Biography of srinivasa ramanujan mathematician contributions

For instance, Ramanujan demonstrated that p 5 equals 7, providing a framework that has had lasting implications in analytic number theory. His unique insights into the divisibility properties of p n led to discoveries that catalyzed advancements in modular forms, a field that plays a critical role in modern mathematics. Ramanujan's legacy extends beyond published papers and theorems; he also left behind a treasure trove of ideas in his remarkable manuscripts.

Notably, he introduced mock theta functions in his final year, a concept that remains poorly understood even today but possesses significant ramifications in both mathematics and theoretical physics, including applications in black hole theory. The sheer volume of his claims—approximately 4, without proofs—has inspired mathematicians to explore and validate his conjectures, affirming his status as one of the most innovative mathematicians of the 20th century.

Srinivasa Ramanujan's life took a significant turn when he began corresponding with the renowned British mathematician G. Hardy in Initially, Hardy suspected that Ramanujan's extraordinary mathematical claims could be a hoax. However, after reviewing his work, Hardy recognized Ramanujan's genius and arranged for him to study at Cambridge University.

This mentorship blossomed into a fruitful collaboration that lasted for five years, during which Ramanujan published over 20 papers, many of which were groundbreaking in the fields of number theory and continued to influence mathematics long after his passing. At Cambridge, Ramanujan thrived under Hardy's guidance, where his intuitive understanding of mathematics was sculpted through formal techniques.

Together, they ventured into the circle method, a powerful analytical technique that enabled them to derive precise formulas for partition numbers. Their work together reflected a symbiotic relationship, blending Ramanujan's raw intuition with Hardy's structured approach, ultimately leading to biography of srinivasa ramanujan mathematician contributions advancements within analytic number theory.

Despite their successful partnership, Ramanujan's time in England was fraught with challenges, particularly his struggle with health issues exacerbated by the English climate. InRamanujan contracted tuberculosis, which increasingly limited his ability to work. Nonetheless, he continued to make groundbreaking discoveries, including the innovative concept of mock theta functions, even as his health deteriorated.

This period at Cambridge not only marked a pinnacle in his career but also laid the groundwork for future explorations of his increasingly complex and visionary ideas in mathematics. Srinivasa Ramanujan's remarkable journey in mathematics was intermittently overshadowed by significant health struggles. After a productive period at Cambridge studying under G.

Hardy, he began experiencing serious health issues, which were exacerbated by the cold, damp climate of England. InRamanujan contracted tuberculosis, a condition that would prove to be life-threatening. His declining health led to his return to India in Despite his illness, Ramanujan's brilliance shone through as he continued to work on complex mathematical theories, even while battling fatigue and deteriorating health.

Main article: number. Mathematicians' views of Ramanujan. Further information: List of things named after Srinivasa Ramanujan. Commemorative postal stamps. Ramanujan, S. Messenger Math. Proceedings of the London Mathematical Society. The Journal of the Indian Mathematical Society. Mathematical Proceedings of the Cambridge Philosophical Society.

Hardy, G. Ramanujan, Srinivasa S2CID Posthumously published extract of a longer, unpublished manuscript. Further works of Ramanujan's mathematics. Selected publications on Ramanujan and his work. Berndt, Bruce C. Butzer, P. Turnhout, Belgium: Brepols Verlag. ISBN Archived PDF from the original on 9 September Ramanujan: Letters and Commentary.

Ramanujan: Essays and Surveys. Number Theory in the Spirit of Ramanujan. Ramanujan's Notebooks: Part I. New York: Springer. Ramanujan's Notebooks: Part II. Ramanujan's Notebooks: Part IV. Ramanujan's Notebooks: Part V. March The American Mathematical Monthly. JSTOR New York: Chelsea Pub. Henderson, Harry Modern Mathematicians. New York: Facts on File Inc.

Kanigel, Robert New York: Charles Scribner's Sons. Leavitt, David The Indian Clerk paperback ed. London: Bloomsbury. Narlikar, Jayant V. New Delhi, India: Penguin Books. Ono, Ken ; Aczel, Amir D. Sankaran, T. Selected publications on works of Ramanujan. Ramanujan, Srinivasa; Hardy, G. Collected Papers of Srinivasa Ramanujan. This book was originally published in [ ] 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 Notebooks 2 Volumes. Bombay: Tata Institute of Fundamental Research. These books contain photocopies of the original notebooks as written by Ramanujan. New Delhi: Narosa.

This book contains photocopies of the pages of the "Lost Notebook". This was produced from scanned and microfilmed images of the original manuscripts by expert archivists of Roja Muthiah Research Library, Chennai. Oxford University Press. Oxford Dictionary of National Biography online ed. Subscription or UK public library membership required.

Geniusp. Cambridge University Press. Ramanujan's Notebooks. Part 5. Notices of the American Mathematical Society. Archived PDF from the original on 21 June Retrieved 23 June August Archived from the original on 25 September Retrieved 20 December New Scientist. Archived from the original on 3 August The Hindu. Retrieved 7 September Maths History.

Retrieved 29 October A to Z of mathematicians. Facts on File.

Biography of srinivasa ramanujan mathematician contributions

Chennai, India. Archived from the original on 26 August Expository address delivered on Sep. Archived from the original on 21 September Live mint. History in adult human sexual behavior with children and adolescents in Western societies". Pedophilia: Biosocial Dimensions. New York: Springer-Verlag. New Series. Bibcode : Sci PMID Chennai: Institute of Mathematical Sciences.

