2012 was celebrated as National Mathematics Year as a tribute to Srinivasa Ramanujan who was born on 22 December 1887 and whose 125th birthday falls on 22 December 2012.
By Prof. K. Smiles Mascarenhas ( He is currently the Dean of Academic Affairs at the Coimbatore Institute of Engineering and Technology, Coimbatore . )
Author’s Disclaimer :
I have developed this article based on lectures on Ramanujan given by my mentor and friend, Dr. S. Ramaseshan (a distinguished Crystallographer and the nephew of the illustrious Nobel Laureate Sir C.V. Raman) and the lectures given by Nobel Laureate Dr. S. Chandrasekhar (a distinguished Cosmologist, and again, another nephew of the same great man!). Ramaseshan had first-hand information about Ramanujan from his father and Chandrasekhar had information about him through his mentor, Prof. Hardy. Of course, here and there I have added tidbits that I have read elsewhere. Since I cannot guarantee the veracity of those accounts, I have added the phrase ‘said to have’ to those accounts.
RAMANUJAN was born on 22 December 1887 to a poor family, at a place in Tamil Nadu called Erode (in his maternal grandmother ’s home). He was destined to be a source of inspiration and a role model for many mathematicians who followed him.
According to Ramaseshan , ‘his life reads like a fairy tale, as melodramatic as a bad Indian film’. His interest in mathematics became evident very early. As a child, he was said to be curious about the distance and shape of stars and calculated the length of equator all by himself. There is no record of how he did this.
When Ramanujan was a year and a half old, his mother gave birth to a son named Sadagopan, who died less than three months later. In December 1889, Ramanujan had smallpox and recovered, unlike thousands in the Thanjavur District who died from the disease that year. He moved with his mother to her parents’ house in Kanchipuram, near Madras (now Chennai). In November 1891, and again in 1894, his mother gave birth to two children, but both children died in infancy. Some of Ramanujan’s class mates and close relatives made some curious observation about how the young boy set about making simple discoveries in mathematics even at a tender age. It is said that he was often seen lying on his stomach on a mat with a pillow under his chest, writing on a slate (a writing pad which acted like a scratch pad memory for poor students). He had a peculiar mannerism of rubbing out his calculations with his elbow. He was often seen smiling and shaking his head. He would talk to himself, and if convinced that he had made some discovery, would enter his results into a notebook. Thus, even at a tender age, he recognized the importance of his discovery and the need to preserve them. He was also very friendly and gregarious, ever punning on Thamizh and English words.
When he graduated from Town Higher Secondary School in 1904, Ramanujan was awarded the K. Ranganatha Rao Prize for Mathematics by the school’s headmaster, Krishnaswami Iyer. Iyer introduced Ramanujan as an outstanding student who deserved scores higher than the maximum possible marks. He received a scholarship to study at Government Arts College, Kumbakonam. However, Ramanujan was so intent on studying mathematics that he could not concentrate on any other subject and failed in most of them. Because of this he lost his scholarship.
Unable to face his family and friends, in August 1905, he ran away from home, and headed towards Visakhapatnam in Andhra Pradesh, about 700 km from Kumbakonam. Why to Visakhapatnam is another question – Did he have a relative or friend there? He however stayed in Rajahmundry for about a month. Who took care of him in Andhra Pradesh is still a mystery, and there is no authentic account on how he came back home. He later enrolled at Pachaiyappa’s College in Chennai.
He again excelled in mathematics but performed poorly in other subjects such as physiology. Ramanujan failed his Fine Arts degree exam in December 1906 and again a year later. Without a degree, he left college and continued to pursue independent research in mathematics. At this point in his life, he lived in extreme poverty and was often on the brink of starvation.
No one knew how to solve cubic equations using radicals (surprisingly, even the great ancient Greeks could not figure it) till an Italian amateur mathematician named Tartaglia succeeded in the year 1535. Tartaglia kept his method a secret, but his close friend Cardan got the method from him in stealth and made it known to the world. In 1902, Ramanujan came to know about Tartaglia’s discovery and went on to find his own method to solve the quartic (fourth degree equation). He was not aware of Galois and Abels’ proof that a quintic equation (fifth degree equation) cannot be solved with radicals. He spent many unfruitful hours trying to find a general solution using radicals for the quintic equation. Since Ramanujan can be placed in the same pedestal as Galois, it is surprising how he failed to find that it was futile to attempt a solution.
Ramanujan tried to impress his peers in India by publishing difficult problems in the Journal of Indian Mathematical Society. He offered six months time to the Indian mathematicians to come up with the solution. Everyone pretended they were too busy to even attempt the problem (the truth is that no one really knew how to tackle them), and in the end, Ramanujan himself had to publish the solution. Ramanujan feared that his genius may go unnoticed and began to send his manuscripts to leading British mathematicians. Many returned them without any comments and it took the genius of two great mathematicians, Prof. G. H. Hardy and Prof. J.E. Littlewood to recognize that the manuscripts were from no ordinary genius. ‘A single look at them is enough to show that they could only be written down by a mathematician of the highest class,’ they said. When they parted that night both Hardy and Littlewood were impressed by ‘his invincible originality’ and compared him with Jacobi, the great German master of formulae.
