he was one of the world ’s great mathematicians. Despite starting out as a relatively unknown Indian clerk, he burst into the world of mathematics like a thunderstorm, changing the future of math and securing his place in history before dying suddenly of tuberculosis at the young age of 33. Even though Ramanujan ’s life was short, his contribution to mathematics was extensive.
Do you know National Mathamatic day ( 22 December) Is celebrated in his memory?
Born, family & early life
Ramanujan was born in a poor Brahmin family on 22nd December 1887 at Erode in Tanjore district of Madras state. His father Srinivasan Ayyangar was an accountant of a cloth merchant at Kumbka Konam while his mother, Komalammal was the daughter of a petty official (Amin) in the district of Munsif ’Court at Erode.
From an early age, he was interested in mathematics and showed signs that he was extraordinarily gifted. He taught himself mathematics from books and was already engaged in an in-depth analysis of the Bernoulli number by the time he was a teenager.
He got much of his earlier education in the town of high school at Kumbka Konam. He always stood first in the class and got a scholarship. He was very much popular for his interest and extraordinary abilities in mathematics. He was so bright that he was declared “child mathematician” at the age of 12 by his teacher. By the age of 10, he was the top student, not just in the school, but in his district. By the time he was 12, he had begun the serious self-study of mathematics, working through arithmetic and geometric series and cubic equations. He discovered his own method of solving equations. Up to class IV, he almost solved all the problems of the Loney’sTrigonometry meant for the degree classes. He used to entertain his friends with theorems and formulae, with the recitation of a complete list of Sanskrit roots and with repeating the value of pi and the square root of two to any number of decimal places.
in the year 1903, when he was 15 and in the sixth form at the school, a friend of his gave him a book “carr’s synopsis of pure and Applied mathematics” from the library of the local Government college. It was this book that awakened and stimulated his genius. He verified many of the results in the book and discovered many new results of his own. Besides engaging in this original work he did not miss his regular studies and as a result, gained a place in first class in the matriculation examination of the University of Madras held in Dec 1903. This enabled him to secure Subramanian Scholarship and join the F.A (First examination in Arts) class in the Government college, Kumbka Konam. Owing to weakness in English for he gave no thoughts to anything but mathematics, he failed in his examination and lost his scholarship. He then left Kumbka Konam, first for Vizagapatam (Andhra Pradesh) and then for Madras. He resumed his studies completed his second-year course in the Pachiappa college in 1906. Unluckily he got ill at this time and also he got failed and then determined not to try again.
Marriage & Job
For the next few years, he continued his independent work in mathematics. In 1909 he was married to Janaki and it became necessary for him to find a job of permanent nature. In the course of his search for work, he was got introduced to the true love of mathematics, Diwan Bahadur R. Ramachandra Rao. For some months he was supported by Shri Ramachandra Rao. Then he accepted his appointment for the post of clerk in the office of Madras Port Trust while working on a clerk he never slackened his interest in mathematics.
He made one of the works published in the journal of the Indian Mathematics Society in 1911 at the age of 23. He wrote a long article on “Some properties of Bernoulli ‘s numbers” in the same year. In 1912 he contributed two more notes to the same journal and also several questions for solutions. Meanwhile, he began correspondence with Professor G.H Hardy, a leading mathematician of his time. In his first letter, he attached 120 theorems of his own creation.
At last in May of 1913, as the result of the help of many friends, Ramanujan was relieved for his clerical post and was given s special scholarship. Hardy made affords to bring Ramanujan to Cambridge and helped him to learn modern mathematics so as to acquaint him with all the up to date development in the field of mathematics. In 1916 he got an honorary B.A degree from the University of Cambridge. About making Ramanujan learn at Cambridge, Hardy writes;
“It was impossible to ask such as man to submit to systematic instruction to try to learn mathematics from the beginning once more. I had to try to teach him and in a measure, I succeeded through obviously I learned from him much more than he learned from me”
In the spring of 1917, Ramanujan first appears to unwell. He went to Nursing home at Cambridge in the early summer and was never out of bed for any length of time again. For a brief period, he resumed some active work, stimulated perhaps by his election to the Royal Society and Trinity Fellowship. Due to Tuberculosis he left for India and died in Chetpet; Madras on account of his disease on April 26, 1920, at the age of thirty-three.
1. Divergent series:- His first investigation in this direction was sent to professor Hardy in the form of 120 theorems in the year 1913. Commenting on the merit of these theorems Hardy wrote “I had never seen anything the least like them before. A single look at them is enough to show that they could only be written down by a mathematician of Highest class”.
2. Hypergeometric series and continued function:- He was unquestionably one of the greatest masters in the field. Commenting on this Hardy wrote “ It was his insights into algebraic formula transformation of infinite series and so forth that was most amazing. On this side, most certainly I have never met this equal and I can compare him with Euler and Jacobi”.
3.Elliptic functions:- He tried to handle elliptic function profusely. Commenting on his ability in this direction Hardy writes “Ramanujan show at his very best in the parts of Theory of Elliptic -functions allied to the Theory of partitions”.
4.partition functions:-Before Ramanujan very little was known about arithmetic properties of a partition function P(n) where n is odd or even. For the first time in1917, Hardy and Ramanujan jointly examined, the question of how large the partitions of n is when n is itself large. They gave an answer in the form of an asymptotic series and also estimated the error involved in taking a definite number of terms only.
5.Fractional Differentiation:- He gave a meaning to Eulerian second Integral for all values of n-negative, positive and fractional. In this way, he proved that the integral of (x)n-1 (e)-x =Gamma(¡) is true for all values of ¡.
6.Theory of Numbers:-Ramanujan also wrote considerable papers on the unresolved Fermat theorem that a prime number of the form 4m+1 is the sum of two squares.
Hardly recalls a meeting of Mr. Little Wood with Ramanujan. He had taken a taxi cab no. 1729 and remarked that the number seemed to him rather a dull one
‘No’ Ramanujan replied, “It is a very interesting number, it is the smallest number expressible as a sum of two cubes in two different ways”
That ‘s why this number is also known as ‘Ramanujan number’.
In this way, one can judge the merit and competency of Ramanujan as a first-rate mathematician. Although he had not got enough opportunity for college education in the subject of Mathematics and most of his time was spent either in struggling for the means of livelihood for fighting his ill health he contributed a lot in the field of mathematics by showing his profound and invincible originality. His work has left a memorable imprint on mathematical thoughts.
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