Indian mathematician ramanujan wife

He had a brother named Sadagopan Ramanujan. He was married to Janakiammal from until his death in Updated On : December 22, Srinivasa Ramanujan Mathematician. Srinivasa Ramanujan Photos. Srinivasa Ramanujan Wiki Link. He is known for his contributions to number theory, mathematical analysis, continued fractions and continued fractions. He provided solutions to the problems which were considered as unsolvable that time.

He passed primary examinations in Tamil, English, arithmetic, and geography in But he did not pass in other subjects because of his interest in Mathematics and failed. He attended Pachaiyappa's College at Madras for his education but failed to pass in rest subjects and left the college without a degree. He solicited support from many influential Indians and published several papers in Indian mathematical journals, but was unsuccessful in his attempts to foster sponsorship.

It might be the case that he was supported by Ramachandra Raothen the collector of the Nellore district and a distinguished civil servant. Rao, an amateur mathematician himself, was the uncle of the well-known mathematician, K. Ananda Raowho went on to become the Principal of the Presidency College. Following his supervisor's advice, Ramanujan, in late and earlysent letters and samples of his theorems to three Cambridge academics : H.

His work remains a subject of study due to its complexity and depth, and many of his theorems continue to inspire mathematicians today. Srinivasa Ramanujan's correspondence with British mathematician G. Hardy transformed his career. Hardy recognized Ramanujan's unique mathematical talent and mentored him during Ramanujan's five years at Cambridge University.

This relationship allowed Ramanujan to publish over twenty papers and engage in significant mathematical research, including collaboration with Hardy. Their mutual respect and complementary skills led to the development of innovative mathematical concepts that are still relevant today. Despite his extraordinary mathematical abilities, Ramanujan faced numerous challenges.

His intense focus on mathematics led to difficulties in other subjects, costing him academic scholarships. Additionally, his humble beginnings and lack of formal education created barriers to recognition. Ramanujan also suffered from poor health throughout his life, ultimately contracting tuberculosis, which forced him to return to India prematurely, where he continued to work until his untimely death at the age of Srinivasa Ramanujan is considered a mathematical genius due to his remarkable ability to develop complex theories intuitively, without formal training.

His pioneering concepts in number theory and novel approaches to mathematical problems demonstrate exceptional insight and creativity. His contributions bridged gaps in existing mathematical knowledge, creating new areas of study and inspiring generations of mathematicians to explore the depths of his findings. The legacy of Srinivasa Ramanujan is profound and enduring.

His collected papers have inspired a wealth of research and discovery in mathematics, and many of his theories remain central to modern mathematical study. Ramanujan's work is celebrated globally, and his story has been told in books and films, most notably in the biography "The Man Who Knew Infinity. We assure our audience that we will remove any contents that are not accurate or according to formal reports and queries if they are justified.

We commit to cover sensible issues responsibly through the principles of neutrality. To report about any issues in our articles, please feel free to Contact Us. Our dedicated Editorial team verifies each of the articles published on the Biographyhost. Biography Host. Srinivasa Ramanujan Biography. Pioneering Mathematician and Memoirist Srinivasa Ramanujan Biography Srinivasa Ramanujan was a pioneering mathematician whose unique contributions to number theory and continued influence remain relevant today.

Nevasa on 17 March Four days later, Neville took him to his house on Chesterton Road in Cambridge. Ramanujan immediately began his work with Littlewood and Hardy. After six weeks, Ramanujan moved out of Neville's house and took up residence on Whewell's Court, a five-minute walk from Hardy's room. Hardy and Littlewood began to look at Ramanujan's notebooks.

Hardy had already received theorems from Ramanujan in the first two letters, but there were many more results and theorems in the notebooks. Hardy saw that some were wrong, others had already been discovered, and the rest were new breakthroughs. Littlewood commented, "I can believe that he's at least a Jacobi ", [ 95 ] while Hardy said he "can compare him only with Euler or Jacobi.

Ramanujan spent nearly five years in Cambridge collaborating with Hardy and Littlewood, and published part of his findings there. Hardy and Ramanujan had highly contrasting personalities. Their collaboration was a clash of different cultures, beliefs, and working styles. In the previous few decades, the foundations of mathematics had come into question and the need for mathematically rigorous proofs was recognised.

Hardy was an atheist and an apostle of proof and mathematical rigour, whereas Ramanujan was a deeply religious man who relied very strongly on his intuition and insights. Hardy tried his best to fill the gaps in Ramanujan's education and to mentor him in the need for formal proofs to support his results, without hindering his inspiration—a conflict that neither found easy.

