# Ramanujan Biography Pdf

. Influences Influenced Signature Srinivasa Ramanujan (; ; 22 December 1887 – 26 April 1920) was an who lived during the Though he had almost no formal training in, he made substantial contributions to, and, including solutions to mathematical problems considered to be unsolvable. Ramanujan initially developed his own mathematical research in isolation; it was quickly recognized by Indian mathematicians. Seeking mathematicians who could better understand his work, in 1913 he began a partnership with the English mathematician at the,. Recognizing the extraordinary work sent to him as samples, Hardy arranged travel for Ramanujan to Cambridge.

In his notes, Ramanujan had produced groundbreaking new, including some that Hardy stated had 'defeated him and his colleagues completely', in addition to rediscovering recently proven but highly advanced results. During his short life, Ramanujan independently compiled nearly 3,900 results (mostly and ).

Many were completely novel; his original and highly unconventional results, such as the, the, formulae, and, have opened entire new areas of work and inspired a vast amount of further research. Nearly all his claims have now been proven correct., a, was established to publish work in all areas of mathematics influenced by Ramanujan, and his notebooks – containing summaries of his published and unpublished results – have been analyzed and studied for decades since his death as a source of new mathematical ideas. As late as 2011 and again in 2012, researchers continued to discover that mere comments in his writings about 'simple properties' and 'similar outputs' for certain findings were themselves profound and subtle number theory results that remained unsuspected until nearly a century after his death and which relied on work published in 2006. He became one of the youngest and only the second Indian member, and the first Indian to be elected a. Of his original letters, Hardy stated that a single look was enough to show they could only have been written by a mathematician of the highest calibre, comparing Ramanujan to other mathematical geniuses such as and.

Background}Born December 22, 1887 in Erode, South India}Ramanujan was born into a family that was very poor and that had no distinguished professional achievements. Srinivasa Ramanujan As PDF. Srinivasa Ramanujan was an Indian mathematician who made significant contributions to mathematical. - Srinivasa Ramanujan Biography.

In 1919, ill health – now believed to have been hepatic (a complication from episodes of many years previously) – compelled Ramanujan's return to India, where he died in 1920 at the age of 32. His last letters to Hardy, written January 1920, show that he was still continuing to produce new mathematical ideas and theorems. His ', containing discoveries from the last year of his life, caused great excitement among mathematicians when it was rediscovered in 1976. A deeply religious, Ramanujan credited his substantial mathematical capacities to, and stated that the mathematical knowledge he displayed was revealed to him by his.

'An equation for me has no meaning,' he once said, 'unless it expresses a thought of.' Main article: Although there are numerous statements that could have borne the name Ramanujan conjecture, there is one that was highly influential on later work.

In particular, the connection of this conjecture with conjectures of in algebraic geometry opened up new areas of research. That is an assertion on the size of the, which has as generating function the discriminant modular form Δ( q), a typical in the theory of. It was finally proven in 1973, as a consequence of 's proof of the.

The reduction step involved is complicated. Deligne won a in 1978 for that work. In his paper 'On certain arithmetical functions', Ramanujan defined the so-called delta-function whose coefficients are called τ( n) (the ). He proved many congruences for these numbers such as τ( p) ≡ 1 + p 11 mod 691 for primes p. This congruence (and others like it that Ramanujan proved) inspired (1954 Fields Medalist) to conjecture that there is a theory of which 'explains' these congruences and more generally all modular forms. Δ( z) is the first example of a modular form to be studied in this way.

Pierre Deligne (in his Fields Medal-winning work) proved Serre's conjecture. The proof of proceeds by first reinterpreting and modular forms in terms of these Galois representations. Without this theory there would be no proof of Fermat's Last Theorem. Ramanujan's notebooks.

Further information: While still in Madras, Ramanujan recorded the bulk of his results in four notebooks of paper. They were mostly written up without any derivations. This is probably the origin of the misapprehension that Ramanujan was unable to prove his results and simply thought up the final result directly. Mathematician, in his review of these notebooks and Ramanujan's work, says that Ramanujan most certainly was able to prove most of his results, but chose not to.

This may have been for any number of reasons. Since paper was very expensive, Ramanujan would do most of his work and perhaps his proofs on, and then transfer just the results to paper. Using a slate was common for mathematics students in the at the time.

He was also quite likely to have been influenced by the style of 's book, which stated results without proofs. Finally, it is possible that Ramanujan considered his workings to be for his personal interest alone and therefore recorded only the results. The first notebook has 351 pages with 16 somewhat organised chapters and some unorganised material. The second notebook has 256 pages in 21 chapters and 100 unorganised pages, with the third notebook containing 33 unorganised pages. The results in his notebooks inspired numerous papers by later mathematicians trying to prove what he had found. Hardy himself created papers exploring material from Ramanujan's work, as did, and Bruce Berndt.

