The Man Who Knew Infinity — Part 2
In the first part, we read about Ramanujan’s life in India — his life at school, his struggles at college and the one letter from G.H. Hardy that was going to change his fortunes. In this part, I will be covering his life at England, his battles with the cold weather, emotional issues and his final days in India
Will Ramanujan Go To England?
Before his letter reached Madras, Hardy contacted the Indian Office to plan for Ramanujan’s trip to Cambridge. Arthur Davies, Secretary of the Advisory Committee for Indian Students met with Ramanujan to discuss the same. The religious customs prevalent at that time forbade Ramanujan from going overseas. Hence, Ramanujan refused to leave his country to “go to a foreign land”. Meanwhile, he sent a letter to Hardy packed with theorems, writing, “I have found a friend in you who views my labour sympathetically.”
Hardy, slightly upset that Ramanujan was not willing to come, enlisted the help of a colleague lecturing in Madras, E.H. Neville, to convince Ramanujan to come to England. But now, Ramanujan needed no convincing, and, in Neville’s own words “needed no converting”. Apparently, Ramanujan’s devout mother had a dream in which their family goddess had commanded her “to stand no longer between her son and the fulfillment of his life’s purpose.
Ramanujan’s Wife
During the days of Ramanujan, child marriage was very common in India. Most girls were married off before they attained puberty, though they didn’t actually live with their husbands, consummating the marriage, until later.
On July 14, 1909, a then 21-year old Ramanujan was married to Janaki, a shy 10-year old girl, who was the daughter of a distant relative. His father did not attend the wedding, apparently riled because he had had no say in the plans. It was Ramanujan’s mother who had arranged everything.
When he left for England, Ramanujan had to leave his wife back in India with his parents.
Off to England
On March 19, the S.S. Nevasa set off for England with Ramanujan aboard it. It skirted south of Cape Comorin and made direct for Aden, a week’s passage across the Arabian Sea. The voyage was a pleasant one for Ramanujan. He had his vegetarian food, met several of the 200 odd passengers. Sometimes, he withdrew to his cabin and played with numbers suggested by the dimensions of the cabin or the number of passengers.
Finally, after docking first at Plymouth, the Nevasa steamed up the English Channel and arrived at the mouth of Thames on April 14.
Early Days At England
London was 10 times larger than Madras in terms of population with 5 million people. The Englishmen Ramanujan had known in Madras were mostly educated and upper class. Whereas in London, he saw Englishmen of all sorts — right from men in bowler hats to men in flat workingmen’s caps and women both in rich clothes and in rags. Fortunately, Ramanujan had Neville by his side, who put the former up in his house in Chestertown Road.
Though he had not gone there to attend school, Ramanujan did attend a few lectures, some on elliptic integrals(given by Arthur Berry, a King’s College mathematician) and some of Hardy’s. Once, when Berry was teaching, he observed Ramanujan’s face glowing with excitement. On being asked whether he would like to add anything, Ramanujan went to the blackboard and wrote down theorems which Berry had not yet proven.
In early June, Ramanujan moved into the rooms in Whewell’s Court, about five minutes from Hardy’s room, stating “it would be inconvenient for the professors and myself if I stay outside the college”. He was sad to leave Neville, who had done much to ease his adjustment to English life. But then, Ramanujan had much to learn and a lot of catching up to do.
With Hardy
Hardy observed that most of the 120 theorems Ramanujan had sent him were from his notebooks, intact. A few of the results, Hardy could see were wrong. Some were not as profound as Ramanujan thought them to be. Some were rediscoveries of what Western mathematicians had found half a century or a century back. But as Hardy would reckon, most of them were breathtakingly new.
It didn’t take long for Hardy to see that Ramanujan’s notebooks were worth publishing. Hardy began to edit his work by shaping his results, casting them into lucid English and making the notations more familiar. The following year, 1915, saw a flood of papers published by Ramanujan. In 1914, he had only one, which appeared in the Quarterly Journal of Mathematics under the title “Modular Equations and Approximations to Pi”.
In short, everything was going fine for Ramanujan. But soon, the War happened and with it, brought a lot of hardships to Ramanujan.
