Srinivasa Iyengar Ramanujan was a genius mathematician, generally accepted as one of the world’s greatest of the 20th century. He has immensely contributed to the analytical theory of numbers, in addition to working on infinite series, continued fractions and elliptic functions. 125 years after his birth, his work is being applied to problems in varied fields such as cancer research, polymer chemistry and computer science. His birth anniversary December 22 is celebrated as National Mathematics Day throughout the country in recognition of his contribution to mathematics.
Ramanujan was born in a very poor, but respectable Brahmin family on December 22, 1887 in Erode, Madras (now Tamil Nadu). Early in his childhood, he showed a keen interest in mathematics. He would wonder about the shape and distance of the stars. His enthusiasm in astronomy was so great that he independently calculated the length of the equator.
Ramanujan attended primary school in Kumbakonam, where his father worked as a clerk in a cloth store. Ramanujan was admitted to ‘Town High School’ in Kumbakonam at the age of ten. He was introduced to basic mathematics. One day he was lent a book on Advanced Trigonometry by a college student. Ramanujan was extremely eager to read the book and mastered it within a year, all by himself.
When he was just sixteen, he received a book, ‘A Synopsis of Elementary Results in Pure and Applied Mathematics’ by George Carr. This book was in two volumes and was a compilation of about 6000 theorems related to all areas of mathematics. Interestingly, most of the theorems did not have any proof, whereas some had little proof. Ramanujan studied the results of the theorems carefully and he realized that he could go far beyond Carr. He was confident that he could derive results with proofs which were not in the book. This was a great inspiration, leading to the beginning of his own creative work in mathematics.
In 1903, Ramanujan secured a first class in the School Leaving Exam. He also won a scholarship and joined Government College. But he was so fascinated with mathematics that he neglected all other subjects. In the exams he excelled in mathematics but failed in the other subjects, and hence lost his scholarship.
This was one of the most difficult periods for Ramanujan. His parents’ finances were dwindling and they had two more sons to look after. His parents pressurised Ramanujan to earn and he started giving tuitions in maths. While giving tuitions, Ramanujan faced a typical difficulty. He was not able to come down to the understanding level of the students and ultimately, the students stopped attending his class.
Even during this difficult situation, his mind was full of mathematical ideas and he kept working on them at a great speed. He would hide under the cot sometimes, in order not to incur his parents’ wrath. His notebooks were full of mathematical calculations and proofs. On many occasions, he was financially supported by his friends.
In 1906, Ramanujan attended Pachaiappa’s College in Madras (now Chennai) with another scholarship. This scholarship was divided into two parts when another student applied for the same. But in the exams in 1907, he failed again in subjects other than maths. In spite of this setback, he immersed himself into investigation of complex problems, coming up with new results.
Ramanujan was so poor that he had to use a slate for his calculations. Rather than search for a cloth to wipe the slate every few minutes, he would wipe it with his elbow, which had become black and rough. At the feverish pace of his calculations, he would have required four reams of paper every month, which he could not afford. For food he had to depend on the charity of his well wishers. Hard pressed to work for a living, he met the founder of the ‘Indian Mathematical Society’ Ramaswamy Ayyar and asked him for a clerk’s job. Ayyar recommended his name to Prof. Seshu Ayyar, who was Ramanujan’s former teacher.
In the meanwhile, Ramanujan continued his independent mathematical work. In 1908 he was taken ill and was operated upon in April 1909. He recovered slowly. In July 1909, his parents, with the hope that he would understand the reality of life got him married. It was in 1911 that Ramanujan’s 17-page work on ‘Bernoulli Numbers’ was published in the ‘Journal of the Indian Mathematical Society’.
It was now that Ramanujan took the letter of introduction given by Prof. Seshu Ayyar, to the Collector of Nellore Ramchandra Rao, who was then the President of the Indian Mathematical Society. After seeing Ramanujan’s notebook, Rao realized that he had found mathematical results, which were then unknown. He offered Ramanujan a monthly stipend for his expenses. This helped him to plunge himself into research. However, he felt that his future was not secure and kept searching for a job. Finally in March 1912, he got a job as a clerk in the Madras Port Trust for Rs. 25/- per month. This meagre salary was not enough to buy the paper he required for his mathematics. He would do his calculations on wrapping paper which lay unused in the Port Trust. He was so focused on his work that he never stopped to eat. His mother and his wife fed him so that he could work without breaks.
As no one in India could evaluate Ramanujan’s work or give him an intellectual impetus, on the advice of his friends, he sent his work to eminent mathematicians in England, one of the centres of world maths. In 1912, some of Ramanujan’s works including his paper on Bernoulli Numbers were sent to M. J. M. Hill, Professor of Mathematics at University College London. Although Hill’s reply was encouraging, he had not understood Ramanujan’s results on Divergent Series.
In January 1913, Ramanujan wrote to the well-known Cambridge mathematician Prof. Godfrey Hardy, asking for his views on 120 theorems which he said he had discovered. With a colleague, Hardy began to evaluate Ramanujan’s worth. A few hours of investigation led Hardy to understand that Ramanujan was indeed a genius. Hardy convinced Ramanujan that he should come and work in Cambridge. But being orthodox Hindus, his mother opposed the idea tooth and nail. Going overseas would mean losing caste and on his return to India he would be socially ostracised. However, in May 1913, Ramanujan secured a scholarship of Rs. 75/- per month from Madras University. This award would now take care of his needs.
