Indian mathematicians srinivasa ramanujan biography

He got the job in as an accounting clerk with the Madras Port Trust and his financial condition improved. His intelligence and genius slowly gained recognition and he began a correspondence in with the British mathematician Godfrey H. Hardy that led to a special scholarship from the University of Madras and a grant from Trinity College, Cambridge.

He travelled to England inwhere Hardy tutored him. He collaborated with him on some research work. He brought his notebooks from India which were filled with thousands of identities, equations, and theorems that he discovered for himself in the years to Some were discovered by earlier mathematicians; some through inexperience, were mistaken, and many were entirely new.

He had very little formal training in mathematics. He spent around 5 years in Cambridge collaborating with Hardy and Littlewood and published part of his findings there. He worked in several areas including the Riemann series, the elliptic integrals, hypergeometric series, the functional equations of the zeta function, and his own theory of divergent series, in which he discovered a value for the sum of such series using a technique he invented and came to be known as Ramanujan summation.

He also made several advances in England, mainly in the partition of numbers the various ways that a positive integer can be expressed as the sum of positive integers; e. His papers were published in English and European Journals. He was elected to the Royal Society of London in and became the second Indian. He was also elected "for his indian mathematicians srinivasa ramanujan biography in elliptic functions and the Theory of Numbers.

He is also known for Landau—Ramanujan constant, Mock theta functions, Ramanujan conjecture, Ramanujan prime, Ramanujan—Soldner constant, Ramanujan theta function, Ramanujan's sum, Rogers—Ramanujan identities, Ramanujan's master theorem, and Ramanujan—Sato series. He contracted tuberculosis in Ramanujan initially developed his own mathematical research in isolation.

According to Hans Eysenck"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". Hardy at the University of CambridgeEngland. Recognising Ramanujan's work as extraordinary, Hardy arranged for him to travel to Cambridge.

In his notes, Hardy commented that Ramanujan had produced groundbreaking new theoremsincluding some that "defeated me completely; I had never seen anything in the least like them before", [ 5 ] and some recently proven but highly advanced results. During his short life, Ramanujan independently compiled nearly 3, results mostly identities and equations.

As late asresearchers 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. Inill health—now believed to have been hepatic amoebiasis a complication from episodes of dysentery many years previously —compelled Ramanujan's return to India, where he died in at the age of His indian mathematicians srinivasa ramanujan biography letters to Hardy, written in Januaryshow that he was still continuing to produce new mathematical ideas and theorems.

His " lost notebook ", containing discoveries from the last year of his life, caused great excitement among mathematicians when it was rediscovered in Ramanujan literally, "younger brother of Rama ", a Hindu deity [ 12 ] was born on 22 December into a Tamil Brahmin Iyengar family in Erodein present-day Tamil Nadu. When Ramanujan was a year and a half old, his mother gave birth to a son, Sadagopan, who died less than three months later.

In DecemberRamanujan contracted smallpoxbut recovered, unlike the 4, others who died in a bad year in the Thanjavur district around this time. He moved with his mother to her parents' house in Kanchipuramnear Madras now Chennai. His mother gave birth to two more children, in andboth of whom died before their first birthdays. On 1 OctoberRamanujan was enrolled at the local school.

He did not like school in Madras, and tried to avoid attending. His family enlisted a local constable to make sure he attended school. Within six months, Ramanujan was back in Kumbakonam. Since Ramanujan's father was at work most of the day, his mother took care of the boy, and they had a close relationship. From her, he learned about tradition and puranasto sing religious songs, to attend pujas at the temple, and to maintain particular eating habits—all part of Brahmin culture.

Just before turning 10, in Novemberhe passed his primary examinations in English, Tamilgeography, and arithmetic with the best scores in the district. A child prodigy by age 11, he had exhausted the mathematical knowledge of two college students who were lodgers at his home. He was later lent a book written by S. Loney on advanced trigonometry.

By 14, he received merit certificates and academic awards that continued throughout his school career, and he assisted the school in the logistics of assigning its 1, students each with differing needs to its approximately 35 teachers. Ramanujan was shown how to solve cubic equations in He would later develop his own method to solve the quartic.

Inhe tried to solve the quinticnot knowing that it was impossible to solve with radicals. Carr 's collection of 5, theorems. Ranganatha Rao prize for mathematics by the school's headmaster, Krishnaswami Iyer. Iyer introduced Ramanujan as an outstanding student who deserved scores higher than the maximum. There, he passed in mathematics, choosing only to attempt questions that appealed to him and leaving the rest unanswered, but performed poorly in other subjects, such as English, physiology, and Sanskrit.

Without an FA degree, he left college and continued to pursue independent research in mathematics, living in extreme poverty and often on the brink of starvation. Inafter a meeting between the year-old Ramanujan and the founder of the Indian Mathematical SocietyV. Ramaswamy AiyerRamanujan began to get recognition in Madras's mathematical circles, leading to his inclusion as a researcher at the University of Madras.