The Great War
The assassination of Austrian Prince Franz Ferdinand on June 28, 1914, triggered a chain of events due to which Germany and France declared war on each other. Subsequently, Cambridge began feeling the war’s impact. In the early days of August, a Division of soldiers from Ireland set up tents in Cambridge, just across Neville’s house. At Trinity, the area near the library was converted into an open-air hospital.
Ramanujan was a vegetarian who clung on to it orthodoxically. During his initial days, he ordered fried potatoes a few times from the college kitchen. One of his Indian friends jokingly commented that it was fried in lard(animal fat). True or not we do not know. But, that was all it took to make sure that Ramanujan never ordered from the college kitchen again.
He began cooking in the tiny alcove in his room using a small gas stove. Whenever he could procure the ingredients, he ate whatever he ate back in India — rice, yogurt, fruits, rasam and sambhar(a thick, spicy vegetable stew)
The constant bother of having to find and prepare food on his own weakened his sense of well-being to some extent. Being used to the humid and tropical climate of South India, Ramanujan found the English chill difficult to withstand. The peculiar absence of letters from his wife Janaki also worried him. But mostly, he did not let himself get affected by these and kept working happily and hard, at mathematics.
To protect King’s College Chapel from attacks, streets were kept dark at night. Cambridge was engulfed in darkness and men had to grope their way about. Ramanujan’s apartment began to feel like a prison. Though driven back to it by the winter chill and wartime gloom, the delight he got from working with Hardy lured him back to it.
S. Ramanujan, B.A
By Mid-October 1915, Ramanujan moved to Bishop’s Hostel. The layout was similar to his old room at Whewell’s court, but it brought him closer to Hardy. Later in the year, Ramanujan’s paper on highly composite numbers (the most important body of work carried out by him during his first year at Cambridge), appeared in the Proceedings of the London Mathematical Society.
At Cambridge, every student had a tutor who monitored his progress. Ramanujan’s was E.W. Barnes, who called him the most brilliant of all the top Trinity students to have come before him. He wrote to Francis Dewsbury, registrar of the University of Madras, of Ramanujan’s progress and requested to extend his two-year scholarship which was coming to an end. Ramanujan, he said, was in line to become a Fellow of Trinity.
The scholarship was extended for a period of one year, with the possibility of further extensions, if required. The scholarship came to 250 pounds a year. Even after setting aside the 50 pounds he sent to his family back in India, Ramanujan was comfortable. Yet, something still nagged at him — the lack of a degree, which was the tangible public marker of academic achievement.
In March 1916, he received a B.A “by research”, on the basis of his paper on highly composite numbers. Now, after a dozen years and two college failures, he had his degree
Partitions
In 1916, one problem lay in the area of number theory known as “partitions”. At first glance, it seemed simple. It would remind you of the mathematics you did in your younger days in school
A partition can be defined as the number of ways in which you can split a number. For example, consider the number 4. You can write it as 2+2 or 1+3 or 1+1+2 or 1+1+1+1 or write it as 4 itself. You get 5 different ways or “partitions”. We can say the number of partitions of 4 is 5 or p(4) is 5, where p(n) represents the number of partitions of a number.
Though it might seem very easy for small numbers, the number of partitions tend to rise very fast. p(3) is just 3 whereas, by the time you get to 10, the number of partitions becomes 42 and for 50, it is a humongous 204,226. The question that arises now is: Can we find a formula for this p(n) wherein, if I give any number “n” to this formula, it gives the corresponding number of partitions without doing all the awful arithmetic?
This was the area in which Ramanujan and Hardy set to work on together which brought them many laurels in the mathematical world. They came up with a method called the circle method which made use of Cauchy’s theorem.
Their solution was big news and the circle method which they’d used, a stunning success. In late 1916, Hardy dashed off an early account, offered “as the joint work of the distinguished Indian mathematician, Mr. S. Ramanujan and myself” to the Quatrieme Congres des Mathematicians Scandinaves in Stockholm. A one-paragraph reference appeared in Proceedings of the London Mathematical Society in March. The 40-page paper setting out their work in full detail didn’t appear until 1918.
Hardy had always been Ramanujan’s friend and supporter. Recognizing the latter’s genius, he only wanted to push it to its limits. And that, if anything, was the problem.