Ramanujan was awarded a Bachelor of Arts by Research degree [ 97 ] [ 98 ] the predecessor of the PhD degree in March for his work on highly composite numberssections of the first part of which had been published the preceding year in the Proceedings of the London Mathematical Society. The paper was more than 50 pages long and proved various properties of such numbers.

Hardy disliked this topic area but remarked that though it engaged with what he called the 'backwater of mathematics', in it Ramanujan displayed 'extraordinary mastery over the algebra of inequalities'. At age 31, Ramanujan was one of the youngest Fellows in the Royal Society's history. He was elected "for his investigation in elliptic functions and the Theory of Numbers.

Ramanujan had numerous health problems throughout his life. His health worsened in England; possibly he was also less resilient due to the difficulty of keeping to the strict dietary requirements of his religion there and because of wartime rationing in — He was diagnosed with tuberculosis and a severe vitamin deficiency, and confined to a sanatorium.

He attempted suicide in late or early by jumping on the tracks of a London underground station. Scotland Yard arrested him for attempting suicide which was a crimebut released him after Hardy intervened. After his indian mathematician ramanujan wife, his brother Tirunarayanan compiled Ramanujan's remaining handwritten notes, consisting of formulae on singular moduli, hypergeometric series and continued fractions.

Ramanujan's widow, Smt. Janaki Ammal, moved to Bombay. Inshe returned to Madras and settled in Triplicanewhere she supported herself on a pension from Madras University and income from tailoring. Inshe adopted a indian mathematician ramanujan wife, W. Narayanan, who eventually became an officer of the State Bank of India and raised a family.

In her later years, she was granted a lifetime pension from Ramanujan's former employer, the Madras Port Trust, and pensions from, among others, the Indian National Science Academy and the state governments of Tamil NaduAndhra Pradesh and West Bengal. She continued to cherish Ramanujan's memory, and was active in efforts to increase his public recognition; prominent mathematicians, including George Andrews, Bruce C.

She died at her Triplicane residence in A analysis of Ramanujan's medical records and symptoms by D. Young [ ] concluded that his medical symptoms —including his past relapses, fevers, and hepatic conditions—were much closer to those resulting from hepatic amoebiasisan illness then widespread in Madras, than tuberculosis. He had two episodes of dysentery before he left India.

When not properly treated, amoebic dysentery can lie dormant for years and lead to hepatic amoebiasis, whose diagnosis was not then well established. While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention.

That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing. Ramanujan has been described as a person of a somewhat shy and quiet disposition, a dignified man with pleasant manners. He looked to her for inspiration in his work [ ] and said he dreamed of blood drops that symbolised her consort, Narasimha.

Later he had visions of scrolls of complex mathematical content unfolding before his eyes.

Indian mathematician ramanujan wife

Hardy cites Ramanujan as remarking that all religions seemed equally true to him. At the same time, he remarked on Ramanujan's strict vegetarianism. Similarly, in an interview with Frontline, Berndt said, "Many people falsely promulgate mystical powers to Ramanujan's mathematical thinking. It is not true. He has meticulously recorded every result in his three notebooks," further speculating that Ramanujan worked out intermediate results on slate that he could not afford the paper to record more permanently.

Berndt reported that Janaki said in that Ramanujan spent so much of his time on mathematics that he did not go to the indian mathematician ramanujan wife, that she and her mother often fed him because he had no time to eat, and that most of the religious stories attributed to him originated with others. However, his orthopraxy was not in doubt.

In mathematics, there is a distinction between insight and formulating or working through a proof. Ramanujan proposed an abundance of formulae that could be investigated later in depth. Hardy said that Ramanujan's discoveries are unusually rich and that there is often more to them than initially meets the eye. As a byproduct of his work, new directions of research were opened up.

This might be compared to Heegner numberswhich have class number 1 and yield similar formulae. One of Ramanujan's remarkable capabilities was the rapid solution of problems, illustrated by the following anecdote about an incident in which P. Mahalanobis posed a problem:. Imagine that you are on a street with houses marked 1 through n. There is a house in between x such that the sum of the house numbers to the left of it equals the sum of the house numbers to its right.

If n is between 50 andwhat are n and x? Ramanujan thought about it and gave the answer with a twist: He gave a continued fraction. The unusual part was that it was the solution to the whole class of problems. Mahalanobis was astounded and asked how he did it. The minute I heard the problem, I knew that the answer was a continued fraction.

