THE MAN WHO KNEW INFINITY

Table of Contents

**About Book **

## Why should you read this summary?

Srinivasa Ramanujan is one of the greatest mathematicians of the past century. . Several important concepts of mathematics were named after him. From the Port of Madras to Trinity College in Cambridge, he proved that India was home to an extraordinary and unforgettable genius. This book tells the incredible life story of Ramanujan.

## Who should read this summary?

• Students who love math and also those who hate it

• Young adults, so that they may be inspired to follow their passion

• Every Indian, to remember the genius of Ramanujan

## About the Author

Robert Kanigel is a writer, professor and biographer. He has written seven books and more than 400 articles. Robert has written for the New York Times, Washington Post, and many other publications. His book “The Man Who Knew Infinity” was adapted into a film in 2015, starring Dev Patel.

# THE MAN WHO KNEW INFINITY

### Robert Kanigel

## Introduction

Who was Srinivasa Ramanujan? He was a genius mathematician, the second Indian to become a Fellow of the Royal Society, and the first Indian to become a Fellow of the Trinity College at Cambridge University, UK. In this book, you will learn more about Ramanujan. You will learn about the man behind the theorems celebrated by mathematicians all over the world. While Ramanujan was a humble man and he died at a young age, he left many great achievements of which India can be proud.

## A Brahmin Boyhood

Srinivasa Ramanujan was born on December 22, 1887. His father, Srinivasa, was a clerk at a sari shop. His mother, Komalatammal, was a housewife and a singer at a local temple. Ramanujan mostly grew up in the village of Kumbakonam in South India. He was a stubborn but sensitive little boy. When Ramanujan was a toddler, he refused to eat except at the temple. If he didn’t get the food he wanted, he would roll in the mud in frustration. Young Ramanujan was quiet and reflective. He asked questions like “How far is it from here to the clouds?” or “Who was the first man in the world?” He liked to be alone and often stayed at home while other children played outside.

Ramanujan was not interested in sports or being active, and for most of his life, Ramanujan was fat. He inherited the body type of his mother. He used to say that if he got into a fight with another kid, all he had to do is to fall on him, and the other boy would be crushed into pieces. Ramanujan studied at Kangayan Primary School. There he learned to speak English at an early age. When he was ten years old, he passed the national primary examinations. Ramanujan scored number one in the district. After that, he enrolled in Town High School, where Ramanujan studied for six years. It was his most satisfying academic experience. He aced all his subjects, especially mathematics.

One day, the math teacher lectured that if you divide any number by itself, the answer would always be one. If there are one thousand fruits and they are divided into one thousand people, each of them will get one fruit each. Ramanujan suddenly spoke, “But if you divide zero by zero, is the answer still one? If you divide no fruits among no one, will each still get one?” This is just one example of the mathematical mind of Ramanujan. Ramanujan’s family was always short on finances, which was why they accepted borders in their home. When he was eleven, two Brahmin boys lived with his family as boarders. They were students at the nearby Government College.

The college students noticed that Ramanujan was interested in mathematics, so they taught him what they knew. But within a few short months, Ramanujan had exhausted all their knowledge. He always asked them for more math books from the college library. One time, the college boys gave him a book in advanced trigonometry. By thirteen years old, Ramanujan had already mastered it. He also learned cubic equations and the complex concepts of infinite series. He was fascinated by the numerical values of π and e.

Ramanujan became a minor celebrity at school. His teachers and fellow students rarely understood him, but most of them treated him with respect. Ramanujan received many certificates and recognition for his academic excellence. At Ramanujan’s graduation ceremony, the school headmaster awarded him the highest prize for mathematics. He introduced Ramanujan to the audience and explained that the boy deserves much more than 100% or an A-plus grade and that his math skills were off the scale.

## Enough is Enough

Ramanujan was a well-rounded student in high school. He earned a full scholarship at the Government College. However, his interest in mathematics became so intense that he neglected all the other subjects. He couldn’t force himself to study English, physiology, Greek, or Roman history. Ramanujan failed all of these subjects. He spent his time at school solving math problems, but he did not follow class lessons or participate in discussions. Ramanujan indulged himself with books in algebra, geometry, and trigonometry.

Eventually, he lost the scholarship. He tried to keep going to school for a while, but the pressure was too much, and when Ramanujan was only 17 years old, he ran away from home. He enrolled for a First Arts degree again in Pachaiyappa College after one year. His new math teacher saw his notebooks and became amazed by them. He spent extra time with Ramanujan to solve math problems. Although the teacher would solve a math problem in a dozen steps, Ramanujan would solve it in three. A senior math professor also noticed his talents. He encouraged Ramanujan to solve the problems published in math journals. If Ramanujan couldn’t figure one out, he would give it to the professor. But the professor would find that he couldn’t solve it either.

