# Biography of Srinivasa Ramanujan

**Srinivasa Aiyanger Ramanujan:**

Date of birth:1887

SRINIVASA AIYANGAR RAMANUJAN,*popularly known as Srinivasa Ramanujan or S.Ramanujan,is remembered as the most brilliant mathematician of India.His mathematician approaches have been proved to be highly intellectual and innovative.*

*Ramanujan,due to his extreme poverty,could not even complete his college education but he made his own formulas to solve the most complicated mathematical problems and brought a revolution to the field of mathematics.He could solve the most complicated sums as easily if they were simple multiplication or addition.He invented and solved many theorems,which are still today very difficult for many serious mathematician to solve.*

*Ramanujan’s untimely death brought an abrupt end to the development of mathematics in India.He had made a great contribution to the study of the analytical theory of numbers.He also work on elliptic functions,continued fraction, and infinite series.*

*Ramanujan developed the concept of the series S(1/n).He found Bernoulli’s numbers very interesting,as a result he began studying Bernoulli’s numbers with deep interest,and in 1911 he published an important research paper on Bernoulli’s numbers.This important research paper was published in the Indian Mathematical Society,a highly reputable scientific journals.*

*Ramanujan also succeeded in developing connections between elliptic modular equation in 1910.In his twenties,Ramanujan made a significant study on hyper-geometric series.Later he developed the concept of Elliptic Functions.*

*During 1912 and 1913 Ramanujan worked on many important theorems which brought him critical acclaim in the country.He also showed some of his latest findings to senior mathematicians in India,but unfortunately most of them could not comprehend what Ramanujan was telling them.Disappointed,Ramanujan wrote a letter to Professor G.H. Hardy was very impressed by Ramanujan’s works and asked him to come to Cambridge University.*

*All the necessary arrangement were made,and Ramanujan went to Cambridge University where he was given the complete freedom to work in mathematics.Ramanujan received a doctorate in 1902 at the age of 33,and published at least five well researched papers in England.Ramanujan was doing well in Cambridge,but his health began to deteriorate rapidly.He returned to India,where even the best medical treatment could not save his life,and on April 26,1920,Ramanujan breathed his last. *

Srinivasa Aiyangar Ramanujan was born in his grandmother’s house o December 12th 1887 in Kombakonam,Tamilnadu,India.When he was about one year old,his mother came to the village of Kombakonam near Madras.The village Kombakonam is located on the banks of the Kaveri river.Ramanujan was from the higher caste of Brahmin.

His father was an accountant in a clothes merchant’s shop,but his family was living in dire poverty,the income of Mr.Aiyangr was barely sufficient to meet the expenses of his family.Ramanujan’s childhood was spent in the dark shadow of poverty and deprivations.Ramanujan was growing up like many other ordinary boys of Kombakonam.

When Ramanujan was 5-years old he was admitted to the local primary school in Kombakonam.The teacher of the primary school was a math teacher,he was teaching the primary rules of numbers,but he found the young boy had an unusual talent in mathematics.One day in the class the teacher gave some problems to the student as a class work.All of the students could not solve the problems,then Ramanujan stood up and said to his teacher,”excuse me,sir!Could you please allow me to show how to solve these problems?” said Ramanujan.”Oh,you Ramanujan!Of course,why not!Please come to the blackboard”,said the teacher.Ramanujan took everyone by surprise when he solved the problems within minutes.The one who was even more surprised was his teacher.He was amazed to see this small,thin boy solving mathematics so easily and with such great speed!

Ramanujan was top in the primary level examination,and he stood first in the whole of the Kombakonam district.As a result he won a scholarship for his further education and he joined the Town High School in Kombhakonam in 1894,age 7.This was a big high school where a large numbers students attended.Ramanujan was the favorite student of his teacher;his extraordinary mathematical ability impressed all of the teachers at the school.

By the age of 10 Ramanujan was able to solve the math of the senior classes.One day he borrowed a trigonometry book written by Professor Loney,after studying the book for a week Ramanujan returned it to his friend.His friend was surprised when he learnt that Ramanujan had already solved all the sums and,moreover,he had also made a few formulas so that the sums could be solved more easily.