On 14 JulyRamanujan married Janaki Janakiammal; 21 March — 13 April[ 38 ] a girl his mother had selected for him a year earlier and who was ten years old when they married. Ramanujan's father did not participate in the marriage ceremony. Inshe and Ramanujan's mother joined Ramanujan in Madras. After the marriage, Ramanujan developed a hydrocele testis.

In Januarya doctor volunteered to do the surgery at no cost. After his successful surgery, Ramanujan searched for a job. He stayed at a friend's house while he went from door to door around Madras looking for a clerical position. To make money, he tutored students at Presidency College who were preparing for their Fellow of Arts exam.

In lateRamanujan was sick again.

Indian mathematicians srinivasa ramanujan biography: Indian mathematician whose contributions to

He feared for his health, and told his friend R. Radakrishna Iyer to "hand [his notebooks] over to Professor Singaravelu Mudaliar [the mathematics professor at Pachaiyappa's College] or to the British professor Edward B. Ross, of the Madras Christian College. InRamanujan met deputy collector V. Ramaswamy Aiyerwho founded the Indian Mathematical Society.

As Aiyer later recalled:. I was struck by the extraordinary mathematical results contained in [the notebooks]. I had no mind to smother his genius by an appointment in the lowest rungs of the revenue department. Aiyer sent Ramanujan, with letters of introduction, to his mathematician friends in Madras. Ramachandra Raothe district collector for Nellore and the secretary of the Indian Mathematical Society.

Ramanujan mentioned a correspondence he had with Professor Saldhana, a notable Bombay mathematician, in which Saldhana expressed a lack of understanding of his work but concluded that he was not a fraud. Rajagopalachari tried to quell Rao's doubts about Ramanujan's academic integrity. Rao agreed to give him another chance, and listened as Ramanujan discussed elliptic integralshypergeometric seriesand his theory of divergent serieswhich Rao said ultimately convinced him of Ramanujan's brilliance.

Rao consented and sent him to Madras. He continued his research with Rao's financial aid. One of the first problems he posed in the journal [ 30 ] was to find the value of:. He waited for a solution to be offered in three issues, over six months, but failed to receive any. At the end, Ramanujan supplied an incomplete [ 59 ] solution to the problem himself.

On page of his first notebook, he formulated an equation that could be used to solve the infinitely nested radicals problem. One property he discovered was that the denominators of the fractions of Bernoulli numbers sequence A in the OEIS are always divisible by six. He also devised a method of calculating B n based on previous Bernoulli numbers.

One of these methods follows:. In his page paper "Some Properties of Bernoulli's Numbers"Ramanujan gave three proofs, two corollaries and three conjectures. As Journal editor M. Narayana Iyengar noted:. Ramanujan's methods were so terse and novel and his presentation so lacking in clearness and precision, that the ordinary [mathematical reader], unaccustomed to such intellectual gymnastics, could hardly follow him.

Ramanujan later wrote another paper and also continued to provide problems in the Journal. He lasted only a few weeks. Sir, I understand there is a clerkship vacant in your office, and I beg to apply for the same. I have passed the Matriculation Examination and studied up to the F. I have, however, been devoting all my time to Mathematics and developing the subject.

I can say I am quite confident I can do justice to my work if I am appointed to the indian mathematicians srinivasa ramanujan biography. I therefore beg to request that you will be good enough to confer the appointment on me. Attached to his application was a recommendation from E. Middlemasta mathematics professor at the Presidency Collegewho wrote that Ramanujan was "a young man of quite exceptional capacity in Mathematics".

Ramanujan's boss, Sir Francis Springand S. Narayana Iyer, a colleague who was also treasurer of the Indian Mathematical Society, encouraged Ramanujan in his mathematical pursuits. Middlemast tried to present Ramanujan's work to British mathematicians. Hill of University College London commented that Ramanujan's papers were riddled with holes. With the help of friends, Ramanujan drafted letters to leading mathematicians at Cambridge University.

The first two professors, H. Baker and E. Hobsonreturned Ramanujan's papers without comment. Hardywhom he knew from studying Orders of Infinity The first result had already been determined by G. Bauer in The second was new to Hardy, and was derived from a class of functions called hypergeometric serieswhich had first been researched by Euler and Gauss.

Hardy found these results "much more intriguing" than Gauss's work on integrals. Littlewoodto take a look at the papers.

Indian mathematicians srinivasa ramanujan biography: Srinivasa Ramanujan.

Littlewood was amazed by Ramanujan's genius. After discussing the papers with Littlewood, Hardy concluded that the letters were "certainly the most remarkable I have received" and that Ramanujan was "a mathematician of the highest quality, a man of altogether exceptional originality and power". Nevillelater remarked that "No one who was in the mathematical circles in Cambridge at that time can forget the sensation caused by this letter On 8 FebruaryHardy wrote Ramanujan a letter expressing interest in his work, adding that it was "essential that I should see proofs of some of your assertions".

To supplement Hardy's endorsement, Gilbert Walkera former mathematical lecturer at Trinity College, Cambridgelooked at Ramanujan's work and expressed amazement, urging the young man to spend time at Cambridge. Hanumantha Rao, a mathematics professor at an engineering college, invited Ramanujan's colleague Narayana Iyer to a meeting of the Board of Studies in Mathematics to discuss "what we can do for S.