But the same pattern continued with Government College; everyone knew that Ramanujan was a math genius. He finished the three-hour math exams in just 30 minutes. But again, he flunked all the other subjects. There was one exam in physiology that covered the digestive system. Ramanujan returned the exam sheet with no answers and no name whatsoever. He just wrote, “Sir, I couldn’t digest the Digestion chapter.” The professor knew at once who it was. Ramanujan failed the F.A. exams. He tried the following year and failed again. Everyone knew that he was gifted in mathematics, but no one could do anything because the education system was rigid. He tried to tutor some students in math for a while, but he couldn’t reconcile with the steps in the book.

Ramanujan would solve it in his way or jump to more advanced lessons, which meant that he was not a very good tutor. At 20 years old, Ramanujan had no job, no degree, and no direction in life. Ramanujan spent most of his time sitting and solving math problems on the pail of his house. While neighbors passed by, busy with daily activities, Ramanujan sat there lost in his world of equations and theorems. His parents understood him for some time, but they grew impatient too. His mother said enough is enough. She gave Ramanujan what one psychologist called “the time-tested Indian psychotherapy.” That is none other than an arranged marriage.

## Search for Patrons

One day, Ramanujan’s mother visited some friends in another village. There she saw a 9-year-old girl who has a pretty face and bright eyes. Her name was Janaki. The mother asked for the girl’s horoscope, and she compared it with Ramanujan. She thought that they were a good match, and so she negotiated their marriage. Janaki’s family was poor. They could only offer a few copper vessels for her dowry as Janaki was one of five daughters. But, Ramanujan was a young man with no job or degree. His family was also poor, but his mother proudly said that her son was a math genius.

On the day of the wedding, Ramanujan and his mother were late. The train they needed took hours to arrive. That’s why they reached Janaki’s house at one o’clock in the morning. The wedding had a few more unfortunate events, but Ramanujan’s mother was still very happy because, in the end, her mission was accomplished. And so, at 22 years old, Ramanujan was a married man. He could no longer stay at home all day and solve problems in his notebook. He started searching for any job or any opportunity that would accept him. Ramanujan went to the city of Madras. He went door-to-door and sought the help of friends. All he had as proof of his skill were his notebooks; they were the most important thing he owned.

If a photographer has a portfolio, then Ramanujan had his notebooks. It was how he marketed himself. It was not an easy path for him. He had no degree, and many distinguished men rejected him. Only a few men saw the potential in Ramanujan and gave him a chance. One of them was Ramachandra Rao, who was a district collector and secretary of the Indian Mathematical Society. Rao didn’t offer a job but instead a scholarship so that Ramanujan could write papers for the Journal of the Indian Mathematical Society. He gave Ramanujan 25 rupees per month for this work. Ramanujan supplied a couple of research papers and interesting math problems for the Journal. He was starting to be noticed. He had a good time living near the beaches of Madras.

A friend once visited Ramanujan in his boarding house. The friend said, “Ramanju, they call you a genius.” But Ramanujan answered that he was hardly a genius. “Look at my elbow. It will tell you my story.” Ramanujan’s elbow was dirty. He used his elbow to erase his equations on the board. He would rather have his elbow black than stop solving and look for a rag. His friend asked, “Why don’t you use paper?” Ramanujan answered that he could not afford it. He would need four reams of paper a month if he wrote out the equations on paper. He would rather spend the money on food. Sometimes, Ramanujan had to improvise, such as writing on used paper with a different color ink. Eventually, Ramanujan got a job working in the Madras Port of Trust. He was employed by the officer-in-charge, Sir Francis Spring, and the second-in-command, Narayana Iyer. They gave Ramanujan the position of an accounting clerk. The pay was 30 rupees per month. Sir Francis and Narayana Iyer were kind to him. They let him study mathematics when there was not much work to do.

They helped him draft letters for mathematicians at Cambridge University. Through Sir Francis, the British authorities became aware of Ramanujan’s extraordinary abilities. But they were not sure what to do with him. Some of them thought that Ramanujan was crazy. Some of them advised that if no one in India understood him, then maybe Ramanujan could get the support and training he needed at Cambridge. Ramanujan sent letters with samples of his work, while two mathematicians from Cambridge rejected him, one G.H. Hardy, accepted his application.

## “I Beg To Introduce Myself”

In his letter, Ramanujan introduced himself as a clerk from the Port of Trust with a small salary. He explained that he had no university education, but he wanted to create a new path for himself. Ramanujan said that he was poor and did not have the means to publish his work. He also enclosed nine pages of around 50 theorems in all. In one part, he argued the research that Hardy had written in Cambridge three years previously. The first time that Hardy read Ramanujan’s letter, he thought that it was another prank. Hardy had been receiving letters from pranksters who claimed to answer the most difficult math equations. But Hardy could not get Ramanujan’s letter out of his mind. He had never seen theorems like those that Ramanujan presented before, he had never even imagined them possible.