A fourth notebook with 87 unorganised pages, the so-called, was rediscovered in 1976. Hardy–Ramanujan number 1729. Main article: The number 1729 is known as the Hardy–Ramanujan number after a famous visit by Hardy to see Ramanujan at a hospital.

In Hardy's words: I remember once going to see him when he was ill. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a, and that I hoped it was not an unfavorable omen. 'No', he replied, 'it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.' Immediately before this anecdote, Hardy quoted Littlewood as saying, 'Every positive integer was one of Ramanujan's personal friends.' The two different ways are 1729 = 1 3 + 12 3 = 9 3 + 10 3. Generalizations of this idea have created the notion of '.

Mathematicians' views of Ramanujan Hardy said: 'He combined a power of generalization, a feeling for form, and a capacity for rapid modification of his hypotheses, that were often really startling, and made him, in his own peculiar field, without a rival in his day. The limitations of his knowledge were as startling as its profundity. Here was a man who could work out and theorems. To orders unheard of, whose mastery of continued fractions was. Beyond that of any mathematician in the world, who had found for himself the functional equation of the and the dominant terms of many of the most famous problems in the analytic theory of numbers; and yet he had never heard of a or of, and had indeed but the vaguest idea of what a function of a was.' When asked about the methods Ramanujan employed to arrive at his solutions, Hardy said that they were 'arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account.' He also stated that he had 'never met his equal, and can compare him only with or.'

Srinivasa Rao has said, 'As for his place in the world of Mathematics, we quote Bruce C. Berndt: ' has passed on to us Hardy's personal ratings of mathematicians. Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100, Hardy gave himself a score of 25, 30, 80 and Ramanujan 100.' ' During a lecture at in May 2011, Berndt stated that over the last 40 years, as nearly all of Ramanujan's theorems have been proven right, there had been greater appreciation of Ramanujan's work and brilliance, and that Ramanujan's work was now pervading many areas of modern mathematics and physics. In his book Scientific Edge, the physicist spoke of 'Srinivasa Ramanujan, discovered by the Cambridge mathematician Hardy, whose great mathematical findings were beginning to be appreciated from 1915 to 1919.

His achievements were to be fully understood much later, well after his untimely death in 1920. For example, his work on the (numbers with a large number of factors) started a whole new line of investigations in the theory of such numbers.' Posthumous recognition. Bust of Ramanujan in the garden of Ramanujan's home state of celebrates 22 December (Ramanujan's birthday) as 'State IT Day'. A stamp picturing Ramanujan was released by the in 1962 – the 75th anniversary of Ramanujan's birth – commemorating his achievements in the field of number theory, and a new design was issued on 26 December 2011, by the.

Since Ramanujan's centennial year, his birthday, 22 December, has been annually celebrated as Ramanujan Day by the where he studied and at the in. A prize for young mathematicians from developing countries has been created in Ramanujan's name by the (ICTP) in cooperation with the, which nominate members of the prize committee.

The, based in the state of in South India, has instituted the of 10,000 to be given annually to a mathematician not exceeding the age of 32 for outstanding contributions in an area of mathematics influenced by Ramanujan. Based on the recommendations of a high level committee appointed by the University Grants Commission (UGC), Government of India, Srinivasa Ramanujan Centre, established by SASTRA, has been declared as an OFF-CAMPUS CENTRE under the ambit of SASTRA University. House of Ramanujan Mathematics, a museum on life and works of the Mathematical prodigy, Srinivasa Ramanujan, also exists on this campus. SASTRA purchased the house where Srinivasa Ramanujan lived at Kumabakonam and renovated it. Named its Department of Computer Science and Information Technology 'Ramanujan Block'. In 2011, on the 125th anniversary of his birth, the Indian Government declared that 22 December will be celebrated every year as National Mathematics Day. Then Indian Prime Minister also declared that the year 2012 would be celebrated as the.

In popular culture. is a of Ramanujan, written in 1991 by and published by Washington Square Press. is a 2015 film based on the book. In the film, Ramanujan is portrayed by British actor., an Indo-British collaboration film, chronicling the life of Ramanujan, was released in 2014 by the independent film company. The cast and crew include director, cinematographer and editor. Popular Indian and English stars Abhinay Vaddi, Kevin McGowan and star in pivotal roles. The thriller novel by weaves Ramanujan and his accidental discovery into its plot connecting religion, mathematics, finance and economics., a play by Ira Hauptman about Hardy and Ramanujan, first performed in 2013.