Which continued fraction, I asked myself. Then the answer came to my mind', Ramanujan replied. His intuition also led him to derive some previously unknown identitiessuch as. InHardy and Ramanujan studied the partition function P n extensively. They gave a non-convergent asymptotic series that permits exact computation of the number of partitions of an integer.

InHans Rademacher refined their formula to find an exact convergent series solution to this problem. Ramanujan and Hardy's work in this area gave rise to a powerful new method for finding asymptotic formulae called the circle method. In the last year of his life, Ramanujan discovered mock theta functions. Although there are numerous statements that could have borne the name Ramanujan conjecture, one was highly influential in later work.

It was finally proven inas a consequence of Pierre Deligne 's proof of the Weil conjectures. The reduction step involved is complicated. Deligne won a Fields Medal in for that work. This congruence and others like it that Ramanujan proved inspired Jean-Pierre Serre Fields Medalist to conjecture that there is a theory of Galois representations that "explains" these congruences and more generally all modular forms.

Deligne in his Fields Medal-winning work proved Serre's conjecture. The proof of Fermat's Last Theorem proceeds by first reinterpreting elliptic curves and modular forms in terms of these Galois representations. Without this theory, there would be no proof of Fermat's Last Theorem. While still in Madras, Ramanujan recorded the bulk of his results in four notebooks of looseleaf 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 indian mathematician ramanujan wife result directly. Mathematician Bruce C. Berndtin 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 record the proofs in his notes.

This may have been for any number of reasons. Since paper was very expensive, Ramanujan did most of his work and perhaps his proofs on slateafter which he transferred the final results to paper. At the time, slates were commonly used by mathematics students in the Madras Presidency. He was also quite likely to have been influenced by the style of G.

Carr 's book, which stated results without proofs. It is also possible that Ramanujan considered his work to be for his personal interest alone and therefore recorded only the results. The first notebook has pages with 16 somewhat organised chapters and some unorganised material. The second has pages in 21 chapters and 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 G. WatsonB. Wilsonand Bruce Berndt. InGeorge Andrews rediscovered a fourth notebook with 87 unorganised pages, the so-called "lost notebook". The number 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 at Putney. I had ridden in taxi cab number and remarked that the number seemed to me rather a dull oneand that I hoped it was not an unfavorable omen. Immediately before this anecdote, Hardy quoted Littlewood as saying, "Every positive integer was one of [Ramanujan's] personal friends.

Generalisations of this idea have created the notion of " taxicab numbers ". That's one reason I always read letters that come in from obscure places and are written in an illegible scrawl. I always hope it might be from another Ramanujan. In his obituary of Ramanujan, written for Nature inHardy observed that Ramanujan's work primarily involved fields less known even among other pure mathematicians, concluding:.

His insight into formulae was quite amazing, and altogether beyond anything I have met with in any European mathematician. It is perhaps useless to speculate as to his history had he been introduced to modern ideas and methods at sixteen instead of at twenty-six. It is not extravagant to suppose that he might have become the greatest mathematician of his time.

What he actually did is wonderful enough… when the researches which his work has suggested have been completed, it will probably seem a good deal more wonderful than it does to-day. Hardy further said: [ ]. He combined a power of generalisation, 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 modular equations and theorems As an example, Hardy commented on 15 theorems in the first letter. Of those, the first 13 are correct and insightful, the 14th is incorrect but insightful, and the 15th is correct but misleading. When asked about the methods Ramanujan used to arrive at his solutions, Hardy said they were "arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account.

Hardy thought his achievements were greatest in algebra, especially hypergeometric series and continued fractions. It is possible that the great days of formulas are finished, and that Ramanujan ought to have been born years ago; but he was by far the greatest formalist of his time. There have been a good many more important, and I suppose one must say greater, mathematicians than Ramanujan during the last 50 years, but not one who could stand up to him on his own ground.

Playing the game of which he knew the rules, he could give any mathematician in the world fifteen. He discovered fewer new things in analysis, possibly because he lacked the formal education and did not find books to learn it from, but rediscovered many results, including the prime number theorem. In analysis, he worked on the elliptic functions and the analytic theory of numbers.

In analytic number theoryhe was as imaginative as usual, but much of what he imagined was wrong. Hardy blamed this on the inherent difficulty of analytic number theory, where imagination had led many great mathematicians astray.