A job in the Madras Port Trust really made Ramanujan free from all financial worries.Now he devoted much of his time to mathematics.As a result,his first research paper was also published in the Indian Mathematical Society(Volume 111,1911).Similarly,another research paper was also published in the December edition in 1911,its subject was,’Some Properties of Bernoulli’s Numbers.’ Two more papers appeared in 1912.
During this period Ramanujan was also given tuition to some college level students,these students were from B.A.Mathematics and M.A Mathematics.Ramanujan was teaching them maths using various methods,he also showed them some of his own formulas which could be used to solve mathematical sums even more easily.These colleges students used to call Ramanujan a wizard of mathematics.
Professor P.V.Seshu Aiyer,who had great confidence in Ramanujan’s ability,suggested that he correspond with G.H.Hardy,a fellow of Trinity College,Cambridge,England.Ramanujan wanted to show his latest works to Professor G.H.Hardy,therefore he wrote a letter to Professor Hardy.Here is the text of the original letter written by Ramanujan to Professor G.H.Hardy:-
” Dear sir,
I beg to introduce myself to you as a clerk in the Accounts Department of the Post Trust Office at Madras of a salary 20 pounds per annual.I am now about 23 years of age.I have had no university education but i have undergone the ordinary school course.After leaving school I have been employing the spare time at my disposal to work at mathematics.I have not trodden through the conventional regular course which is followed in a university course,but i am striking out a new path for myself.I have made a special investigation of divergent series in general and the result I get are termed by the local mathematicians as ‘Starling’.
Just as in elementary mathematics you give a meaning to an when n is negative and fractional to confirm to the law which holds when n is a positive integer,similarly the whole of my investigations proceed on giving a meaning to Eularian Second Integral for all values of n.My friend who have gone through the regular course of university education told me that(vide separate piece of paper for mathematical signs) is true only when n is positive.They say that this integral relation is not true when n is negative.Supposing this is true only for positive values of n and also supposing the definition(vide separate piece of paper for mathematical signs) to be universally true,I have given meaning to these integral.My whole investigations are based upon this and i have been developing this to a remarkable extent so much so that the local mathematician are not able to understand me in my higher flights.
Very recently i came across a tract published by you styled Orders of Infinity in page 36 of which I find a statement that no definite_expression has been as yet found for the numbers of prime numbers less then any given number.I have found an expression which very nearly approximates to the real result,the error being negligible.I would request you to go through the enclosed papers.Being poor if you are convinced that there is anything of value i would like to have my theorems published.I have not given the actual investigations nor the expression that I get but i have indicated the lines on which i proceed.Being inexperienced,I would very highly value any advice you give me.Requesting to be excused for the trouble I give you,I remain,dear Sir,
Yours truly,
S.Ramanujan
This letter of Ramanujan’s created great sensation among the scholars at Cambridge.Professor Hardy was stunned at seeing these writings of an unknown Indian clerk.Professor Hardy was surprised,as he had never seen before such examples of highly sophisticated and well written mathematics.He was sure they could only have been written by a mathematician of highest class
Professor Hardy was very impressed with the works of Ramanujan and he decided to invite Ramanujan to Cambridge,England, as soon was possible.Being a man of shrewd judgement,Professor Hardy knew the works of Ramanujan were not cranked,but a self-taught mathematician of the highest order.
After a few months of formalities Ramanujan was finally invited to Cambridge.He arrived in Cambridge on April 14,1914,and joined Trinity College on a special scholarship of 60pounds.
Ramanujan and many other Cambridge scholars were busy exchanging their experiences in mathematics.Once professor Berry was explaining some mathematics complexities to expert mathematicians and Ramanujan was also present.When Professor Berry was doing maths on blackboard ha asked Ramanujan if he wished to say anything.Ramanujan went straight to the blackboard and wrote some of the results which Professor Berry still had to reach.
Later Prof.Berry said”Ramanujan must have reached those results by pure intuition.His ability in the theory of numbers was in large measure like other mathematicians.Many of the results apparently came to his mind without any effort.He was,however,aware that a good deal of intellectual effort would be required to establish his philosophical theories.”
Professor Hardy published 12 papers about Ramanujan’s mathematical concepts in different science journals. Ramanujan also went through formal studies at Cambridge and graduated in Science on March 16, 1916, aged 29. Ramanujan, for his distinctive work, was awarded the highest British honor he was made a Fellow of the Royal Society in February, 1918.Professor Hardy informed Madras University about Ramanujan’s great achievements as a Fellow of the Royal Society,”He should be treated with a mark of special respect”,emphasized Professor Hardy.
Ramanujan was doing very well in his studies but his poor health made him worried.His health was continuously plummeting and finally,on February 27,1919,Ramanujan returned home to India.He was granted a handsome scholarship by Madras University and every possible facility was given to him for his research in Mathematics.
Due to his deep dedication to his work he became run down and caught tuberculosis (T.B).Despite his ill-health he continued to work hard but eventually he had to be admitted into hospital.Every possible effort was made to save his life,but on the fateful day April 26,1920,he passed away at the young age of 32.
Although Ramanujan died long ago,he is always remembered for his supernatural ability in mathematics.Researcher and scholars are still working on various mathematical concepts proved by Ramanujan in his famous ‘Notebooks’.
The only bright star that India could produce in the field of mathematics was Ramanujan.But it was India’s misfortune that they could not recognize this precious jewel early on.When Ramanujan was struggling against his fatal penury no one came to his rescue.But when he was dying of tuberculosis life was desperately attempted to save,but it was too late.Ramanujan died young,but he had made n immense contribution to enrich mathematics.
The many mathematical concepts developed by Ramanujan are still not outdated.Many scholars have been studying the rich amount of theorems and mathematical concepts developed by Ramanujan.A few of his mysterious mathematical formulas have recently been understood,but there are still many theorems which are to be proved.Ramanujan did not live long enough for him to explain how his formulas would work to solve a particular sum.
Professor Hardy,head of the mathematical department in Cambridge University,was one of the leading mathematician in England.He lavishly praised Ramanujan with the following words:
“My account of Mr.Ramanujan’s work has been necessarily fragmentary and incomplete.I have said enough,I hope,to give some ideas of its astonishing individuality and power.India has produce many talented mathematician in recent years, a number of whom have come to Cambridge and attained high academic distinctions.They will be the first to recognize that Mr.Ramanujan’s work is of different category.In him India now possesses a pure mathematician of the first order,whose achievements suggest the brightest hopes for its scientific future”.
Ramanujan’s talent was recognized by great Prof Hardy….
Still there are many talents in INDIA who has not been recognized for there real talents…there is no other Hardy too…
Who will support them….we INDIANS should…
Proud to be an INDIAN and support the real talents,so that our Nation will be at the top compared to all other countries..
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