world view that seeks to obfuscate a rich tradition of scientific thought and analysis in India. Much of the evidence for how India's ancient logicians and scientists developed their theories lies buried in polemical texts that are not normally thought of as scientific texts. While some of the treatises on mathematics, logic, grammar, and medicine have survived as such many philosophical texts enunciating a rational and scientific world view can only be constructed from extended references found in philosophical texts and commentaries by Buddhist and Jain monks or Hindu scholars (usually Brahmins). Although these documents are usually considered to lie within the domain of religious studies, it should be pointed out that many of these are in the form of extended polemics that are quite unlike the holy books of Christianity or Islam. These texts attempt to debate the value of the real-world versus the spiritual-world. They attempt to counter the theories of the atheists and other skeptics. But in their attempts to prove the primacy of a mystical soul or "Atman" they often go to great lengths in describing competing rationalist and worldly philosophies rooted in a more realistic and more scientific perception of the world. Their extensive commentaries illustrate the popular methods of debate, of developing a hypothesis, of extending and elaborating theory, of furnishing proofs and counter-proofs.

63. Fantasy And Science Fiction - Science The indian mathematicians who invented zero knew all this. Mahavira, an Indianmathematician living in 830 AD, published that 1/0 = 0, http://www.sfsite.com/fsf/2005/pmpd0503.htm

You can read a digital version of . Copies are available at: Available Format: Palm Reader Available Formats: Adobe Acrobat (PDF), Palm Reader (PDB), Rocket/REB1100 (RB), Microsoft Reader (LIT), Franklin eBookMan (FUB), Hiebook (KML), iSilo (PDB), Mobipocket (PRC) PC Digital Audio: PocketPC models, Apple iPod, Audible Otis, Rio players, Iomega HipZip, Visor with AudibleAdvisor, Digisette Duo-Aria MP3 player, Franklin eBookman PDA, Palm OS5 handhelds Mac (Mac OS X and iTunes3) Digital Audio: Apple iPod, Audible Otis Science Much Ado About Nothing SCIENCE fiction is about revolutionary ideas and amazing inventions. In this column, we’re going to talk about something that is both. It’s a very simple thing — so simple that most people don’t think about it at all. Over the centuries, people have come to take this invention for granted. But at the Exploratorium we are in the business of paying attention to things that other people ignore, and we’ve decided it’s time to call attention to this remarkable invention. This idea was the brainchild of a group of astronomers in the Indus Valley about fifteen hundred years ago (give or take a century). Back in the fifteenth century, the impact of this invention on the mathematics of Europe could be compared to the social changes resulting from computers today. What is it?

64. Historia Matematica Mailing List Archive: Re: [HM] The Zero Story: A Question assuming that the three bestknown indian mathematicians-Aryabhata, than 200BC Certainly, indian mathematicians were habitually using http://sunsite.utk.edu/math_archives/.http/hypermail/historia/apr99/0197.html

Re: [HM] The Zero Story: a question Kim Plofker Kim_Plofker@Brown.edu Mon, 26 Apr 1999 19:49:14 -0400 (EDT) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Luigi Borzacchini: "Re: [HM] Question regarding Dedekind and numbers" Previous message: James T. Smith: "[HM] Toepell's book" Maybe in reply to: Elena Marchisotto: "[HM] The Zero Story: a question" Next in thread: Milo Gardner: "Re: [HM] The Zero Story: a question" This is all so inaccurate and/or totally mistaken that I don't know where to begin. I'll try to take it point-by-point, and I'll try to concentrate only on major errors of fact and shaky assumptions rather than on what can be considered allowable hyperbole for a general audience. And I'll leave discussion of ancient Greek and Near Eastern zero concepts for those more knowledgeable about them. It may spread out over two postings... Kim Plofker Dept. of History of Mathematics Brown University 14 (1995), 4561, for a much more knowledgeable and informative overview of the subject. This author's chief mistake seems to be assuming that the three best-known Indian mathematicians-Aryabhata

65. INDOlink Arts-Culture Discussion Forum Forum - MATHEMATICS IN The main mathematicians of the tenth century in India were Aryabhata II and Quite a few results of indian mathematicians have been rediscovered by http://www.indolink.com/Forum/Arts-Culture/messages/4971.html

66. Patrika For their contacts and influences on indian mathematicians he also covered GHHardy, Andre Weil and the inspiring Jesuit priest and teacher Rev. http://www.ias.ac.in/patrika/patrika37/patrika37.html

