Srinivasa Ramanujan – World Famous Mathematical Genius

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Ramanujan was born in 1887 in Erode, the native place of his mother, but his family lived at Sri Sarangapani Swami East Sannidhi Street in the town of Kumbakonam, which was the scene of his early life and career. He belonged to a poor Sri Vaishnava Brahmin family. His father was an accountant in a cloth shop and his mother the daughter of a court bailiff. There is nothing extraordinary about his parents or his ancestors, which could be said to have been inherited by him to account for the greatness that awaited him later in life.

He was put in a pail school till his seventh year and from there he was sent to the Town High School where he studied from 1894 to 1903. Even during this period, indications in the remarkable powers were not wanting. He stood first in the whole of the Tanjore District in the Primary Examination. While in the III From he questioned the teacher whether the quotient could be unity in the case of zero by zero as in the case of other numbers divided by in the themselves-a problem which will be nowadays introduced only in the collegiate course. He had studied not only the entire High School mathematics but mastered the College text books as well. At twelve he could solve unaided, every problem in Loney’s Trigonometry, Part II. He borrowed, through a friend from this College, Carr’s Synopsis of Pure Mathematics, containing 6165 formulae without proofs in Algebra, Trigonometry, Geometry and Calculus and worked out all of them, each being a piece of research by itself. This opened up in him a vista to all higher branches of Mathematics. In this period his teachers and classmates were struck by his amazing powers and he readily helped one and all including even undergraduates who came to him for getting difficult problems solved.

The first public recognition of his extraordinary powers was on the occasion of the Annual Prize distribution in 1904. He was the recipient of Sri K. Ranganatha Rao’s prize for Mathematics, when Sri Krishna Iyer, the reputed Headmaster of the Town High School introduced him Sri V. Krishnaswamy Iyer, the President of the function, and to the distinguished audience in such terms as these “Here is a student who, my mathematics assistant says, has displayed in his answer papers a remarkable ability and deserved many more marks than even the maximum itself.” He passed the Matriculation examination in 1904. Unfortunately he was detained on the score that he obtained only three marks out of hundred in English, with the result that he lost the scholarship he had earned.

I matriculated in 1904 and was his classmate at college for two years. We used to sit together in the class and I developed a friendship with him which continued till his death. I had thus an opportunity of observing his powers somewhat at close quarters. The goddess of number seemed to dance before him and unravel to him her mysteries without reserve. He could repeat prime numbers up to a crore. He taught me the method of constructing magic squares. He was at that time going through a book on Integral Calculus which he had taken from the library. On hearing this a professor who wanted the book for his use asked him to return it with the remark that he was doing ‘aimless things’ without attending to class work. He would jump from Arithmetic to Algebra and from Algebra to Trigonometry and so on to higher mathematics and evolve a theorem or formula of general application. In the senior F. A. Class we were put together in the mathematics section under Mr. P. V. Seshu Iyer, who later on became Principal of the College. Strangely enough I was the monitor of the class, though by virtue of his talents he deserved that post. He was quite unmindful of what was going on around him being preoccupied with his own researches and reducing them to writing and incorporating them in note books after note books. He had no inclination whatsoever for either following the class lessons or taking any interest in any subject other than Mathematics. By this time Mr. P. V. Seshu Iyer who had conscious of Ramanujans’s innate powers let him alone while other students including myself were asked to do home exercise, to work problems on the board and to write impositions, a rare punishment nowadays even in the High School, not to speak of the College Classes. It may be noted that the professor encouraged him to solve problems in the mathematical journals like the London Mathematical Gazette.

