The great mathematician of India, Srinivasa Ramanujan, did such the work only at the age of 32 years, which can be compared rarely. That is why he is considered to be one of the greatest mathematicians of modern times. His birth anniversary is also celebrated as ‘”National Mathematics Day” in India. Srinivasa Ramanujan was a largely self-taught pure mathematician. He was one of India’s greatest mathematical geniuses. Hindered by poverty and ill-health, his highly original work has considerably enriched the analytical theory of numbers and worked on elliptic functions, continued fractions, infinite series and, more recently, physics.

Srinivas Iyengar Ramanujan was born in his grandmother’s house in Erode, a small village about 400 km southwest of Madras on December 22, 1887. When Ramanujan was a year old his mother took him to the town of Kumbakonam, about 160 km nearer Madras. His father worked in Kumbakonam as a clerk in a cloth merchant’s shop. When he was nearly five years old, Ramanujan entered the primary school in Kumbakonam and attended several different primary schools before entering the Town High School in Kumbakonam in January 1898. At the Town High School, Ramanujan showed himself an able all round scholar. In 1900 he began to work on his own on mathematics summing geometric and arithmetic series. By the time he was 12, he had begun serious self-study of mathematics, working through arithmetic and geometric series and cubic equations. He discovered his own method of solving quartic equations. His memory for mathematical formulas and constants seems to have been boundless: he amazed classmates with his ability to recite the values of irrational numbers like π, e, and √2 to as many decimal places as they asked for.

In 1904 Ramanujan left high school; his future looked promising: he had won the school’s mathematics prize and, more importantly, a scholarship allowing him to study at the Government Arts College in the town of Kumbakonam. Obsessed with mathematics, Ramanujan failed his non-mathematical exams and lost his scholarship. In 1905 he traveled to Madras and enrolled at Pachaiyappa’s College, but again failed his non-mathematical exams.

At the beginning of 1907, at the age of 19, with minimal funds and a stomach all too often groaning with hunger, Ramanujan continued on the path he had chosen: total devotion to mathematics. The mathematics he was doing was highly original and very advanced. By 1910 he realized he must find work to stay alive. In the city of Madras he found some students who needed mathematics tutoring and he also walked around the city offering to do accounting work for businesses. Ramanujan tried to find work at the government revenue department, and there he met an official whose name was Ramaswamy Aiyer. Ramanujan’s good fortune was that Ramaswamy Aiyer was a mathematician. He had only recently founded the Indian Mathematical Society, and his jaw dropped when he saw Ramanujan’s work. Ramaswamy Aiyer contacted the secretary of the Indian Mathematical Society, R. Ramachandra Rao, suggesting he provide financial support for Ramanujan. At first Rao resisted the idea, believing Ramanujan was simply copying the work of earlier great mathematicians but a meeting with Ramanujan, however, convinced Rao that he was dealing with a genuine mathematical genius and Ramaswamy Aiyer began publishing Ramanujan’s work in the Journal of the Indian Mathematical Society. In March 1912 his financial position improved when he got a job as an accounting clerk with the Madras Port Trust.

In July 1909 Ramanujan married S. Janaki Ammal, who was then just 10 years old. The marriage had been arranged by Ramanujan’s mother. The couple began sharing a home in 1912.

Ramanujan and his supporters contacted a number of British professors and an eminent pure mathematician at the University of Cambridge, Godfrey Harold Hardy, known to everyone as G. H. Hardy, had received a letter from Ramanujan in January 1913. By this time, Ramanujan had reached the age of 25 and professor Hardy puzzled over the nine pages of mathematical notes Ramanujan had sent. Hardy reviewed the papers with J. E. Littlewood, another eminent Cambridge mathematician, telling Littlewood they had been written by either a crank or a genius ? After spending two and a half hours poring over the outlandishly original work, the mathematicians came to a conclusion that they were looking at the papers of a mathematical genius. Hardy was eager for Ramanujan to move to Cambridge, but in accordance with his Brahmin beliefs, Ramanujan refused to travel overseas so an arrangement was made to fund two years of work at the University of Madras. During this time, Ramanujan’s mother had a dream in which the goddess Namagiri told her she should give her son permission to go to Cambridge, and this she did. Ramanujan arrived in Cambridge in April 1914, three months before the outbreak of World War – I. Ramanujan’s prodigious mathematical output amazed Hardy and Littlewood.

In 1918 Ramanujan became the first Indian Mathematician to be elected a Fellow of the British Royal Society. In his short lifetime he produced almost 4000 proofs, identities, conjectures and equations in pure mathematics. In 1917 he was diagnosed with tuberculosis and worryingly low vitamin levels. He spent months being cared for in sanitariums and nursing homes. In February 1919 his health seemed to have recovered sufficiently for him to return to India, but sadly he would only live for about a year on his return. Srinivasa Ramanujan died aged 32 in Madras on April 26, 1920. His death was most likely caused by hepatic amoebiasis caused by liver parasites common in Madras. His body was cremated.

In his word-

While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing. – SRINIVASA RAMANUJAN

Professor Bruce Berndt is an analytic number theorist who, since 1977, has spent decades researching Ramanujan’s theorems. He has published several books about them, establishing that the great majority are correct. He was told an interesting story by the great Hungarian mathematician Paul Erdős about something G. H. Hardy had once said to him-

Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100. Hardy gave himself a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100. – PAUL ERDŐS