No. 37 March 2003 Newsletter of the Indian Academy of Sciences 2002 Annual meeting 8-10 November 2002, Chandigarh The Panjab University invited the Academy to hold its 2002 annual meeting in Chandigarh. This meeting, sixty-eighth in the series, was held from 8 to 10 November 2002. It was attended by over 120 fellows and associates and 30 invited teachers from outside Chandigarh and a large number of students and researchers from within. The inaugural session was held at the university auditorium on the forenoon of 8 th . The University Vice-Chancellor K.N. Pathak welcomed the audience and this was followed by the traditional introduction of Fellows by the President of the Academy K. Kasturirangan. Kasturirangan then delivered his scientific address. K. Kasturirangan In his address Kasturirangan traced the emergence of X-ray astronomy as a new tool to study the universe in a hitherto unexplored part of the electromagnetic spectrum. Recent advances in instrumentation and space technology have made thisfield a full-fledged component of astronomy, especially able to probe strong gravitational and magnetic fields and regions of very high matter density. A large number of X-ray sources, including accreting compact objects, have been studied in detail.He related these developments to the proposed 2006 launch of India's first dedicated astronomical satellite, ASTROSAT, which will offer unique capabilities all the way from optical and UV to hard X-ray energies.

67. Book Reviews: "Lost Discoveries" By Dick Teresi, And "The Letters Of H. P. Blava He called the indian mathematicians fools (p. indian mathematicians notonly used the zero and devised algebra, logarithms, trigonometry, http://www.theosociety.org/pasadena/sunrise/53-03-4/bkr2-04.htm

Book Reviews By Sarah Belle Dougherty Lost Discoveries: The Ancient Roots of Modern Science from the Babylonians to the Maya Science, we are generally told, originated with the Greeks around 600 BC, developed in the European Renaissance, and was perfected in the modern West. Because of educators' interest in cultural diversity, multicultural science curricula began to appear in various school districts in the 1980s, but unfortunately many contained distorted, inaccurate, and speculative information. In the early 1990s Dick Teresi, science writer and cofounder of Omni magazine, accepted an assignment to expose and document faulty multicultural science being taught in American schools. I began to write with the purpose of showing that the pursuit of evidence of nonwhite science is a fruitless endeavor. I felt that it was only responsible, however, to attempt to find what meager legitimate non-European science might exist. Six years later, I was still finding examples of ancient and medieval non-Western science that equaled and often surpassed ancient Greek learning. My embarrassment at having undertaken an assignment with the assumption that non-Europeans contributed little to science has been overtaken by the pleasure of discovering mountains of unappreciated human industry, four thousand years of scientific discoveries by peoples I had been taught to disregard. p. 15

68. A Science History Quiz This source claims that indian mathematicians picked up the Babylonian placevalue indian mathematicians simplified the Babylonian number notation and http://www.lhup.edu/~dsimanek/scihist.htm

A SCIENCE HISTORY QUIZ by Donald E. Simanek This quiz has answers below, but please don't look at them too soon. I've used these questions in history of science seminars at Lock Haven University to give students practice in library research. 1. Who first described Newton's rings? 2. Who first successfully explained Newton's rings? 3. Who first gave a correct physical explanation of why the sky is blue? 4. Who invented the Wheatstone bridge? 5. Who first patented the telegraph? 6. Who invented Morse code? 7. Who first experimentally verified Coulomb's law of electric attraction? 8. Who first performed Faraday's ice pail experiment demonstrating electrostatic shielding? 9. Who invented the decimal point notation in mathematics? 10. Who invented the drip coffee pot? 11. Who first made carbonated water? 12. What chemist was the first to discover and describe color blindness? 13. Who first formulated L'Hospital's rule for evaluating indeterminate algebraic forms? 14. Who first made a `Galilean' (non-inverting) type telescope consisting of a positive objective lens and a negative eyelens at opposite ends of a tube?

