The Great Indian Scientists---Srinivasa Ramanujan (Lesson-6)

Srinivasa Ramanujan (1887-1920)

Srinivasa Ramanujan is a name that needs no introduction. He was one of the foremost Indian mathematicians who made significant contributions to mathematical analysis, number theory and continued fractions. He had no formal training in pure mathematics. He started working in isolation out of his sheer love for the subject. This made his achievements really standout.

Early life

Ramanujan was born on 22 December 1887 in Erode, Chennai. Later, he was brought to his father’s town Kumbakonam. His father was a clerk in a sari shop. Ramanujan passed his primary education in 1897 and showed promising signs by standing first in the whole district. He passed matriculation and then entered Kumbakonam’s Government College. He was awarded scholarship there. By this time, he was obsessed with maths that he lost interest in all other subjects. As a result he couldn’t do well in other subjects and hence failed. He then tried once again in Madras Pachaiyappa’s College, but again failed.

In 1909, he married a 9 year old girl. Ramanujan had to face many hardships. He even didn’t have money to buy food; and he needed 4 reams of paper (1 ream=500 sheets) every month to write his propositions. He had no scholarship; he failed in examinations; he also had failed as a tutor of the subject he was very fond of. He was unable to maintain family until he got a job as a clerk in the Madras Port Trust with the help of Narayana Iyer in 1912. Also, his association with the other mathematicians helped him. He was introduced to the then Nellore Collector Diwan Bahadur R. Ramachandra Rao who was also the secretary of the Indian Mathematical Society. This society was founded by V. Ramaswami Iyer, a government servant. The society’s journal became popular. Ramaswamy Iyer met Ramanujan in 1910. He introduced Ramanujan to others who shared common passion for mathematics.

Obsession with Mathematics

Ramanujan came across a book, A Synopsis of Elementary Results in Pure and Applied Mathematics by George Shoobridge Carr. It was a compilation of about 5000 equations in algebra, calculus, trigonometry and analytical geometry. It was in two volumes and Ramanujan had the first one. The book was not a really good one, but it was simple and clear. This book had great influence on Ramanujan. According to Hardy, Carr’s name was kept alive because of Ramanujan. He says, people remember the book only because it had great influence on Ramanujan. It had given an academic direction to Ramanujan. Carr simply gave the formulae and some hints to proceed. Ramanujan found it challenging and exciting. He was so intrigued by the book that he wanted to solve all the problems in it. While doing so, he compiled the results in his notebooks. So between 1903 and 1914, he had compiled 3 notebooks.

Turning point

Ramanujan wrote a letter, with all the discoveries he had made in mathematic,s  to G. H. Hardy, a British mathematician. Ramanujan requested Hardy  for his advice and to help getting his results published. Hardy was a leading light in mathematics and dominated the mathematical landscape of England. He was widely known for his works on and contributions in “Pure Mathematics”. He, along with J. E. Littlewood wrote over 100 papers on mathematical topics. Hardy and Littlewood studied Ramanujan’s propositions and understood that he had an exceptional intelligence in mathematics. However, they also understood that Ramanujan was not aware of formal and basic tools needed to be a seasoned mathematician. Hardy invited Ramanujan to England to study at Cambridge and continue his research. He also arranged for a research scholarship by the Madras University. Gilbert walker, a former fellow and mathematics lecturer at Trinity College, recommended Ramanujan to the University in this process. Ramanujan’s mother didn’t accept for his travel, but later agreed for that. Ramanujan left Madras by S.S.NEVASA, accompanied by E. H. Nivelle in 1914. His coming was awaited with eager anticipation in the mathematical circles.

Achievements

Ramanujan was awarded B.A. degree in March 1916. He had submitted extensive work on ‘Highly composite numbers’ which was published in the journal of the London Mathematical Society. In 1918 he was elected a fellow of the Royal Society, owing to his work on Elliptic Functions and the Theory of Numbers. He was also elected the Fellow of Trinity College, Cambridge. He was the first Indian to achieve this. But, even before the full recognition of powers, he breathed his last. 

He showed the first signs of illness in 1917, slightly recovered in 1918; but returned home in 1919 and unfortunately at a very young age, died the following year.

G.H. Hardy

According to J. R. Newman, Hardy was also to be credited for Ramanujan’s achievement. Hardy himself worked so hard along with Ramanujan in refining the way he arrived at results as Ramanujan had no formal training of that. Hardy had the internal conflict in deciding how to proceed with this brilliant man who could work with ease on complex equations, who had mastery of continued fraction had a very little idea of what a mathematical proof is. Ramanujan’s results were arrived at by a combination of intuition and induction, which he couldn’t reason or argue for. Hardy had recognized his originality and helped him carry out his work.

Hardy in his book entitled Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work said that he had to form himself to help Ramanujan in his work. he wrote that Ramanujan was a keen philosopher and an enthusiastic politician. He was a strict vegetarian. All religion to him was similar in nature. He said, Ramanujan was a genius in his own right. He was very hard-working. He had a deep sense of form and great capacity of fast amendments of his hypotheses which was often surprising. He has no competitor in his day. Ramanujan’s greatest achievement was his deep and flawless originality of work. It had lasting impact on the research on mathematics.

Contributions and their significance

Ramanujan made significant contributions to mathematical analysis, number theory and continued fractions.

His work in mathematics majorly encompassed Number theory--the most basic form of mathematics. It includes analytic number theory, geometric theory and probabilistic number theory.

His other discovery was the mock-theta functions

He recognized the multiplicative properties of the coefficients of modular forms.

His work has some applications in particle physics as well as in calculation of pi up to a very large number of decimal places.

His research on Reiman’s Zeta Function has been applied to the pyrometry—the investigations of the temperature of furnaces.

His work on the partition numbers resulted in two applications—new fuels and fabrics like nylons.

He did mathematics for the sake of mathematics, for the joy he got in doing it, for the excitement he felt in peeping through the numbers, theorems, problems, and solving them. His achievement was so great, so impactful, so powerful that those who can understand his work will wonder at his achievements in such a short span of time. The Ramanujan museum was founded by P. K. Srinivasan, a mathematics teacher in 1993.

In 2012, Dr Manmohan Singh declared Ramanujan’s birthday, December 22, as National Mathematics day.

‘The man who knew infinity: A Life of the Genius Ramanujan’ is a biography written in 1991 by Robert Kanigel. A film was released with the same title in 2015.