The family deity Goddess Namagiri had a special significance for Ramanujan and his family. It was only after praying to Namagiri with Her blessing that Ramanujan was born. His mother now had a dream in which she saw Ramanujan seated with some Europeans, with a large aura around him. This dream convinced his mother and she gave him permission to go to England. His friends, in their eagerness to change his dress style, persuaded him to wear a European dress, have an Englishman’s haircut and to wear a hat instead of his turban. Although he accepted these changes reluctantly, he was adamant about eating only vegetarian food.
In March 1914, Ramanujan left Madras for England by ship and arrived at Trinity College Cambridge in April, just before World War I started. Thus a unique collaboration started with Hardy which led to important results. Their personalities were contrasting – Hardy was slim and handsome, a cricket lover and a rationalist. Ramanujan on the other hand, was a shy and modest person, very religious and an obedient, devoted son. He was short, with a big head and penetrating eyes. Being a devout Hindu, he saw the divine all around. He had once mentioned that an equation had no meaning if it did not express a thought of God. Although Hardy was Ramanujan’s mentor, Hardy admitted that he learned from Ramanujan more than what he learned from Hardy.
Ramanujan used his intuitions in maths and was not concerned about rigorous proofs of his results. Further, as he had learnt maths all by himself, he was unaware of the latest work in modern maths. It was Hardy who updated Ramanujan with these areas, at the same time maintaining the latter’s enthusiasm and confidence. Together, Hardy and Ramanujan were instrumental in contributing to the best mathematical papers ever written, during Ramanujan’s five–year stay in England. This was despite his dislike of the cold and damp weather in England, unlike the sunny Madras weather.
In June 1914, Ramanujan was admitted to Cambridge, in spite of not being properly qualified. He secured a ‘Bachelor of Science by Research’ degree in March 1916. The topic for his dissertation was ‘Highly Composite Numbers’, which contained his seven published papers in England.
In England, Ramanujan lived the life of an orthodox Hindu. He would wear British clothes outside, but in his room he would wear his caste mark and a dhoti. He was a good cook and host, and made delicious vegetarian food. Due to winter and also due to the outbreak of World War I, vegetables were not available. As a result his health deteriorated and he contracted T.B. in 1917.
Though doctors felt that he would recover if he went back home, it was dangerous to travel because of the war. Ramanujan was in and out of hospital for the next two years, without much relief. However, his sharp intellect in maths was maintained by him. Once, Hardy visited Ramanujan in a hospital. He mentioned that he had alighted from a cab with an insignificant number 1729. “No, Hardy, no!” Ramanujan replied excitedly. He said the number 1729 is an interesting number. It is the smallest number which could be expressed as the sum of two cubes in two distinct ways: 1729 = (9 X 9 X 9) + (10 X 10 X 10) and (12 X 12 X 12) + (1 X 1 X 1)
In December 1917, Ramanujan was elected to the London Mathematical Society. Soon thereafter, he was elected to the Royal Society of London as a Fellow, being only the second Indian to receive such an honour, and at the young age of 30. In 1918, he was elected to the Cambridge Philosophical Society as a Fellow. He was also the first Indian to be honoured as a Fellow of the Trinity College of the University of Cambridge in the later part of 1918.
Ramanujan greatly improved in health by November 1918. But by 1919, he was again unwell and very weak. In February that year, he set sail for home. He was welcomed like a hero. In spite of the warm weather and loving care of his family in Madras, his health did not improve. He continued to work and also wrote to Hardy, but he died on April 26, 1920 at the young age of 32.
Ramanujan left behind numerous notebooks and scrap papers, full of thousands of theorems, which intrigue mathematicians even today. In the efforts to improve these theorems, new disciplines in mathematics have emerged. His colossal work, even after 95 years of his death, is relevant to present complex problems in several disciplines. Prof Richard Askey of the University of Wisconsin, Madison USA, lamented that if Ramanujan had been born 100 years later, his intuitive capacity would have helped solve several problems.
To become a professional mathematician, Ramanujan had to face insurmountable hurdles. In spite of his abject poverty, his achievements were extremely remarkable. He did not receive encouragement from any quarter in India. Perhaps nobody could understand his talents. Ramanujan’s genius and his relationship with Hardy attracted certain writers abroad. Three plays containing this subject explore this relationship and Ramanujan’s genius. They are ‘Partition’, ‘First Class Man’ and ‘A Disappearing Number’. In 1991, Robert Kanigel wrote a biography on Ramanujan – ‘The Man Who Knew Infinity’.
Excerpts from ‘World Famous Indian Scientists’
Anup Y. Attavar
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Indeed, their lives, with their sincerity of purpose, along with their grit and determination to overcome all odds and their struggles will serve as role models for the current and future generations who, by and large are not aware of the giant contributions made by these truly great heroes in the fields of science and technology, industry, business, etc. The youth will definitely benefit by reading about these giants in their own fields. Even if a small percentage of our youth and students strive to follow the footsteps of these towering personalities, attempt to imbibe a scientific temper and if these articles instill a sense of patriotism among the youth, these articles will have served their purpose.