A play, First Class Man by Alter Ego Productions, was based on David Freeman's First Class Man. The play is centred around Ramanujan and his complex and dysfunctional relationship with Hardy. On 16 October 2011, it was announced that, best known for his, is working on the film version, starring actor. Like the book and play it is also titled The First Class Man. is a recent British stage production by the company that explores the relationship between Hardy and Ramanujan. The novel by explores in fiction the events following Ramanujan's letter to Hardy.

honoured him on his 125th birth anniversary by replacing its logo with a on its home page. Ramanujan was mentioned in the 1997 film, in a scene where professor Gerald Lambeau explains to Sean Maguire the genius of Will Hunting by comparing him to Ramanujan. On 22 March 1988, the series aired a documentary about Ramanujan, 'The Man Who Loved Numbers' (, Episode 19).

In the book by, Ramanujan's contributions to and a brief synopsis of his life are given in Part II Unification in Ten Dimensions in the chapter Superstrings under the sections Mystery of Modular Functions and Reinventing 100 Years of Mathematics. Selected publications on Ramanujan and his work. Berndt, Bruce C. L.; Oberschelp, W.; Jongen, H. Turnhout, Belgium: Brepols Verlag. Berndt, Bruce C.; Andrews, George E. Ramanujan's Lost Notebook.

New York: Springer. Berndt, Bruce C.; Andrews, George E.

Ramanujan's Lost Notebook. New York: Springer. Berndt, Bruce C.; Andrews, George E. Ramanujan's Lost Notebook. New York: Springer. Berndt, Bruce C.; Andrews, George E. Ramanujan's Lost Notebook.

New York: Springer. Berndt, Bruce C.; Rankin, Robert A. Ramanujan: Letters and Commentary. Providence, Rhode Island:. Ramanujan: Essays and Surveys. Providence, Rhode Island:.

Berndt, Bruce C. Number Theory in the Spirit of Ramanujan. Providence, Rhode Island:. Berndt, Bruce C. Ramanujan's Notebooks. New York: Springer. Berndt, Bruce C.

Ramanujan's Notebooks. New York: Springer. Berndt, Bruce C. Ramanujan's Notebooks.

New York: Springer. Berndt, Bruce C. Ramanujan's Notebooks. New York: Springer.

Berndt, Bruce C. Ramanujan's Notebooks. New York: Springer. (March 1937). 'The Indian Mathematician Ramanujan'.

The American Mathematical Monthly. 44 (3): 137–155.

New York: Chelsea Pub. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work. Providence, Rhode Island: American Mathematical Society. Henderson, Harry (1995). Modern Mathematicians.

New York: Facts on File Inc. Kanigel, Robert (1991). The Man Who Knew Infinity: a Life of the Genius Ramanujan. New York: Charles Scribner's Sons. (19 June 1987).

'Remembering a 'Magical Genius '. Science, New Series. American Association for the Advancement of Science. 236 (4808): 1519–1521. (paperback ed.).

London: Bloomsbury. Scientific Edge: the Indian Scientist From Vedic to Modern Times. New Delhi, India: Penguin Books.; (2016-04-13). My Search for Ramanujan: How I Learned to Count. 'Srinivasa Ramanujan- Ganitha lokathile Mahaprathibha' (in Malayalam).

Kochi, India: Kerala Sastra Sahithya Parishath. Selected publications on works of Ramanujan.

Ramanujan, Srinivasa; Hardy, G. H.; Seshu Aiyar, P. V.;; Berndt, Bruce C. Collected Papers of Srinivasa Ramanujan. This book was originally published in 1927 after Ramanujan's death.

It contains the 37 papers published in professional journals by Ramanujan during his lifetime. The third reprint contains additional commentary by Bruce C. Ramanujan (1957).

Notebooks (2 Volumes). Bombay: Tata Institute of Fundamental Research. These books contain photocopies of the original notebooks as written by Ramanujan. Ramanujan (1988). The Lost Notebook and Other Unpublished Papers. New Delhi: Narosa.

This book contains photo copies of the pages of the 'Lost Notebook'., Journal of the Indian Mathematical Society. Ramanujan (2012). Notebooks (2 Volumes). Bombay: Tata Institute of Fundamental Research. This was produced from scanned and microfilmed images of the original manuscripts by expert archivists of Roja Muthiah Research Library, Chennai. See also.

Oxford Dictionaries. Retrieved 2017-07-30. Berndt, Bruce C. Springer Science & Business Media. (June–July 2006). Mathematical Association of America. Retrieved 23 June 2007.

16 (17): 650. Retrieved 20 December 2012.

Alladi, Krishnaswami; Elliott, P. A.; Granville, A. (30 September 1998). Springer Science & Business Media. Kanigel, Robert (2016-04-26). Simon and Schuster. 'The Man Who Knew Infinity', (1991), Kanigel, Robert, page 7 of Prologue.