After some break in his studies in this College, Ramanujan joined Pachayappa’s College, Madras. He failed in the F. A. Examination of 1907. This was a setback in his career, as he could not get a job unless he possessed a University diploma. The university with its water-tight system of examinations and rigid courses of study is not a congenial soil for the growth of genius like that of Ramanujan. Oppressed by ‘child penury’s and finding it impossible to earn his livelihood he had to seek some job which would sustain him and at the same time allow his leisure to carry on his research. In 1909 he was married and the burden of maintaining his family and his poor aged parents added to his troubles and difficulties. He was conscious that he had something new to give to the world and he yearned for any help he could get for having his papers printed and published. Nowhere could he find any encouragement. I have heard of an instance where he had a rebuff from a mathematics professor, who remarked that unless he passed his B. A. Degree there was no hope for him. Fortunately for him, he soon got in touch with reputed mathematicians of the day, who were destined to play an important role in shaping his future career Mr. V. Ramaswamy Iyer, the founder of the Indian Mathematical Society, to whom Ramanujan went for a clerical post, found out on perusing his note-books that a clerical job would stifle the genius in him. He therefore sent him to Madras with notes of introduction to Mr. P. V. Seshu Tyer and some other professors. After serving as a temporary clerk in the Accountant General’s office Ramanujan sought an interview with Mr. Ramachandra Rao, the then Collector of Nellore, who has given us a vivid account of his first interview with him. Mr. Rao sent him Madras, offering him a monthly allowance with a note to Sir Francis Spring, Chairman of the post Trust, to take interest in him. He served as a clerk in the Post Trust office for some time on a salary of Rs. 30/- per month. Mr. Narayanaswamy Iyer of that office and Sir Francis Spring were impressed with his abilities and encouraged him in everyway possible. At that time G. T. Walker F. R. S. fellow of Trinity College, Cambridge, happened to visit Madras and both Sir Francis Spring and Mr. Narayanaswamy Iyer took this opportunity to bring Ramanujan’s works to his notice. At his instance, a scholarship of 75/- per month from the University of Madras was offered to him. This was in the year 1913 and from this he was able to pursue his researches without interruption and without the trouble of toiling for his livelihood.

It was during this period that the historic contact of Ramanujan with Professor Hardy, Fellow of Trinity College, Cambridge, occurred, and proved to be of momentous importance in the whole of Ramanujan’s career. A paper entitled Orders of Infinity’ had been published by Mr. Hardy. Ramanujan wrote to Mr. Hardy on 16th January 1913 a letter in which he made a reference to this ‘……………… on page 36…….. I find a statement that no definite expression has found yet for the number of prime numbers less than any given number. I have found an expression which very nearly approximates the real number, the error being negligible. Being poor, if you are convinced that there is anything of value, I would like to have my theorems published….’ Along with this letter and the solution, he sent papers containing his discoveries and solutions to problems which baffled the intellect of the best mathematicians of the time. Mr. Heardy showed the papers to the other Professors of the University and they all decided that he should he brought to England for affording him scope for the full display of his genius so that he might contribute his own share to the advancement of mathematical knowledge. Early in 1914, N. H. Neville, a Fellow of Trinity College, Cambridge, happened to come to Madras to deliver a course of lectures. Mr. Hardy had instructed him to persuade Ramanujan to go to England. His mother’s caste scruples stood in my way of Ramanujan’s acceptance of the officer; but eventually, prompted, it is said, by the family deity, Namagiri, whom she saw in her vision one night, she consented to her son proceeding to England. Mr. Neville got him a University scholarship of 250/- a year, tenable for two years in England.

Ramanujan set sail for England in March 1914 and was admitted to the University College. Cambridge, which supplemented his scholarship by an award of Rs. 60/- a year. He remained in England from 1914 to 1919. There under guidance of Prof. Hardy, Mr. Littlewood and other he showed great improvement in his studies and acquainted himself fully with up-to-date material then available in the field of Mathematics and was able to direct his researches in channels unchartered by predecessor. He published a number of original papers embodying his researches and containing new formulae and theorems which were highly admired. The results, however, were arrived at by him by a process of intuition and so he was not able to supply the proof himself but left them to be worked out by the professors of the Cambridge University. His mastery of number was marvelous. “Every positive integer was a personal friend of Ramanujan,” says Prof. Littlewood.

His wonderful researches won the admiration of the world of Science. On the 28th of February 1918, he was elected a Fellow of the Royal Society, the greatest honour that England could confer on any of her scientists. Ramanujan was the first Indian to secure that distinction and the only Indian F. R. S. in mathematics so far. On the 13th October he was elected a fellow of Trinity College a prize fellowship of 250/- a year with no duties or conditions attached.

