Friday, February 20, 2015

RAMANUJAN- LOST BOOK OF MATHMATICS)

'Christmas special post-1
Srinivasa Ramanujan - A Remarkable Mathematical Genius
(HIS BIRTHDAY)
Srinivasa Ramanujan Aiyangar was an Indian Mathematician who was born in Erode, India in 1887 on December 22. So, its his birthday today. He is considered as one of the fractal brain with extra ordinary capabilities. The only Ramanujan Museum in the country, founded by Shri P. K. Srinivasan, a mathematics teacher, operates from March 1993 in the Avvai Academy, Royapuram, Madras. The achievement of Ramanujan was so great that those who can really grasp the work of Ramanujan ‘may doubt that so prodigious a feat had ever been accomplished in the history of thought’.
"Sheer intuitive brilliance coupled to long, hard hours on his slate made up for most of his educational lapse. This ‘poor and solitary Hindu pitting his brains against the accumulated wisdom of Europe’ as Hardy called him, had rediscovered a century of mathematics and made new discoveries that would captivate mathematicians for next century"- by Robert Kanigel in The Man who Knew Infinity : A Life of the #GeniusRamanujan
Ramanujan’s life is full of strange contrasts. He had no formal training in mathematics but yet “he was a natural mathematical genius, in the class of Gauss and Euler.” Probably Ramanujan’s life has no parallel in the history of human thought. Godfrey Harold Hardy, (1877-1947), who made it possible for Ramanujan to go to Cambridge and give formal shape to his works, said in one of his lectures given at Harvard Universty (which later came out as a book entitled Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work): “I have to form myself, as I have never really formed before, and try to help you to form, some of the reasoned estimate of the most romantic figure in the recent history of mathematics, a man whose career seems full of paradoxes and contradictions, who defies all cannons by which we are accustomed to judge one another and about whom all of us will probably agree in one judgement only, that he was in some sense a very great mathematician.”
Contributions and Achievements:
Ramanujan went to Cambridge in 1914 and it helped him a lot but by that time his mind worked on the patterns on which it had worked before and he seldom adopted new ways. By then, it was more about intuition than argument. Hardy said Ramanujan could have become an outstanding mathematician if his skills had been recognized earlier. It was said about his talents of #Continued_Fractions and #hypergeometric series that, “he was unquestionably one of the great masters.” It was due to his sharp memory, calculative mind, patience and insight that he was a great formalist of his days. But it was due to his some methods of working in the work analysis and theories of numbers that did not let him excel that much. In mathematics, there is a distinction between having an insight and having a proof.
Ramanujan's talent suggested a plethora of formulae that could then be investigated in depth later. It is said by G. H. Hardy that Ramanujan's discoveries are unusually rich and that there is often more to them than initially meets the eye. As a by-product, new directions of research were opened up. Examples of the most interesting of these formulae include the intriguing infinite series for π
He got elected as the fellow in 1918 at the Trinity College at Cambridge and the Royal Society. He departed from this world on April 26, 1920.
Big Conspiracy
Ramanujan's #Lost_Notebook is the manuscript in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries of the last year (1919–1920) of his life. Its whereabouts was unknown to all but a few mathematicians until it was rediscovered by George Andrews in 1976, in a box of effects of G. N. Watson stored at the Wren Library at Trinity College, Cambridge. The "notebook" is not a book, but consists of 87 loose and unordered sheets of paper, with more than 600 of Ramanujan's formulas.
George Andrews and Bruce C. Berndt (2005, 2009, 2012, 2013) have published several books in which they give proofs for Ramanujan's formulas included in the notebook. Berndt says of the notebooks' discovery: "The discovery of this 'Lost Notebook' caused roughly as much stir in the mathematical world as the discovery of Beethoven’s tenth symphony would cause in the musical world." (Peterson 2006). Rankin (1989) described the lost notebook in detail. The majority of the formulas are about q-series and mock theta functions, about a third are about modular equations and singular moduli, and the remaining formulas are mainly about integrals, Dirichlet series, congruences, and asymptotics.