^ Kanigel, Robert (1991). The Man Who Knew Infinity: a Life of the Genius Ramanujan. New York: Charles Scribner's Sons., p. 89.

Srinivasan, Pankaja (19 October 2012). Retrieved 7 September 2016., p. 9. Hardy, G. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work.

Providence, Rhode Island:. A to Z of mathematicians by Tucker McElroy 2005 221. ^ Ramanujan Aiyangar, Srinivasa; Hardy, Godfrey Harold; Aiyar, P. Veṅkatesvara Seshu (2000), 'Collected papers of Srinivasa Ramanujan', Nature, 123 (3104): xii,:,:,. Chennai, India. 25 December 2011.

Krishnamachari, Suganthi (27 June 2013). Retrieved 7 September 2016. Krishnamurthy, Prof. (Expository address delivered on Sep.16, 1987 at Visvesvarayya Auditorium as part of the celebrations of Ramanujan Centenary by the IISC, Bangalore). Retrieved 7 September 2016. Bullough, V.L.

(Pedophilia: Biosocial Dimensions ed.). Springer-Verlag New York Inc. Retrieved 27 April 2016., p. 236. ^ (PDF). Institute of Mathematical Sciences, Chennai.

Retrieved 10 November 2012. ^ Janardhanan, Arun (6 December 2015). Indian Express. Retrieved 7 September 2016. Ramanujan, Srinivasa (1968). Srinivasan, ed.

Ramanujan Memorial Number: Letters and Reminiscences. Madras: Muthialpet High School. Bombay: Asia Publishing House., p. 23. Srinivasan (1968), Vol. Institute of Mathematical Sciences, Chennai.

Retrieved 7 September 2016. The Ramanujan Institute. Retrieved 7 September 2016. Srinivasan (1968), Vol.

Srinivasan (1968), Vol. Neville, Eric Harold (January 1921). 'The Late Srinivasa Ramanujan'. 106 (2673): 661–662., p. 24. Seshu Iyer, P.

'The Late Mr. Ramanujan, B.A., F.R.S'. Journal of the Indian Mathematical Society. Neville (March 1942), p292.

Srinivasan (1968), p176. Srinivasan (1968), p31.

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Srinivasan (1968), p49. Letter from M. Griffith (a former student who sent the request to Hill on Ramanujan's behalf), 28 November 1912. Variety of Men. ^ (June 1920). 'Obituary, S.

^ Neville, Eric Harold (March 1942). 'Srinivasa Ramanujan'.

149 (3776): 293. Letter, Hardy to Ramanujan, 8 February 1913. Letter, Ramanujan to Hardy, 22 January 1914. Letter, Ramanujan to Hardy, 27 February 1913,. Ram, Suresh (1972). Srinivasa Ramanujan.

New Delhi: National Book Trust., pp. 30–31., p. 12. Hardy, G. Letter, Littlewood to Hardy, early March 1913. Collected Papers of G. Oxford, England:. Ramanujan's illness. Notes and records of the Royal Society of London, 48(1), 107-119.

^ Peterson, Doug. Retrieved 11 January 2014. C., & SAVAGE, B. Report on the Treatment of Entamoeba Histolytica Infections. Journal of the Royal Army Medical Corps, 33(5), 418-426.

Chaitin, Gregory (28 July 2007). 'Less Proof, More Truth'. NewScientist (2614): 49. Berndt, Bruce C.; Rankin, Robert Alexander (2001). Retrieved 8 June 2015., p. 82.

Calyampudi Radhakrishna Rao (1997). World Scientific.

Retrieved 7 June 2010. 28 December 2012. Ono (June–July 2006), p 649. Ramanujan, Srinivasa (1916). Transactions of the Cambridge Philosophical Society. Retrieved 2016-05-15.

The tau function is discussed in pages 194–197.; (2016-04-13). Ideas that were critical to the proof of Fermat's last theorem. ^ Ramanujans Notebooks. Archived from on 16 July 2012.

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34: 783–784. External links. Find more about Srinivasa Ramanujanat Wikipedia's. from Wikimedia Commons. from Wikiquote.

from Wikisource Media links. Biswas, Soutik (16 March 2006). Retrieved 24 August 2006.

## Ramanujan Biography Wife

Biographical links. at the.;,. Other links. A Study Group For Mathematics:. – An international journal devoted to Ramanujan., including a Ramanujan Prize.

Hindu.com:,. Hindu.com:. Bruce C. Berndt; Robert A. Rankin (2000). 'The Books Studied by Ramanujan in India'.

Mathematical Association of America. 107 (7): 595–601.

## Ramanujan Biography Videos

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