Hardy and Ramanujan began to correspond, and Ramanujan began to send some of the striking formulae he had discovered. Ramanujan himself did not know the proof of some his results! It was purely out of his intuition and hence they are now called ‘Ramanujan’s conjectures’. When Hardy requested for the proof, he was silent. This made Hardy suspect that he was holding out the proof for fear of plagiarism. Hardy assured him that he could have his letter as a proof of his authorship in case he cheated him. This letter made Ramanujan sad. He wrote back to Hardy saying that he had found a sympathetic friend in him and would never hold anything from him. He also added that it was getting difficult for him to get ‘a proof on an empty stomach’.
Hardy at once joined forces with others in Madras in obtaining a research studentship for him so that he could pursue mathematical research full time, and in arranging his visit to Trinity College, Cambridge in April 1914 to work with him and to have first-hand contact with European mathematicians. After arriving in London he had a setback due to the outbreak of war. Soon many Cambridge mathematicians, most significantly Littlewood, left on war service. Another consequence more serious for Ramanujan’s well-being was food shortage. He was a Brahmin Hindu and a strict vegetarian and he remained uncompromising about dietary observance. In the absence of another Brahmin to cook for him, he had to cook all his food. Not finding enough time for cooking in the midst of his mathematical endeavours, he often skipped his meals.
Hardy once remarked that Ramanujan showed little inclination to those branches of mathematics that did not interest him. Hardy tried to get him interested in the theory of complex variables and failed miserably!
P.C. Mahalanobis, the well-known statistician who established the Indian Statistical Institute in Calcutta, shared his room with Ramanujan while they were in London. He one day shared a problem with Ramanujan (about ‘n’ houses in a row with natural numbers) and remarked that he was finding it difficult to arrive at a solution. Ramanujan immediately gave the solution in a totally unconventional way – in terms of continued fractions! When asked how he arrived at the solution, he answered: “It is simple. The minute I heard the problem, I knew that the answer was a continued fraction. Which continued fraction, I asked myself. Then the answer came to my mind.”
Ramanujan’s Attempted Suicide
It is now a confirmed fact that in a fit of depression (we will come to the reason later), Ramanujan attempted to commit suicide by throwing himself on the railroad track of a London underground station. But by a ‘series of miracles’, like the switch being turned off by a guardsman and the train coming to a stop just a few feet away from him, he was saved. Ramanujan sustained only superficial injuries in his legs. But since attempted suicide was a criminal offence, the Scotland Yard promptly arrested him. Ramanujan called Hardy for help and through a series of manipulations, Hardy bailed him out.
The story on Ramanujan’s attempted suicide became known in India when Chandra mentioned it in a lecture in Delhi. Chandra had to face a lot of public wrath including much rebuke from his paternal uncle, Sir C.V. Raman. Raman accused Chandra of defaming Ramanujan by publicly narrating this episode which was closely guarded by Hardy. On his part Chandra declared that there was nothing so bad about the incident, except that it illustrated that even intellectuals like Ramanujan can go through bouts of depression.
For sixteen years, Hardy guarded the secret of Ramanujan’s attempted suicide fearing it would damage the reputation of his friend. But one evening in 1936, he appeared late at dinner in Trinity, with his hand bandaged. When questioned, he narrated the following story to his fellow diners which included Chandra seated right in front of him. That morning while he was crossing the Piccadilly Circus in London, he was hit by a motorcyclist and dragged to a certain distance.
Luckily, he suffered only minor injuries in hand. Hardy was escorted to Scotland Yard by the policeman who arrested the motorcyclist. Hardy was about to leave after giving his statement, when a policeman said that a senior official wanted to meet him. In a lighter vein, the senior officer taxed Hardy with having once given him false evidence. The officer then revealed that he had handled the arrest of Ramanujan for attempted suicide and that Hardy had intervened by telling the police that Ramanujan could not be arrested since he was a Fellow of the Royal Society. Ramanujan was released; but not, the officer emphasized, because the police were bluffed by Hardy’s assertion, for they had known all along that Hardy was lying by stating that Ramanujan was an F.R.S., whereas in fact he did not become a Fellow until a month later. But the officer assured Hardy that he was not going to be arrested. Many consider this story narrated by Hardy as being fanciful, since being an F.R.S. can never confer immunity from arrest!
Janakiammal, wife of Ramanujan, when she heard about his suicide attempt directly from Chandra, had an explanation for it. While Ramanujan was in England, apparently, Ramanujan’s mother, Komalattammal would destroy letters written by Ramanujan to Janakiammal and even those from Janakiammal to Ramanujan. Ramanujan later confided to her that absence of any communication from her caused anxiety and a sense of depression in him. This could have led to his suicidal attempt.
Hardy cites Ramanujan as remarking that all religions seemed equally true to him. But he firmly believed in a god who promptly punished his devotees whenever they made mistakes. Once he inadvertently drank a beverage made out of milk and beaten eggs. Being a pure vegetarian, he considered it to be a sin and feared that he had offended the gods. On 19 October 1917, there was an air raid in the vicinity of the place he lived. Ramanujan narrowly escaped, but believed the raid as ‘punishment meted out to him by the gods for having partaken of anything non-vegetarian’.
In 1919, Ramanujan returned back to India. He was diagnosed with tuberculosis and a severe vitamin deficiency and was confined to a sanatorium. On 29 April 1920, a letter was sent from the registrar of the University of Madras to Hardy, informing him of Ramanujan’s death which occurred on April 26.
Suggested Further Reading : The Man Who Knew Infinity: A Life of the Genius Ramanujan By Robert Kanigel