While thus honours were heaped upon him and while he was at the height of his renown and material advancement he had a fatal attack of tuberculosis. He was brought to Madras where he died at the early age of thirty-three in April 1920. THE LONDON TIMES’ Obituary read ‘there is something peculiarly sad in the spectacle of a genius dying tasted, young, dying with the first sweets of recognition and success tasted, but before the full realization of the powers that lie latent within.’

His personal appearance is best described in the words of Mr. Ramachandra Rao in his account of his interview with Ramanujan; “A short uncouth figure, stout, unshaved, not overclean, but with the conspicuous feature shining eyes.” His dress was of the simplest kind. Clad in a dhoti and with a towel on, he used to call on me at my residence, on his way to house of a relative of mine to whom he was giving tuition for a remuneration of Rs. 7/- a month. Later on, at Madras, friends taught him to wear a decent dress, especially on the eve of his departure for England Simple, unostentatious, innocent like a child, unconscious of his own genius, and without pride or vanity, he combined in himself rare gifts with an exemplary character. His knowledge of the world was poor and he was not able to judge men or things properly. I had occasions to visit him at ‘Summer’ house in Triplicane, when he would open his note books and explain to me intricate theorems and formulae with in the least suspecting that they were beyond my understanding or knowledge. His orthodoxy was of an extreme type. He was a strict vegetarian, observed all caste rules punctiliously and cooked his own food during his stay in England.

In religion he had a firm belief in the existence of a supreme being and he practiced it by trying to lead a pure and pious life. He did not know much of philosophy. He used to talk about God and our conduct in life in a mathematical way. He told me that we should regulate our lives to reach Godhead by approximating to the upright path, even as an asymptote approaches along the curve and finally touches it at infinity. A peculiar feature in his character was his utmost credulousness. This is instanced by his adoration of one Sathyapriya Rao, the then gymnastic instructor of the Town High School, who had a mental aberration. The latter used to gaze at the sun and blurt out some nonsense of which nothing could be made out, but which struck Ramanujan as extraordinary and which he attributed to his occult powers. He himself believed that Goddess Namagiri inspired him in his dreams with formulae which, rising from bed, he would jot down and verify. Besides mathematics, the only subject in which he took some interest was palmistry. On seeing the lines on his palms he used to tell his friends that his span of life was short and that it would not extend beyond 35 years or so a prophecy, which, alas! proved to be too true.

He was a dutiful son his parents and had always cared for the welfare of the members of his family. He set apart for the due maintenance of his family during his absence in England a decent portion of his scholarship a mount which was given every month by the University as directed by him.

Though estimate may differ as regards the nature and importance of his work, in his profound originality and the processes by which he arrived at mathematical truths, he stands unique and has few rivals in the field. In this connection, the tribute paid to him by Prof. Hardy is worth quoting. “He is beyond question the best mathematician of the modern times………..He will always be rather eccentric in his choice of subjects and methods of dealing with them…… But of his extraordinary gifts there can be no question. In some ways he is the most remarkable mathematician I have ever known”.

A full account of his discoveries and papers published by him is beyond the scope of the present article and must be reserved for a separate treatise.

A brief reference to some of his important contributions my not be out of place. Ramanujan;s work lay mainly in the theory of numbers, one of the oldest branches of Mathematics. Here a brilliant genius could discover a new result by repeated experiment with numbers. But even if a guessed formula is true in a large number of cases where it has been tested, it would be no proof but only a conjecture. Ramanujan’s work contains many proof and conjectures. He had an uncanny insight into algebraic form and took up some of the most difficult problems, which mathematics in various countries had taken up in different times, but quite independently and in ignorance of what they had done. It was but natural that many of his guesses should have been proved true and some wrong, but even the wrong guesses revealed the brilliance of his genius. Besides the Theory of Numbers, special mention may be made of his theorems regarding series, Elliptic functions, Theory of Partitions, modular relation and mock theta functions.

It is to be fervently hoped and prayed on this occasion of the centenary of the College that more mathematicians of the type of Ramanujan may be produced by our Alma Mater and that the city of Kumbakonam may maintain its reputation of being the Cambridge of South Indian’.

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