Hardy’s curiosity disturbed him the whole day, so he decided to share the letter with his closest colleague, John Littlewood. For three hours that night, Hardy and Littlewood studied all the theorems in Ramanujan’s letter. Hardy recalled that it was the most remarkable letter he had ever received. He said that Ramanujan’s theorems defeated him completely. According to Hardy, it only took one look to conclude that they were written by a mathematician of the highest class, a man of extraordinary power and originality. Hardy became sure that Ramanujan was not a fraud because no one would have the imagination to invent the things which he wrote. Hardy went on to show Ramanujan’s letter to all his colleagues at Trinity College. He also wrote to the Indian Office in London and expressed his intention to bring Ramanujan to Cambridge University.

Hardy, of course, replied to Ramanujan. He wrote, “Dear Sir, I was exceptionally interested in your theorems…I should see more proofs of your assertions as soon as possible.”With Hardy’s support, the British authorities took Ramanujan seriously. Ramanujan still had no degree, but the chancellor of Madras University stretched the rules for him. They granted him a research scholarship at the Presidency College and granted him 75 rupees per month. Ramanujan declined Hardy’s invitation for him to come to Cambridge. As a devoted Hindu, he wanted to keep the tradition of Brahmins of not crossing the seas. Hardy was slightly offended, but he still wanted to get Ramanujan to Cambridge.

Hardy asked for the help of his friend. E.H. Neville. Neville was supposed to give some lectures in Madras, but Hardy gave him another mission: to convince Ramanujan to go with him to England. Part of Ramanujan’s letter in reply to Hardy stated, “I have found in you a friend who appreciates my work.” Hardy was a distinguished mathematician and a fellow of the Royal Society. Because of him, Ramanujan was given a stable job and he was able to support his family. What finally convinced Ramanujan to travel to England? A vision in the temple of Namakkal. In March 1914, he crossed the sea to meet Hardy.

## Ramanujan’s Spring

Ramanujan came to Cambridge in the spring of 1914. Many flowers bloomed in the warm and lovely weather. He was provided accommodations inside the campus and began his work with Hardy and Littlewood. Ramanujan remarked that they were kind and helpful to him. Ramanujan wore Western-style clothing, but with his traditional slippers. He said that shoes tormented his feet. While he was at Cambridge with Hardy, Ramanujan showed all the theorems that he had written in his notebooks for the past decade. There were around 3,000 of them. Hardy said that a few of them were wrong, and others had already been discovered by other mathematicians many years before. But an astonishing two-thirds of Ramanujan’s theorems were breathtakingly new and captivating.

Months after Ramanujan arrived, Hardy and Littlewood felt like they were just on the tip of the iceberg of Ramanujan’s theorems. Hardy said that he had never met a mathematician with the same level of skills and that Ramanujan could only be compared to the geniuses of mathematicians such as Euler and Jacobi. Hardy wrote, “Ramanujan was my discovery. But I didn’t invent him- he invented himself.” Hardy was greatly satisfied that he was the first to see the potential in Ramanujan. He edited all of Ramanujan’s manuscripts and approved them for publication. In 1914, the genius work of Ramanujan was finally published. Hardy was quick to share it with his friends in the London Mathematical Society. The title of Ramanujan’s first paper was “Modular Equations and Approximations to Pi”.

Ramanujan, at last, belonged to an intellectual community at Cambridge. He was among fellow mathematicians who understood him and saw the brilliance of his work. In 1915, nine papers by Ramanujan had already been published. The Indian students admired him and he became known as the math genius for whom Englishmen had moved heaven and earth to bring to Cambridge. Sometimes, Ramanujan visited the zoo in London or the British Museum. There was a particular comedy play he liked called “Charley’s Aunt”, which was about college undergraduate life. The acts were so funny that Ramanujan laughed until he cried. To become a research student in Cambridge, one had to have a university degree, but they made an exception for Ramanujan.

The authorities in Madras extended his two-year scholarship because an officer correctly predicted that he would become a Fellow at Trinity College. Ramanujan received 250 pounds a year as a scholarship grant from Madras. He also received 60 pounds a year from Cambridge. Ramanujan sent 50 pounds of it to his family. Even so, he had no financial problems because he lived frugally. In 1916, the Trinity College bestowed on Ramanujan the Bachelor of Arts degree that had eluded him for years. Ramanujan received a B.A.degree through his research; he earned it for his long paper on highly composite numbers. He posed for a graduation photo with other students, wearing trousers a couple of inches too short and a suit with buttons that strained. But finally, he became S. Ramanujan, B.A.