Mathematics was the common thread of their relationship. Hardy did not want to and did not like to intrude into Ramanujan’s private life. He was not suited to draw out a lonely Indian, ease his adjustment to an alien culture and shelter him from the English chill.
Trouble Back Home
Ramanujan got no letters from his wife Janaki. Not because his wife didn’t write. But because his mother shrewdly intercepted them. Janaki could not say anything back. She was a young girl of seventeen and consoled herself that was just how things were.
In those days, mother-in-law and wife troubles were a given thing in Indian households (Even today they are, as is evident from the innumerable Indian television serials centering around the same)
Soon, Janaki found an excuse to get away using her only brother’s marriage, who was in Karachi (present-day Pakistan). In Karachi, she wrote and this time it got through. She asked if he could send her money for a new Sari, which he sent dutifully. But by now, the long silence from his wife had made him bitter and knowing only what he had heard from his mother, he let no warmth or feeling slip into his reply.
Soon, Ramanujan’s relationship with his whole family became distorted. In 1914, he had written home thrice or four times a month. By 1916, sometimes 2 or 3 months passed before he wrote. During 1917, the family had not heard from him at all.
The English Chill and its Effect on his Health
In May 1917, Hardy wrote to the University of Madras that Ramanujan was sick and affected by some incurable disease.
He was admitted to a small private hospital catering to Trinity patients. The prognosis was very poor and Hardy asked the master of Trinity whether they could bring Dr. Ramachandra Rao from India by special dispatch. By that time, Ramanujan was out of hospital and back in Bishop’s Hostel.
Ramanujan was a terrible patient. He was terribly picky about his food, forever complained about aches and pains and had no faith in medicines. This led to him seeing at least 8 doctors and 5 English hospitals and sanatoriums over the next 2 years.
Around October, he was admitted at the Mendip Hills sanatorium near the city of Wells, in Somerset, where he was treated for tuberculosis. Soon, he was transferred to Matlock House Sanatorium in Derbyshire.
The most widely accepted treatment during Ramanujan’s time for tuberculosis was open-air treatment which was pioneered in the late nineteenth century. It called for bed rest in open lodges exposed to fresh air, lots of food and measured amounts of exercise.
To add to all of this, Ramanujan’s tutor, Barnes, believed Ramanujan would be elected a Fellow of Trinity College the following October. But October 1917 came and Ramanujan was not elected. This left his mood all the more darker.
Meanwhile, hoping to boost his friend’s morale, Hardy tried to get Ramanujan the recognition he deserved. On December 6, 1917, Ramanujan was elected to the London Mathematical Society. Two weeks later, Hardy and eleven other mathematicians together put him up for an honor more esteemed than any fellowship of a Cambridge College: they signed the Certificate of a Candidate for Election that nominated him to become a Fellow of the Royal Society (F.R.S)
Hardy’s concern for Ramanujan’s health made him to press his claim with unusual urgency. “Ramanujan might not make it to the next election”, he was saying, “and the society would have to live forever with its failure to honour him”.
Attempt at Suicide
Meanwhile, unaware of his friend Hardy’s efforts, one day in January or February of 1918, Ramanujan threw himself onto the tracks in front of an approaching train. Fortunate for him (and for the rest of the world), a guard spotted him and pulled a switch, bringing the train to a halt a few feet in front of him.
Suicide, being a crime, led to him being arrested and hauled off to Scotland Yard. Hardy, on being called, rushed to the scene and explained to the police about Ramanujan. The police, on investigating, learned that Ramanujan was indeed an eminent mathematician and let him go.
We can’t exactly put our finger on what led Ramanujan to consider ending his life. A bevy of factors, like Rejection by Trinity, lack of communication with his wife, inability to produce mathematical results due to his sickness, all these coupled together might have resulted in him taking this extreme step.
Getting The Recognition He Deserved
Around March, Ramanujan received a telegram from Hardy, sent from London, mentioning that he had been elected as a Fellow of the Royal Society. Of 104 candidates passed up for election that year, he was 1 out of the 15 that had been selected. “My words are not adequate to express my thanks to you” he wrote Hardy. In May, he would become Ramanujan F.R.S.