69. Shortage Of Math Teachers - A Threat To America? - Stormfront White Nationalist There may be other outstanding indian mathematicians, but the fact that I haveto strain Can you provide examples of outstanding indian mathematicians, http://www.stormfront.org/forum/showthread.php?t=217512&page=3

70. SACNAS Biography Project Biographies of important American indian and Latino scientists, mathematicians, and engineers. http://64.171.10.183/biography/default.asp

Video requires quicktime Order the SACNAS Biography Project on CD "As you read these biographies, you will see that these scientists and engineers are intimately involved, not only in scientific matters, but in helping set policy for this country." more... Biography Project initiated with support from: Sloan Foundation National Institutes of Health Verizon Foundation Home ... Contact Us

71. Indian Of The Month The soil of India has given birth to great mathematicians such as, Aryabhata (475AD 550 AD) the first well known indian mathematician, Brahmagupta (598 AD http://www.indoaust.com/IndianFebruary03.htm

Rooma Nanda who works for IBM Australia will be writing this monthly article. Rooma has an MBA from UTS and has worked for multi nationals like Pacific Access (Yellow Pages) and Optus. Rooma has also made a documentary on Online Education in India. Email Successful Indian of the Month India, as a country, has contributed to the world of mathematics in an unparalleled way. It is a well known fact that the most fundamental contribution of ancient India in mathematics is the invention of decimal system of numeration, including the invention of zero. The Vedas and Valmiki Ramayana are also believed to have used this system. Ancient civilizations like MohanjoDaro and Harappa excavations around 3000 B.C. old also give specimens of writing in India. The soil of India has given birth to great mathematicians such as, Aryabhata (475 A.D. -550 A.D.) the first well known Indian mathematician, Brahmagupta (598 A.D. -665 A.D.) renowned for introduction of negative numbers and operations on zero into arithmetic and Bhaskara (1114 A.D. -1185 A.D.) Bhaskaracharaya - the most well known ancient Indian mathematician.

72. MSN Encarta - Mathematics mathematicians in India also were the first to recognize zero as both an integer The bestknown indian mathematician of the early period was Bhaskara, http://encarta.msn.com/encyclopedia_761578291_7/Mathematics.html

MSN Home My MSN Hotmail Shopping ... Sign In Web Search: Encarta Subscriber Sign In Help Home ... Upgrade your Encarta Experience Search Encarta Upgrade your Encarta Experience Spend less time searching and more time learning. Learn more Tasks Find in this article Print Preview Related Items Math Homework Help Mathematics more... Further Reading Editors' picks for Mathematics Search for books and more related to Mathematics Encarta Search Search Encarta about Mathematics Editors' Picks Great books about your topic, Mathematics ... Click here Advertisement document.write(' Page 7 of 12 Mathematics Encyclopedia Article Multimedia 45 items Article Outline Introduction Mathematics: The Language of Science Branches of Mathematics History of Mathematics A Roman Mathematics The Alexandrian period of Greek civilization ended in 31 bc with Rome’s conquest of Egypt, the last of Alexander’s kingdoms. Roman orator Cicero boasted that the Romans were not dreamers like the Greeks but applied their study of mathematics to the useful. Nothing mathematically significant was accomplished by the Romans. The Roman numeration system was based on Roman numerals, which were cumbersome for calculation. Despite this drawback, the use of Roman numerals continued in some European schools until about 1600 and in bookkeeping for another century. B Indian and Islamic Mathematics After the decline of Greece and Rome, mathematics flourished for hundreds of years in India and the Islamic world. Mathematics in India was largely a tool for astronomy, yet Indian mathematicians discovered a number of important concepts. Their mathematical masterpieces and those of the Greeks were translated into Arabic in centers of Islamic learning, where mathematical discoveries continued during the period known in the West as the Middle Ages. Our present numeration system, for example, is known as the Hindu-Arabic system.

73. Scientific Perspectives From The Vedas: Math By 500 CE mathematicians of India had solved problems that baffled the world s 7 The great indian mathematician Bhaskaracharya (1150 CE) produced http://www.geocities.com/CapeCanaveral/7348/math.html

Mathematics and the Spiritual Dimension I remember the time my father pulled me aside and said, "Son, you can explain everything with math." He was a rationalist, and for him God existed only in the sentiments of the uneducated. At the time I believed him, and I think his advice had a lot to do with my decision to pursue a degree in physics. Somewhere along the way, however, in 1969, something happened (something many people are still trying to figure out) which drew me away from the spirit of that fatherly advice and subsequently my once promising career. Unfortunately, I think I went too far to the other side. I threw reason to the wind, so to speak, and unceremoniously became a self-ordained "spiritual person." Science, the foundation of which is mathematics, as I saw it, had nothing to offer. It was only years later, when the cloud of my sentimentalism was dissipated by the sun of my soul's integrity, that I was able to separate myself from yet another delusion-the first being the advice of my father, and the second being the idea that I could wish myself into a more profound understanding of the nature of reality. Math cannot take the mystery out of life without doing away with life itself, for it is life's mystery, its unpredictability-the fact that it is dynamic, not static-that makes it alive and worth living. We may theoretically explain away God, but in so doing we only choose to delude ourselves; I = everything is just bad arithmetic.