Archived from the original PDF on 24 December Retrieved 10 November Indian Express. Archived from the original on 5 September Srinivasan ed. Ramanujan Memorial Number: Letters and Reminiscences. Madras: Muthialpet High School. Ramanujan: The Man and the Mathematician. Bombay: Asia Publishing House. Institute of Mathematical Sciences, Chennai.

Archived from the original PDF on 10 January The Ramanujan Institute. Archived from the biography of srinivasa ramanujan mathematician contributions on 6 October Bibcode : Natur. ISSN June Ramanujan, B. Journal of the Indian Mathematical Society. Hill to a C. Griffith a former student who sent the request to Hill on Ramanujan's behalf28 November Godfrey Harold Variety of Men.

Srinivasa Ramanujan. New Delhi: National Book Trust. Archived from the original on 11 December Retrieved 1 September Cambridge: Cambridge University Press. Collected Papers of G. Oxford, England: Clarendon Press. Retrieved 9 August The Royal Society. Archived from the original on 16 February Retrieved 16 February Chandrasekhar, An Incident in the Life of S.

Ramanujan F. Conversations with G. Littlewood FRS and their Sequel. Reprinted in Berndt, Bruce C. Ramanujan: essays and surveys. Providence: American Mathematical Society, Notes and Records of the Royal Society of London. Most of these claims have now been proved, and like his published work, continue to inspire modern-day mathematics. We strive for accuracy and fairness.

If you see something that doesn't look right, contact us! Benjamin Banneker. Charles Babbage. Blaise Pascal. Leonhard Euler. Ada Lovelace. Valerie Thomas. John Venn. Early Life Srinivasa Ramanujan was born on December 22,in Erode, India, a small village in the southern part of the country. Cambridge Around this time, Ramanujan had become aware of the work of British mathematician G.

In his letter of application he wrote [ 3 ] :- I have passed the Matriculation Examination and studied up to the First Arts but was prevented from pursuing my studies further owing to several untoward circumstances. I have, however, been devoting all my time to Mathematics and developing the subject. Despite the fact that he had no university education, Ramanujan was clearly well known to the university mathematicians in Madras for, with his letter of application, Ramanujan included a reference from E W Middlemast who was the Professor of Mathematics at The Presidency College in Madras.

Middlemast, a graduate of St John's College, Cambridge, wrote [ 3 ] :- I can strongly recommend the applicant. He is a young man of quite exceptional capacity in mathematics and especially in work relating to numbers. He has a natural aptitude for computation and is very quick at figure work. On the strength of the recommendation Ramanujan was appointed to the post of clerk and began his duties on 1 March Ramanujan was quite lucky to have a number of people working round him with a training in mathematics.

He wrote to Hill on 12 November sending some of Ramanujan's work and a copy of his paper on Bernoulli numbers. Hill replied in a fairly encouraging way but showed that he had failed to understand Ramanujan's results on divergent series. The recommendation to Ramanujan that he read Bromwich 's Theory of infinite series did not please Ramanujan much.

In Ramanujan's letter to Hardy he introduced himself and his work [ 10 ] :- I have had no university education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at mathematics. I have not trodden through the conventional regular course which is followed in a university course, but I am striking out a new path for myself.

I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as 'startling'. Hardytogether with Littlewoodstudied the long list of unproved theorems which Ramanujan enclosed with his letter. On 8 February he replied to Ramanujan [ 3 ]the letter beginning:- I was exceedingly interested by your letter and by the theorems which you state.

You will however understand that, before I can judge properly of the value of what you have done, it is essential that I should see proofs of some of your assertions. Your results seem to me to fall into roughly three classes: 1 there are a number of results that are already known, or easily deducible from known theorems; 2 there are results which, so far as I know, are new and interesting, but interesting rather from their curiosity and apparent difficulty than their importance; 3 there are results which appear to be new and important Ramanujan was delighted with Hardy 's reply and when he wrote again he said [ 8 ] :- I have found a friend in you who views my labours sympathetically.

I am already a half starving man. To preserve my brains I want food and this is my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship either from the university of from the government. Indeed the University of Madras did give Ramanujan a scholarship in May for two years and, inHardy brought Ramanujan to Trinity College, Cambridge, to begin an extraordinary collaboration.

Setting this up was not an easy matter. Ramanujan was an orthodox Brahmin and so was a strict vegetarian. His religion should have prevented him from travelling but this difficulty was overcome, partly by the work of E H Neville who was a colleague of Hardy 's at Trinity College and who met with Ramanujan while lecturing in India. Ramanujan sailed from India on 17 March It was a calm voyage except for three days on which Ramanujan was seasick.

He arrived in London on 14 April and was met by Neville. After four days in London they went to Cambridge and Ramanujan spent a couple of weeks in Neville 's home before moving into rooms in Trinity College on 30 th April. Right from the beginning, however, he had problems with his diet. The outbreak of World War I made obtaining special items of food harder and it was not long before Ramanujan had health problems.

Right from the start Ramanujan's collaboration with Hardy led to important results. Hardy was, however, unsure how to approach the problem of Ramanujan's lack of formal education. He wrote [ 1 ] :- What was to be done in the way of teaching him modern mathematics? The limitations of his knowledge were as startling as its profundity. Littlewood was asked to help teach Ramanujan rigorous mathematical methods.