During the fall of 1918, his name was once again put up for a Trinity fellowship. By then, word of his suicide attempt had gotten around, giving his opponents an opportunity to jump on it. Littlewood wrote a report furnishing two medical certificates showing that Ramanujan was mentally sound, thus quashing all doubts about his mental state. “You cannot reject an F.R.S”, Littlewood told Herman, who opposed Ramanujan. Subsequently, he got his Trinity fellowship.
As Hardy had expected, the honors conferred on him had succeeded in lifting Ramanujan’s spirits leading to a brief period of brilliant invention. On October 28, 1918, two newly founded proofs, along with one of Ramanujan’s papers on congruence, were read at the annual general meeting of the Philosophical Society. Two weeks later, the war ended.
The Ramanujan Number
Soon after the war ended, Ramanujan left Matlock for another nursing home in the suburbs of Putney on the south bank of the Thames called Colinette House. He was more accessible here for Hardy since he was just a cab ride away.
Once, Hardy had engaged a cab with the number 1729 to visit Ramanujan. On arriving, he remarked it was “rather a dull number” and hoped it was not a bad omen.
“No, Hardy,” said Ramanujan. “ It is a very interesting number. It is the smallest number expressible as the sum of two different cubes in two different ways” (One of the pairs is 1 & 12 i.e 1³ + 12³ = 1729. I will leave it to you to figure out the other pair)
On March 13, 1919, Ramanujan boarded the Pacific and Orient Lines ship Nagoya, steaming to Bombay.
Home Sweet Home
The first words that escaped Ramanujan when he set foot in Bombay on 27 March 1919 were “Where is she?”. She here was Janaki. His mother was there, his brother Lakshmi Narasimhan was there. But he wanted to meet his wife. She was back in her hometown, where she had gone for her brother’s wedding more than a year before. She was well aware of Ramanujan’s arrival — thanks to the Madras papers that carried the news. Her mother-in-law had not even bothered to informed her.
Since Ramanujan had defied religious customs by travelling abroad, he had to do a purification ceremony to remove the “taint”. His mother planned to take him to Rameshwaram, a coastal town in the southern part of Tamilnadu. One look at him made her decide against it. He was just too sick. After a few nights at Bombay, they boarded the Bombay Mail to Madras.
Ramanujan was offered a university professorship, which he promised he would accept when his health improved. Notables from Madras trooped up to meet him. They offered him their homes, they offered to meet his medical expenses. To shield him from visitors, his doctor had him moved to a quieter place called Venkata Vilas on Luz Church Road. It was here in April that Janaki finally caught up with him. It was here that they began to build a real relationship. But the man they saw was different from the Ramanujan who had left India 5 years back. “I found him not a cheerful and affectionate Ramanujan,” one of his childhood friends said, “but a thoroughly depressed, sullen and cold Ramanujan”.
Last Days
With the approach of the Madras summer, on his doctor’s advice, he was shifted to a sleepy little town called Kodumudi. From here, Janaki began occupying a larger place in his heart. He told her, more than once “If only you had come with me to England, I would not have fallen ill”. He used to watch her oil and wash her hair on Friday afternoons which gave him great pleasure, sometimes enough to draw him away from his work.
For two months he stayed there, after which he moved to Kumbakonam, his hometown where the familiar surroundings of his childhood made him nostalgic and mellowed him down a little.
But the zeal for mathematics inside him did not die down. Even in his last few months, he was actively working on theta functions, filling page after page with theorems and shared them with Hardy. Towards the end, “he was only skin and bones”, Janaki remembered later. He complained terribly of pain. Through all the pain and fever, he kept working, lying on his bed, his head propped up on pillows. “It was always maths…Four days before he died he was scrabbling” said Janaki.
Early on April 26, 1920, he lapsed into unconsciousness. For two hours, Janaki sat with him, feeding him sips of dilute milk. Around midmorning or perhaps a little later, he died. With him were his wife, his parents, his two brothers and a few friends. He was 32 years old.
A Son of India
Though Ramanujan died early, the body of work that he has done in this short span of 32 years continues to baffle mathematicians and researchers to date. His works find numerous applications in many real-life problems today.
Thank you for reading!!
References
The Man Who Knew Infinity by Robert Kanigel
Those interested in reading the book can purchase it from Amazon or Flipkart. It contains a lot more interesting anecdotes and insights into his life which I have not included in my post
