.InfluencesInfluencedSignatureSrinivasa 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 then considered unsolvable. Ramanujan initially developed his own mathematical research in isolation: 'He tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered'. Seeking mathematicians who could better understand his work, in 1913 he began a partnership with the English mathematician at the,. Recognizing Ramanujan's work as extraordinary, Hardy arranged for him to travel to Cambridge. In his notes, Ramanujan had produced groundbreaking new, including some that Hardy said 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work in all areas of mathematics influenced by Ramanujan, and his notebooks—containing summaries of his published and unpublished results—have been analyzed and studied for decades since his death as a source of new mathematical ideas.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. 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 mathematical geniuses such as and.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 in 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 said the mathematical knowledge he displayed was revealed to him by his family goddess.
'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, one 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 that '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. Deligne (in his Fields Medal-winning work) proved Serre's conjecture.
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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 work 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 has 256 pages in 21 chapters and 100 unorganised pages, and the third 33 unorganised pages.
The results in his notebooks inspired numerous papers by later mathematicians trying to prove what he had found. Hardy himself wrote papers exploring material from Ramanujan's work, as did, and Bruce Berndt. In 1976 rediscovered a fourth notebook with 87 unorganised pages, the so-called. Hardy–Ramanujan number 1729. Srinivasa Ramanujan on stamp of India (2011)The year after his death, listed Ramanujan among other distinguished scientists and mathematicians on a 'Calendar of Scientific Pioneers' who had achieved eminence. Ramanujan's home state of celebrates 22 December (Ramanujan's birthday) as 'State IT Day'. Stamps picturing Ramanujan were issued by the in 1962, 2011, 2012 and 2016.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.
The (ICTP) has created a prize in Ramanujan's name for young mathematicians from developing countries in cooperation with the, which nominates members of the prize committee., a private university based in, has instituted the of 10,000 to be given annually to a mathematician not exceeding age 32 for outstanding contributions in an area of mathematics influenced by Ramanujan. Based on the recommendations of a committee appointed by the University Grants Commission (UGC), Government of India, the Srinivasa Ramanujan Centre, established by SASTRA, has been declared an off-campus centre under the ambit of SASTRA University. House of Ramanujan Mathematics, a museum of Ramanujan's life and work, is also on this campus. SASTRA purchased the house where Ramanujan lived at Kumabakonam and renovated it.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 2012 would be celebrated as.Ramanujan IT City is an information technology (IT) special economic zone (SEZ) in Chennai that was built in 2011. Situated next to the Tidel Park, it comprises 25 acres with two zones, with a total area of 5.7 million square feet, including 4.5 million square feet of office space. In popular culture., a best-selling 1941 novel by the novelist (1900-1954) published by MacMillan, has the hero Charles Rainier becoming friends with a genius-level Hindu mathematician called Pal who lives in rooms next to his in the mythical St. Swithin's College at in 1920. Pal claims to feel numbers emotionally and is moved to tears over the 'shatteringly beautiful' Binomial Theorem. There can be little doubt that the fictional Pal was inspired by Ramanujan. Hilton and Ramanujan were near contemporaries at.
( ) is a 1991 of Ramanujan by and published by Washington Square Press. ( ) is a 1992 novel by Greek author in which Ramanujan appears. is a 2015 film based on Kanigel's book. British actor portrays Ramanujan., an Indo-British collaboration film chronicling Ramanujan's life, 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.
M. Krish's thriller novel The Steradian Trail weaves Ramanujan and his accidental discovery into its plot connecting religion, mathematics, finance and economics. Partition, a play by Ira Hauptman about Hardy and Ramanujan, was first performed in 2013. The play First Class Man by Alter Ego Productions was based on David Freeman's First Class Man.
The play centres around Ramanujan and his complex and dysfunctional relationship with Hardy. Berndt, Bruce C. L.; Oberschelp, W.; Jongen, H. Turnhout, Belgium: Brepols Verlag. Pp. 119–146. Berndt, Bruce C.; Andrews, George E.
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Collected Papers of Srinivasa Ramanujan. AMS.This book was originally published in 1927 after Ramanujan's death.
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