## The English Chill

While he was at Cambridge, Ramanujan mostly ate alone in his room. He had a small stove where he cooked vegetables for his meals. While Hardy and the other fellows dined at the High Table, Ramanujan chose to eat on his own. The reason was that he wanted to keep to his strict vegetarian diet. The Englishmen were fond of eating mutton and beef and the waiters at the High Table bustled around offering these dishes. Meanwhile, Ramanujan was content with sambhar, rice, rasam, fruits, and yogurt. He was not an outgoing person or the kind to hang out with many friends. Ramanujan felt more comfortable in small groups. Most of the time, he stayed in his room.

Hardy played cricket or baseball in his free time and he was also a member of the Sunday Essay Society. The other Indian students joined the Majilis debating society, but Ramanujan did not. He was content to be alone. During WWI, in the middle of an exceptionally harsh winter, Ramanujan missed India. He missed the traditions and culture he grew up with, but most importantly, he longed for the love of his wife and mother. The situation became more difficult for Ramanujan in 1917. He was diagnosed with tuberculosis and was confined for several months at an English hospital.

The doctors associated the disease with the food shortages and nutrient deficiency that was rampant in Europe at the time. What made matters worse was that he didn’t receive letters from home for several months. There were no letters from his mother or Janaki while he was recovering. Later, he discovered that his mother had been intercepting the letters between Ramanujan and his wife, Janaki. She kept Janaki from seeing Ramanujan’s letters and she also restricted Janaki from sending letters to Ramanujan. His mother told Janaki that her letters were childish and stupid. At one point, Ramanujan wanted Janaki to go to Cambridge, but his mother wouldn’t allow it. Soon, Janaki had had enough of her mother-in-law, and she used her brother’s wedding as an opportunity to escape from her grasp. Janaki never went back to Ramanujan’s household until much later.

Ramanujan was greatly worried and felt extremely sad about not receiving any letters from home. Tuberculosis deteriorated his body and mind. He refused to give up his strict vegetarian diet even if he desperately needed more nutrition, and as a result, Ramanujan lost a great amount of weight.1917 was the most difficult year for Ramanujan, with the war and the sickness, the time away from his family and mathematics, the harsh winter and the extreme feeling of sadness. It all came together in January 1918 when Ramanujan tried to kill himself. While a fast-moving train approached, Ramanujan jumped onto the railroad tracks. It was a miracle that a guard spotted him and quickly pulled a switch to make the train stop. The train came to a halt a few feet in front of Ramanujan.

Ramanujan did not die. He received a few injuries, and he ended up at the police station. Hardy came to pick him up and used his charms to persuade the police not to detain Ramanujan. Hardy lied and said that Ramanujan was a Fellow of the Royal Society like him. They could not possibly arrest a Fellow of the Royal Society. The police investigated and learned that Ramanujan was indeed a distinguished mathematician, and they decided to let him go. A month after this incident, Hardy’s lie came true: Ramanujan could not believe it! He had to read the letter three times to confirm his acceptance. Out of 104 candidates nominated to become Fellow of the Royal Society that year, only 15 were elected, and Ramanujan was one of them. In May 1917, he officially became S. Ramanujan, F.R.S.

## Svayambhu

The war ended, and Ramanujan prepared to return home to India. Hardy and the doctors suggested that it might be good for Ramanujan’s health if he returned home. Meanwhile, the Indian Mathematical Society was celebrating Ramanujan’s success. They honored his great achievement as a Fellow of the Royal Society. The news of his homecoming was on the front page of the society’s Journal. In March 1919, Ramanujan arrived in Mumbai. There, waiting at the docks, was his mother and younger brother. Together, they boarded a ship to Madras. In Madras, Ramanujan has reunited with his wife and the rest of his family. By this time, Janaki was 18 years old.

Ramanujan was offered a position as a professor at Madras University. His health, however, only got worse. He predicted that he would not live past thirty-five years old. Janaki took care of him; she was beside him until the very end. While in childhood, Ramanujan had been fat, now he was only skin and bones and complained of excruciating pain in his stomach. On April 26, 1920, S. Ramanujan, FRS died. He was only thirty-two years old. Hardy noted that Ramanujan’s death was one of the worst blows of his life. Twenty years later, he still treasured the opportunity of working with Ramanujan. Hardy had always insisted that Ramanujan was a self-made man.

## Conclusion

In this book, you learned about Srinivasa Ramanujan’s childhood and education, his struggles and dreams, and his failures and successes. You learned that Ramanujan was not a perfect man, but all his life, he only wanted one thing, and that was to pursue mathematics. The education system of his time was rigid. Many people misunderstood him. But his mind was unstoppable. In his short life, he contributed so much to the field of mathematics which e he loved. As long as we remember him, Ramanujan’s efforts will not be in vain. He is a great source of inspiration and pride for every Indian.