74. Encyclopedia: Srinivasa Aaiyangar Ramanujan He published several papers in indian mathematical journals and later got theinterests of leading European mathematicians in his work. http://www.nationmaster.com/encyclopedia/Srinivasa-Aaiyangar-Ramanujan

Supporter Benefits Signup Login Sources ... Pies Related Articles People who viewed "Srinivasa Aaiyangar Ramanujan" also viewed: Ramanujan Srinivasa Ramanujan Ramanujan conjecture 1729 (number) ... K. S. Ranjitsinhji What's new? Our next offering Latest newsletter Student area Lesson plans Recent Updates St©phane Dion Spratly Islands Southbridge, Virginia South Park ... More Recent Articles Top Graphs Richest Most Murderous Most Taxed Most Populous ... More Stats Encyclopedia: Srinivasa Aaiyangar Ramanujan Updated 214 days 20 hours 27 minutes ago. Other descriptions of Srinivasa Aaiyangar Ramanujan Ramanujan Srinivasa Aiyangar Ramanujan Tamil December 22 April 26 ) was a groundbreaking Indian mathematician . A child prodigy , he was largely self-taught in mathematics and never attended a university Ramanujan mainly worked in analytical number theory and is famous for many summation formulas involving constants such as prime numbers and the partition function . Often, his formulas were stated without proof and were only later proven to be true. Contents 1 Life 2 The Ramanujan conjecture and its role 3 Ramanujan's notebooks 4 See also ... 7 External links Life Born in Erode Tamil Nadu India , by the age of twelve Ramanujan had mastered trigonometry so completely that he was inventing sophisticated theorems that astonished his teachers. In

75. Mathematicians Born In India mathematicians born in India. mathematicians birthplaces are given relative tomodernday boundaries. Click on the name below to go to the biography. http://www-groups.dcs.st-and.ac.uk/~history/BirthplaceMaps/Countries/India.html

Mathematicians born in India Mathematicians' birthplaces are given relative to modern-day boundaries. Click on the name below to go to the biography. Apastamba Aryabhata I Aryabhata II Baudhayana ... Yavanesvara Click HERE to see a clickable map of India and Pakistan. Places Index Birthplace Maps Index Countries Index Main index ... Societies, honours, etc. JOC/EFR/BS January 1998 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/BirthplaceMaps/India.html

76. Ramanujan, Srinivasa (1887-1920) -- From Eric Weisstein's World Of Scientific Bi indian mathematician who was selftaught and had an uncanny mathematical Hardy, GH The indian Mathematician Ramanujan. Ch. 1 in Ramanujan Twelve http://scienceworld.wolfram.com/biography/Ramanujan.html

Branch of Science Mathematicians Nationality Indian Ramanujan, Srinivasa (1887-1920) Indian mathematician who was self-taught and had an uncanny mathematical manipulative ability. Ramanujan was unable to pass his school examinations in India, and could only obtain a clerk's position in the city of Madras. However, he continued to pursue his own mathematics, and sent letters to three mathematicians in England (which arrived in January of 1913) containing some of his results. While two of the three returned the letters unopened, G. H. Hardy recognized Ramanujan's intrinsic mathematical ability and arranged for him to come to Cambridge. Because of his lack of formal training, Ramanujan sometimes did not differentiate between formal proof and apparent truth based on intuitive or numerical evidence. Although his intuition and computational ability allowed him to determine and state highly original and unconventional results which continued to defy formal proof until recently (Berndt 1985-1997), Ramanujan did occasionally state incorrect results. Ramanujan had an intimate familiarity with numbers, and excelled especially in

77. SRINIVASA RAMANUJAN Finally he met with modest success when the indian mathematician Ramachandra Raoprovided him with first a modest subsidy, and later a clerkship at the http://www.usna.edu/Users/math/meh/ramanujan.html