Source-Ancient Indian Scientific Knowledge Forum'Srinivasa Ramanujan Aiyangar was an Indian Mathematician who was born in Erode, India in 1887 on December 22. So, its his birthday today. He is considered as one of the fractal brain with extra ordinary capabilities. The only Ramanujan Museum in the country, founded by Shri P. K. Srinivasan, a mathematics teacher, operates from March 1993 in the Avvai Academy, Royapuram, Madras. The achievement of Ramanujan was so great that those who can really grasp the work of Ramanujan ‘may doubt that so prodigious a feat had ever been accomplished in the history of thought’.
"Sheer intuitive brilliance coupled to long, hard hours on his slate made up for most of his educational lapse. This ‘poor and solitary Hindu pitting his brains against the accumulated wisdom of Europe’ as Hardy called him, had rediscovered a century of mathematics and made new discoveries that would captivate mathematicians for next century"- by Robert Kanigel in The Man who Knew Infinity : A Life of the ‪‎Ramanujan-
Ramanujan’s life is full of strange contrasts. He had no formal training in mathematics but yet “he was a natural mathematical genius, in the class of Gauss and Euler.” Probably Ramanujan’s life has no parallel in the history of human thought. Godfrey Harold Hardy, (1877-1947), who made it possible for Ramanujan to go to Cambridge and give formal shape to his works, said in one of his lectures given at Harvard Universty (which later came out as a book entitled Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work): “I have to form myself, as I have never really formed before, and try to help you to form, some of the reasoned estimate of the most romantic figure in the recent history of mathematics, a man whose career seems full of paradoxes and contradictions, who defies all cannons by which we are accustomed to judge one another and about whom all of us will probably agree in one judgement only, that he was in some sense a very great mathematician.”
Contributions and Achievements:
Ramanujan went to Cambridge in 1914 and it helped him a lot but by that time his mind worked on the patterns on which it had worked before and he seldom adopted new ways. By then, it was more about intuition than argument. Hardy said Ramanujan could have become an outstanding mathematician if his skills had been recognized earlier. It was said about his talents of fractions and  hypergeometric series that, “he was unquestionably one of the great masters.” It was due to his sharp memory, calculative mind, patience and insight that he was a great formalist of his days. But it was due to his some methods of working in the work analysis and theories of numbers that did not let him excel that much. In mathematics, there is a distinction between having an insight and having a proof.
Ramanujan's talent suggested a plethora of formulae that could then be investigated in depth later. It is said by G. H. Hardy that Ramanujan's discoveries are unusually rich and that there is often more to them than initially meets the eye. As a by-product, new directions of research were opened up. Examples of the most interesting of these formulae include the intriguing infinite series for π
He got elected as the fellow in 1918 at the Trinity College at Cambridge and the Royal Society. He departed from this world on April 26, 1920.
Big Conspiracy
Ramanujan's "LOST NOTEBOOK" is the manuscript in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries of the last year (1919–1920) of his life. Its whereabouts was unknown to all but a few mathematicians until it was rediscovered by George Andrews in 1976, in a box of effects of G. N. Watson stored at the Wren Library at Trinity College, Cambridge. The "notebook" is not a book, but consists of 87 loose and unordered sheets of paper, with more than 600 of Ramanujan's formulas.
George Andrews and Bruce C. Berndt (2005, 2009, 2012, 2013) have published several books in which they give proofs for Ramanujan's formulas included in the notebook. Berndt says of the notebooks' discovery: "The discovery of this 'Lost Notebook' caused roughly as much stir in the mathematical world as the discovery of Beethoven’s tenth symphony would cause in the musical world." (Peterson 2006). Rankin (1989) described the lost notebook in detail. The majority of the formulas are about q-series and mock theta functions, about a third are about modular equations and singular moduli, and the remaining formulas are mainly about integrals, Dirichlet series, congruences, and asymptotics.
Source-Ancient Indian Scientific Knowledge Forum