May 30, 2021

# Srinivasa Ramanujan-Essay for 5th to 8th Std Students

**Ramanujan** was born in December 22, 1887 in a poor Brahmin family at Erode in Madras district. He was educated in a village near Kumbakonam. He initially studied trigonometry himself, and at the age of 14, he presented the theorems of jinn and cosines predicted by Leonard Euler (1707–83). In 1903, he was awarded the G.I.S.Carr had the opportunity to study Synopsis of Elementary Results in Pure and Applied Mathematics. In this book There were 6,000 theorems, all before 1860.

This book gave impetus to Ramanujan’s sharp intellect. He checked the theorems in Carr’s texts. But before that he had no contact with good standard texts in mathematics, so he had to do basic research himself every time. In this work he also discovered many new Algorithms. In 1904, he was admitted to the Government College, Kumbakonam and received a scholarship. His professor P. V. Sheshu Iyer noticed Ramanujan’s extraordinary mastery of mathematics and under his guidance Ramanujan continued his reading and research, but in the absence of continuous study of mathematics, he neglected English language and other subjects and failed the examination, thus closing his scholarship.

**He then went first to Visakhapatnam and then to Madras.** In 1906, he appeared for the exam again but failed and so he gave up trying to sit for the exam again. For the next few years he had no definite business But he continued his independent work in mathematics.

**Srinivasa Ramanujan was an Indian mathematician **Although he was probably not officially trained in pure mathematics, he made significant contributions to mathematical analysis, numerical theory, infinite series, and continuous subdivisions, including solutions to problems that were considered unresolved .What he had to show them was a very new, unusual story, and moreover presented in unusual ways Seeking out mathematicians who could better understand his work, in 1913 he began working with the postman and English mathematician G. H. Hardy at the University of Cambridge, England. Seeing Ramanujan’s work as unusual, Hardy arranged for him to go to Cambridge. In a letter, Hardy noted that Ramanujan has produced new scholars, including some who have “completely defeated me; I have never seen anything like it”, as well as other recently proven but highly developed results. During his short life, Ramanujan independently collected nearly 3,900 results. Many were completely sound; his original and very unusual results, such as the Ramanujan prime, the work of the Ramanujan theta, the formulas for dividing and performing theta functions, opened up new workplaces and encouraged dozens of ongoing research. Almost all of his requests have been found to be valid. The Ramanujan Journal, a scientific journal, was set up to publish work on all mathematical areas influenced by Ramanujan, and his manuscripts — containing summaries of his published and unpublished results — have been analyzed and studied for decades since his death as a new source of mathematical ideas.

Then he got married in 1909 After marriage, Ramanujan underwent hydrocele testis. After his successful surgery, Ramanujan sought employment. He lived in a friend’s house while going from house to house around Madras seeking the position of priest. To make money, he taught Presidency College students who were preparing for their F.A. In 1912, Ramanujan moved with his wife and mother to a house on Saiva Muthaiah Mudali street, George Town, Madras, where they stayed for a few months.

and while looking for a livelihood, He received a letter of recommendation from Ramchandra Rao, the District Collector of Nellore. Since Ramchandra Rao himself was interested in Mathematics and in view of Ramanujan’s work, he found it unsuitable to work as a clerk, so he sent Ramanujan back to Madras. He helped his character for some time and also tried to get a scholarship. After these attempts failed, in 1912, Ramanujan was able to get a job in the office of the Madras Port Trust Board In a letter dated 9 February 1912, **Ramanujan wrote:** 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.A. 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. I can say I am quite confident I can do justice to my work if I am appointed to the post. 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. W. Middlemast, a mathematics professor at the Presidency College, who wrote that Ramanujan was “a young man of quite exceptional capacity in Mathematics”. Three weeks after he applied, on 1st March, Ramanujan learned that he had been accepted as a Class III, Grade IV accounting clerk, making 30 rupees per month. Although Hill did not offer to take Ramanujan on as a student, he gave thorough and serious professional advice on his work. With the help of friends, Ramanujan drafted letters to leading mathematicians at Cambridge University. It was at this time that he began publishing his writings in the Journal of the Indian Mathematical Society. The first of these essays was on Bernoulli numerals, followed by series and infinite multiplication and geometric constructs to find the value of..

Encouraged by some friends interested in his mathematical work, Ramanujan began correspondence with Sir Godfrey Harold Hardy, a professor of mathematics at Cambridge. In the first letter he wrote about his research on the distribution of prime numbers, as well as over a hundred theorems he had discovered in various branches of mathematics. Hardy was impressed by the correspondence and invited Ramanujan to come to Cambridge, but he refused on religious grounds and was offered a two-year scholarship from the University of Madras.

Hardy’s colleague E.H. When Neville came to Madras, he tried to get Ramanujan’s consent and in 1914 Ramanujan was admitted to Trinity College, Cambridge. Hardy and J. E. Under Littlewood’s guidance, Ramanujan developed rapidly. With his help, Ramanujan’s essays were published in English and other European journals. During his five years in England, 21 of his essays were published, many of them in collaboration with Hardy. Apart from this, in the Journal of the Indian Mathematical Society, his 12 essays were published. Ramanujan’s work was well developed due to his experience at Cambridge University, but this time his attitude was somewhat strengthened.

So he continued his work in the same way as before, in a way that gave more importance to intuition than causation. According to Hardy, if Ramanujan’s Natural Intelligence had been known earlier, he would have become a relatively Great Mathematician.

**Ramanujan’s knowledge of mathematics was amazing** and most of it was acquired by him. Although he had no idea what had been developed before about conventional fractions, his proficiency in the subject was unique compared to other mathematicians of the time. He himself researched and found the Theory of Elliptical integration [⟶ differentiation and integration], hyperbolic series [⟶ series], Riemann series, equations of zeta function and their own theory of divergent series. On the other hand, due to lack of systematic training in mathematics or lack of opportunity to use a good quality library, their knowledge was equally amazing. His idea of mathematical proof was very ambiguous.

Although many of his theorems on prime numbers show the brilliance of his intellect, he was later proved wrong. In his first essay on realism in England, he gave various methods for calculating the approximate value of (a value close to the true value). He then worked specifically on the properties of the number division function, which is considered to be very valuable. His work in number theory has recently been shown to be very useful in solving some of the problems in physics and computer science. His work is still being studied by mathematicians from various countries. On the occasion of his birth centenary, seminars and conferences were organized in 1987 in many countries to discuss his work.

Towards the end of 2012, researchers continued to discover that mere comments in his writings about “easy places” and “similar effects” of certain findings were profound and subtle effects of numbers that remained unresolved until nearly a century after his death. He became one of the youngest boys in the Royal Society and became the only second member of India, and was the first Indian to be appointed as the Yellow of Trinity College, in Cambridge. In his early works, Hardy argued that one look was enough to show that they could only be written by a highly accomplished mathematician, comparing Ramanujan with such mathematicians as Euler and Jacobi. In 1919, poor health — now believed to be liver amoebiasis — forced Ramanujan back to India, where** he died in 1920 at the age of 32**. His last letters to Hardy, written in January 1920, indicate that he was still developing new mathematical and theoretical concepts. His “lost diary”, containing the findings of the last year of his life, sparked great excitement among the figures when it was rediscovered in 1976. A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, Ramanujan praised his great mathematical skills in the deity, and said that the mathematical knowledge** he displayed was revealed to him by his family goddess Namagiri Thayar.** **He once said, “Numbers to me mean nothing but to express the mind of God’’.**

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