Srinivasa Ramanujan It is one of the most romantic stories in the history of mathematics: in 1913, the English mathematician G. H. Hardy received a strange letter from an unknown clerk in Madras, India. The ten-page letter contained about 120 statements of theorems on infinite series, improper integrals, continued fractions, and number theory (Here is a .dvi file with a sample of these results). Every prominent mathematician gets letters from cranks, and at first glance Hardy no doubt put this letter in that class. But something about the formulas made him take a second look, and show it to his collaborator J. E. Littlewood. After a few hours, they concluded that the results "must be true because, if they were not true, no one would have had the imagination to invent them". Thus was Srinivasa Ramanujan (1887-1920) introduced to the mathematical world. Born in South India, Ramanujan was a promising student, winning academic prizes in high school. But at age 16 his life took a decisive turn after he obtained a book titled A Synopsis of Elementary Results in Pure and Applied Mathematics . The book was simply a compilation of thousands of mathematical results, most set down with little or no indication of proof. It was in no sense a mathematical classic; rather, it was written as an aid to coaching English mathematics students facing the notoriously difficult Tripos examination, which involved a great deal of wholesale memorization. But in Ramanujan it inspired a burst of feverish mathematical activity, as he worked through the book's results and beyond. Unfortunately, his total immersion in mathematics was disastrous for Ramanujan's academic career: ignoring all his other subjects, he repeatedly failed his college exams.

78. Mathematics The great indian mathematician Aryabhata (born 476 AD) wrote the Aryabhatiya a volume of 121 verses. Apart from discussing astronomy, http://www.indiaheritage.com/science/math.htm

A Living Portrait of India India Heritage Science Mathematics A s early as the Vedic period (1500-1000BC), the Shulvasutras facilitated the construction of sacrificial altars by their principles of plane geometry particularly through the figures of the triangle and the rectangle, the circle and the rhombus. Negative numbers, the zero, place-value notations and simple algorithms were already a part of mathematics. The great Indian mathematician Aryabhata (born 476 AD) wrote the Aryabhatiya - a volume of 121 verses. Apart from discussing astronomy, he laid down procedures of arithmetic, geometry, algebra and trigonometry. He calculated Pi at 3.1416 and covered subjects like numerical squares and cube roots. Aryabhata is credited with the emergence of trigonometry through sine functions. The eleventh century saw the solving of Diophantine equations (second order), and by the fourteenth century tremendous progress had been made in trigonometry. Sine and cosine functions as well as high-level approximations were tabulated and the essential irrationality of trigonometry recognized. Around the beginning of the sixteenth century Madhava developed his own system of calculus based on his knowledge of trigonometry. He was an untutored mathematician from Kerala, and preceded Newton and Liebnitz by more than a century.

79. Aryabhata --  Encyclopædia Britannica Aryabhata first unmanned Earth satellite built by India. It was named for aprominent indian astronomer and mathematician of the 5th century AD;. http://www.britannica.com/eb/article?tocId=9009748

80. Ramanujan SR I went to the founder of the indian Mathematical Society, naturally as I wastrying to procure a job in that field. They helped me to get in touch with http://www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/ramanujan.html

Ramanujan It is the year 1919, close to the time when Ramanujan would sadly pass away of an incurable illness. His achievements are immortal and his contributions too many to count to the mathematical world. MA: Mr. Ramanujan, I am pleased to meet you finally after hearing about the wonderful feats that you have performed in math without the aid of a proper or extensive education of any sort. How is it that without any extensive higher education you have surpassed boundaries that will propel you into immortality with other famous mathematicians? SR: Yes, it was very hard as a child for me and later on as an adult to procure money for my researches lacking an all-around liberal education. For me, math was the only subject in which I had increasing interest in and thus excelled. MA: Who taught you at such a young age to love the art of math? MA: I can imagine what a stir you were as a child being the first in the class and always inquisitive. Is this not so? SR: Some are shocked when I reply no. As a child, I was considered a slow minded one as my verbal abilities did not come into play until I was three years old. But, later on when I entered school the teachers were more open to me and did not think I was as slow as others previously had. Yes, I did do well in school, especially math. Inquisitiveness was always in me as I, at times, even challenged my teachers; this they were not as open to, let me tell you. MA: With little resources or other intellectuals around you, what gave impetus to your ideas and thoughts as well as providing a background on previous math concepts formulated by other great mathematicians?

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