While he was engaged as a research student, Ramanujan continued to submit papers to the Journal of the Indian Mathematical Society. In one instance, Iyer submitted some of Ramanujan's theorems on summation of series to the indian mathematicians srinivasa ramanujan biography, adding, "The following theorem is due to S. Ramanujan, the mathematics student of Madras University.

Ross of Madras Christian Collegewhom Ramanujan had met a few years before, stormed into his class one day with his eyes glowing, asking his students, "Does Ramanujan know Polish? Working off Giuliano Frullani's integral theorem, Ramanujan formulated generalisations that could be made to evaluate formerly unyielding integrals. Hardy's correspondence with Ramanujan soured after Ramanujan refused to come to England.

Hardy enlisted a colleague lecturing in Madras, E. Neville, to mentor and bring Ramanujan to England. Ramanujan apparently had now accepted the proposal; Neville said, "Ramanujan needed no converting" and "his parents' opposition had been withdrawn". Ramanujan departed from Madras aboard the S. 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 indian mathematicians srinivasa ramanujan biography 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. The book, published inwas of course well out of date by the time Ramanujan used it. By Ramanujan had begun to undertake deep research. He began to study the Bernoulli numbersalthough this was entirely his own independent discovery.

Ramanujan, on the strength of his good school work, was given a scholarship to the Government College in Kumbakonam which he entered in However the following year his scholarship was not renewed because Ramanujan devoted more and more of his time to mathematics and neglected his other subjects. Without money he was soon in difficulties and, without telling his parents, he ran away to the town of Vizagapatnam about km north of Madras.

He continued his mathematical work, however, and at this time he worked on hypergeometric series and investigated relations between integrals and series. He was to discover later that he had been studying elliptic functions. In Ramanujan went to Madras where he entered Pachaiyappa's College. His aim was to pass the First Arts examination which would allow him to be admitted to the University of Madras.

He attended lectures at Pachaiyappa's College but became ill after three months study. He took the First Arts examination after having left the course. He passed in mathematics but failed all his other subjects and therefore failed the examination. This meant that he could not enter the University of Madras. In the following years he worked on mathematics developing his own ideas without any help and without any real idea of the then current research topics other than that provided by Carr's book.

Continuing his mathematical work Ramanujan studied continued fractions and divergent series in At this stage he became seriously ill again and underwent an operation in April after which he took him some considerable time to recover. He married on 14 July when his mother arranged for him to marry a ten year old girl S Janaki Ammal. Ramanujan did not live with his wife, however, until she was twelve years old.

Ramanujan continued to develop his mathematical ideas and began to pose problems and solve problems in the Journal of the Indian Mathematical Society. He devoloped relations between elliptic modular equations in After publication of a brilliant research paper on Bernoulli numbers in in the Journal of the Indian Mathematical Society he gained recognition for his work.

Despite his lack of a university education, he was becoming well known in the Madras area as a mathematical genius. In Ramanujan approached the founder of the Indian Mathematical Society for advice on a job. After this he was appointed to his first job, a temporary post in the Accountant General's Office in Madras. It was then suggested that he approach Ramachandra Rao who was a Collector at Nellore.

Ramachandra Rao was a founder member of the Indian Mathematical Society who had helped start the mathematics library. He writes in [ 30 ] :- A short uncouth figure, stout, unshaven, not over clean, with one conspicuous feature-shining eyes- walked in with a frayed notebook under his arm. He was miserably poor. He opened his book and began to explain some of his discoveries.

I saw quite at once that there was something out of the way; but my knowledge did not permit me to judge whether he talked sense or nonsense. I asked him what he wanted. He said he wanted a pittance to live on so that he might pursue his researches. Ramachandra Rao told him to return to Madras and he tried, unsuccessfully, to arrange a scholarship for Ramanujan.

In Ramanujan applied for the post of clerk in the accounts section of the Madras Port Trust. 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. Ken Ono ultimately showed that a mock modular form could be computed just as Ramanujan predicted.

It was found as the output of mock modular forms shoot off to enormous numbers, the corresponding ordinary modular form expand at a similar rate and thus their difference is a relatively small number. Expansion of mock modular forms is now used to compute the entropy, or level of disorder, of black holes.

Indian mathematicians srinivasa ramanujan biography: Srinivasa Ramanujan Aiyangar (22

Thus even through black holes were virtually unknown during his time, Ramanujan was able to do mathematics which may unlock their secret. What is plus and minus infinity, he used in his theta function? Infinity in two opposite directions? Srinivasa Ramanujan. Ramanujan formula for estimating the value of Pi. Robert Langlands — Founder of the Langlands program.

Godfrey Harold Hardy — Who collaborated with Ramanujan on several projects. Ramanujan theta function. Do not sell my personal information. Manage consent. Necessary Necessary. It does not store any personal data. Functional Functional. Performance Performance. Analytics Analytics.