A book which made a great impact on Ramanujan’s outlook on mathematics was,”A Synopsis of Elementary Result in Pure and Applied Mathematics”.Th is book was published in two volumes,the first appeared in 1880 and the second volume volume appeared in 1886.The author of the book was George Shoobridge Carr.This book was the result of many years of hard work and research,but,unfortunately,the book did not make much impact of scholars.As a result,the book was left in obscurity.

One day Ramanujan was browsing through the shelves of book on library where,by chance,he found George Shoobridge Carr’s book .While studying it he found the book was immensely useful for the senior student of mathematics. Ramanujan highlighted several important aspect of the book and as a result,the book became gain popularity among the teachers and students.

Now Ramanujan decided to work on theorems.He invented some formulas and use them to solve mathematical approaches.Most of the formulas invented by Ramanujan are available in his notebooks.

Ramanujan came first in the Matriculation examination in Kombhakonam district.This great success awarded him a scholarship for his college education.

Ramanujan’s deep love for mathematics consumed most of his time and,as a consequence,he failed in his First Arts examination.This made him very frustrated and later he even changed to another college.

Ramanujan joined Pachaiyapa’s College in Madras as a First Arts student in 1906 at the age of 19.He had already carved a niche as a mathematics wizard in Kombhakonam and Madras.Ramanujan was given a grant from the principal and he only had to pay half the fees.

In ‘Reminiscences of Ramanujan’,one of the his friends C.R. Krishanaswami Aiyar said,”When our teacher,Professor Ramanujachanar sometimes drew Ramanujan’s attention to a problem he was doing on the blackboard and asked him to give the next step,or continue the problem,Ramanujan would have the boldness to say that the several intermediate steps worked out by the professor were not necessary,and he would jump to the last step and give the answers,Quite to the surprise of the whole class and especially to the professor.The professor would then ask to come to the blackboard to explain to the class how he had arrived at the answer”.

Due to Ramanujan’s excessive work at mathematics,his frail body succumbed to serious illness.He had to stop going to college.Later,when Ramanujan recovered from his long illness,he rejoined the college as a private candidate.He took the college examination a number of times,but he was unsuccessful.He had to stop going to college.

Although Ramanujan was not attending college anymore,his work on mathematics did not stop.Professor S.R.Ra nganthan,the author of Ramanujan’s biography,”Ramanujan,the Man and the Mathematician”,says in his book,”Inner light began to lead him.And the joy of cultivating the region of knowledge lighted up by it began to spur him on and on.The urge for the pursuit of mathematics became irrepressible.The depression due to failure in the F.A.Examination could not repress it.Failure to get explored could not shake it.Poverty and penury could not obstruct it.His research marched on undeterred,by any environmental factors physical,personal,economic,or social.Magic squares,continued fraction,hyper geometric series,properties of numbers prime as well as composite partition of numbers,elliptic integrals,and several other such regions of mathematics engaged his thought was created in the the west had not even been disseminated in the country.Everything had to be done and discovered by him de noro.Ramanujan had cultivated an usual systematic habit.Each result that he obtained he recorded in a quarto notebook.Proofs were often absent.This might have been due to to two causes.Probably he saw some of these results directly unmediated by formals proofs.Again,even where he arrived at them by laborious work,he could not find the mental set to copy all the steps in the proofs.Ideas were pouring in at a rate which militated against copying at leisure.The result has been his extraordinary Note Book-the first of his three Note Books.The profundity of these notebooks is still staggering.These contents have stimulated many workers in their respective fields.The proofs of many are yet to be worked out.The accuracy of some is yet to be established.Surely,all this could not have been seized by the intellect alone.Intuition should have played a large part in this period of super activity.Ramanujan was indeed a Drashta(seer) in mathematics.”

Increasing financial burdens made Ramanujan search for a job.He approached the founder of the Indian Mathematical Society and requested a job,eventually he was appointed as a clerk in the Madras Port Trust on March 1,1912.This job was a great relief to Ramanujan.Now he was at least free from financial worries and in his spare time he could do mathematics.

Moreover,he found the Chief Accountant for the Madras Port Trust,S.N.Aiyer,was himself a mathematician.S.N.Aiyer had published a research paper on”The Distribution of Primes”based on Ramanujan’s work.

Professor C.L.T Griffith of Madras Engineering College was interested in the works of Ramanujan.Educated in London,he knew many senior mathematicians there,helped Ramanujan to correspond with Professor G.H.Hardy.

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”.