The Man Who Knew Infinity-Part 1

Allow me to take you through the life of legendary mathematician Srinivasa Ramanujan - a “rags to riches” story filled with ups and downs.

Since one post will not suffice to cover the life and works of Ramanujan, I have split this into 2 parts. The first part covers the early parts of his life until the time he left for England. The second part talks about his life in England and the subsequent years until his death

Early Life

Srinivasa Ramanujan was born on 22 December 1887 in Erode and later shifted to Kumbakonam where he did his schooling. His father was a clerk in a garments shop and his mother used to sing bhajans at the nearby temple. He passed his primary examinations from the Kangeyan Primary school at the age of 10 with the best scores in the district and subsequently was enrolled to the Town Higher Secondary School where he began to show signs of intelligence and his tryst with formal mathematics began

When he was in the third form(The equivalent of today’s 8th standard in India), the teacher was explaining division one day. He quoted that anything, when divided by itself, was one. “Divide three fruits among three people and each will get one”, to which the young Ramanujan asked “Is zero divided by zero also one? If no fruits are divided among nobody, will each one get one?”

Since his family was poor, to supplement their income, they took in 2 students from the nearby Government college as lodgers in their house. Noticing his interest in mathematics, they fed it with whatever they could. But nothing could satiate his intellectual hunger and within months, he had exhausted all of their knowledge and began pestering for more books from the college library. They introduced him to S.L. Loney`s Trigonometry which was advanced for a school level kid. But it was not so for Ramanujan who mastered the book by the age of 13.

In 1904, when he graduated, he was awarded the K. Ranganatha Rao prize for mathematics, the headmaster remarked that he was a student who deserved higher than the maximum possible marks. It was also the time when he was introduced to G.S.Carr`s A Synopsis of Elementary Results in Pure and Applied Mathematics which had a collection of around 5000 theorems. This is a book that is greatly acknowledged with awakening the genius inside him

College Life

Ramanujan joined Kumbakonam`s Government College in 1904 armed with a scholarship awarded on the strength of his high school work. Till this point, Ramanujan had somehow been able to balance his mathematics with his other subjects quite well. But Carr`s book had an unprecedented effect on him. It ignited a burst of intellectual activity within him. He lost interest in everything else. While the professor used to be lecturing about Roman History, his mind was preoccupied with manipulating mathematical formulas. As a result of this, he failed the English paper due to which his scholarship was taken away. Given his family`s financial situation, he badly needed the scholarship.

He stayed on for a few months, but the effort was taxing. He had lost his scholarship, his parents were under a heavy financial burden, coupled with these, the pressure to do well in other subjects also. But, he could not give up mathematics for their sake. He was torn between both ends. Not able to take it anymore, in August 1905, he ran away from home, heading towards Vishakapatnam for a month

Later, he came back and joined the Pachaiyappa`s College in Madras in 1906. Though initially, all was well, his experience at Kumbakonam repeated itself. There it was English, here it was physiology. He failed the F.A (Fellow Arts) exam the same year and also the subsequent year. Hence, he left college and began to pursue independent research in mathematics, living in poverty and struggling to make ends meet

The Notebooks

In proving one formula, he discovered many others, and he began to compile a notebook to record his results. It was in working through Carr`s Synopsis from 1904 to 1907 during his college days, that he began keeping them in their earliest form

Though he did set out to prove Carr`s theorems, soon he began to branch out and saw new theorems

In Pursuit of a Job

In 1910, Ramanujan met deputy collector V. Ramaswamy Iyer, founder of the Indian Mathematical Society, showed him his notebooks and requested for a job at the revenue department where Iyer worked. Not wanting to confine him to a job in the lowest rungs of the revenue department, Iyer sent Ramanujan to his mathematical friends with letters of introduction.

Some of those friends, in turn, sent him to R. Ramachandra Rao, the district collector of Nellore and secretary of the Indian Mathematical Society. Rao listened as Ramanujan discussed elliptic integrals, hypergeometric series and his theory of divergent series which convinced Rao of Ramanujan`s brilliance. When Rao asked him what he wanted, Ramanujan replied that he needed work and financial support. Rao consented and sent him to Madras. He continued his research with Rao’s financial aid. With Iyer`s help, Ramanujan had his work published in the Journal of the Indian Mathematical Society

In early 1912 he got a temporary job in the Madras Accountant General`s office, with a monthly salary of 20 rupees, but lasted only for a few weeks there. Toward the end of his assignment there, he applied for a position under the Chief Accountant of the Madras Port Trust.

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, Ramanujan learned that he had been accepted as a Class III, Grade IV accounting clerk, making 30 rupees per month. At his office, Ramanujan quickly completed the work he was given and spent his spare time doing mathematical research. However, Ramanujan’s boss, Sir Francis Spring, was kind and encouraged him in his mathematical pursuits.

Dear sir, I beg to introduce myself …..

In the spring of 1913, Narayana Iyer, treasurer of the Indian Mathematical Society, Ramachandra Rao and E.W. Middlemast tried to present Ramanujan`s work to British mathematicians in the hope of getting him recognition outside of India. He said that although Ramanujan had “a taste for mathematics, and some ability”, he lacked the necessary educational background and foundation to be accepted by mathematicians. With the help of friends, Ramanujan wrote letters to leading mathematicians at Cambridge University

The first two professors, H.F.Baker and E.W. Hobson returned his papers without comment

On Jan 16 1913, Ramanujan wrote to another professor at Cambridge University, G.H.Hardy. Hardy said yes. And, the rest, as they say, is history

Dear Sir,
I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras on a salary of only £20 per annum. 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 results I get are termed by the local mathematicians as ‘startling’.

Thus began Ramanujan`s letter to Hardy. Those interested in reading the full letter can read it here

Along with this letter, Ramanujan enclosed nine pages of some of his proven theorems also. After a perfunctory glance, Hardy put the letter aside and went ahead with the day`s work. But this letter from an Indian clerk remained at the corner of his mind. According to Hardy, the theorems were “such as he had never seen them before, nor imagined”. He could not decide whether these were the work of some genius or the work of some crackpot.

Hardy sought out his friend and colleague, J.E.Littlewood to take a look at the papers. Both started investigating Ramanujan`s papers and by midnight, they had reached a conclusion that for the past three hours, they had been going through the works of a mathematical genius

(This marks the end of Part 1. In Part 2, I will be writing about his collaboration with Hardy, his experiences in England and subsequent return to India)

Reference

The Man Who Knew Infinity by Robert Kanigel