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.
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. Not particularly introspective, he was never able to give a completely coherent account of how he came up with his ideas — indeed, although his religious beliefs were later downplayed by Hardy an atheist , there is evidence that Ramanujan believed that some form of divine inspiration was involved.
In any case, he seems to have been quite modest about his own abilities and scrupulously keen to acknowledge help from any other sources.
Littlewood famously remarked [2, p. I remember once going to see him when he was lying ill at Putney. I had ridden in taxi-cab No. With regard to his mathematics, its prime characteristic is its overwhelming wealth of algebraic formulae and vast computational complexity. Ramanujan was gifted with a power of calculation and symbolic dexterity unavailable to most mathematicians prior to the computer age.
He also had an uncanny ability to spot patterns that nobody knew existed. For example, from the list of partition numbers from 1 to , he deduced a number of attractive, but hitherto unknown, congruences, including. Most mathematicians would be satisfied with the mere discovery of relationships such as these, but in order to prove them Ramanujan was led to an even more stunning result.
His ability to conjure up a myriad of bizarre yet almost supernaturally accurate approximations was another overwhelming feature of his mathematics.
From his work on elliptic and modular functions came irrational expressions surprisingly close to integer values, such as. It also yielded a series of tremendously accurate approximations to , for example,.
The Hardy—Ramanujan partition formula itself was refined and improved by Hans Rademacher in the s and, as well as its utility in mathematics, now serves as a useful function in superstring theory in physics and the study of phase transitions in chemistry. Hardy was kind in giving opportunity for an Indian and to share his work.
There was a French Mathematician prodigy who died young. This Indian Mathematician is framed in that manner. Your email address will not be published. This site uses Akismet to reduce spam. Learn how your comment data is processed.
All Rights Reserved. Site by Measured Designs. Home » Publications » Mathematics Today » Srinivasa Ramanujan — : The Centenary of a Remarkable Mathematician This month marks the centenary of the death of one of the most remarkable mathematicians of the 20th century.
Figure 1: Srinivasa Ramanujan — Upon graduation from secondary school in , he was awarded a scholarship to study at the Government College in Kumbakonam, also in Tamil Nadu.
Firstly, there were theorems that, unbeknown to Ramanujan, were already known, such as the integral formula: Secondly, there were results that, while new, were interesting rather than important, for example: where and is the gamma function.
And finally, there were entirely original results that were simply astonishing, such as: These formulae, Hardy later wrote [4, part II, p. Figure 2: G. Hardy — Adapting to life in Britain was equally challenging for Ramanujan. Figure 3: Extract from a postcard sent by Ramanujan to Hardy as their work on partitions neared completion [5, p.
So for instance, the integer can be written in five different ways, namely, meaning that. If and where , , , and is a -th root of unity, then, for some , They then proceeded to show that their formula was capable of producing results of unprecedented accuracy. Even on his deathbed, he had been consumed by math, writing down a group of theorems that he said had come to him in a dream.
His collected papers were published by Cambridge University Press in Of Ramanujan's published papers — 37 in total — Berndt reveals that "a huge portion of his work was left behind in three notebooks and a 'lost' notebook. These notebooks contain approximately 4, claims, all without proofs.
Most of these claims have now been proved, and like his published work, continue to inspire modern-day mathematics.
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