Srinivasa Ramanujan: A Man With An Infinite Sense Of Numbers

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What was to be done in the way of teaching him modern mathematics? The limitations of his knowledge were as startling as its profundity. 

– Prof. G. H. Hardy talking about Srinivas Ramanujan

 Such was the genius of one of the great mathematicians of all time, Srinivas Ramanujan. A legendary genius, Ramanujan’s contribution to the field of mathematics is impeccable and profound. Indeed a mathematical phenomenon of the twentieth century, Ramanujan is among all-time greats like Euler and Jacobi. A largely self-taught pure mathematician, hindered by poverty and ill-health, his highly original work has considerably enriched the number theory. His discoveries have been applied to physics, where his theta function lies at the heart of the String Theory.

Srinivasa Ramanujan was born on December 22, 1887, in the town of Erode in Tamil Nadu, in the south of India. His father was K. Srinivasa Iyengar, an accounting clerk for a clothing merchant. His mother was Komalatammal, who earned a small amount of money each month as a singer at the local temple. Ramanujan attended the local grammar school and high school and early on demonstrated an affinity for mathematics. 

He was a solitary child by nature. It is believed that he was born as a result of ardent prayers to the goddess Namgiri. Later Ramanujan attributed his mathematical power to this goddess of creation and wisdom. For him, nothing was useful unless it expressed the essence of spirituality. He found mathematics as a profound manifestation of the Reality. He was an expert in the interpretation of dreams and astrology. These qualities he had inherited from his mother. By age 12, he had begun serious self-study of mathematics, working through cubic equations and arithmetic and geometric series. He invented his own method of solving quadratic equations.

His interest and devotion to mathematics were to the point of obsession. One day he came to possess G.S Carr’s “Synopsis of Pure Mathematics”, which contained over 6,000 formulae in Algebra, Trigonometry and Calculus but contained no proofs. He made it his constant companion and improved it further on his own. At the end of high school, the strength of his schoolwork was such that he obtained a scholarship to the Government College in Kumbakonam. However, he lost his scholarship to both the Government College and later at the University of Madras because his devotion to math caused him to let his other courses fall by the wayside. 

 At the beginning of 1907, at age 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. In July 1909, Ramanujan married S. Janaki Ammal, who was then just 10 years old. The marriage had been arranged by Ramanujan’s mother. 

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. And then a piece of luck came his way. Ramanujan tried to find work at the government revenue department, and there he met an official whose name was Ramaswamy Aiyer. Ramanujan did not have a resume to show Ramaswamy Aiyer; all he had were his notebooks – the results of his mathematical work. Ramanujan’s good fortune was that Ramaswamy Aiyer was a mathematician. He had only recently founded the Indian Mathematical Society, and he was astounded 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. 

A meeting with Ramanujan convinced Rao that he was dealing with a genuine mathematical genius. He agreed to provide support for Ramanujan, and Ramaswamy Aiyer began publishing Ramanujan’s work in the Journal of the Indian Mathematical Society. Ramanujan continued to make strides in his mathematical work, and in 1911, published a 17-page paper on Bernoulli numbers 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. There he was encouraged to do mathematics at work after finishing his daily tasks by Sir Francis Spring, an engineer, who was Chairman of the Madras Port Trust. He began pressing for Ramanujan’s mathematical work to be supported by the government and for him to be appointed to a research position at one of the great British universities. Ramanujan and his supporters contacted several British professors, but only one was receptive – an eminent pure mathematician at the University of Cambridge – Godfrey Harold Hardy, known to everyone as G. H. Hardy, who received a letter from Ramanujan in January 1913. By this time, Ramanujan had reached the age of 25.

 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, but he wasn’t quite sure which. After spending two and a half hours poring over the outlandishly original work, the mathematicians concluded:

      “I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written by a mathematician of the highest class. They must be true because, if they were not true, no one would have the imagination to invent them.”

– Prof. G. H. Hardy

Ramanujan arrived in Cambridge in April 1914, three months before the outbreak of World War 1. Within days he had begun work with Hardy and Littlewood. During their subsequent five-year mentorship, Hardy provided the formal framework in which Ramanujan’s innate grasp of numbers could thrive, with Ramanujan publishing upwards of 20 papers on his own and more in collaboration with Hardy. Ramanujan was awarded a bachelor of science degree for research from Cambridge in 1916 and became a member of the Royal Society of London in 1918.

  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 lived for only one more year. 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.

Ramanujan lived just for 32 years but during this short span, he produced such theorems and formulae which even today remain unfathomable in the present age of supercomputers. Of Ramanujan’s published papers — 37 in total — Bruce C. Berndt, Professor of Mathematics at the University of Illinois, reveals that “a huge portion of his work was left behind in three notebooks and a ‘lost’ notebook. These notebooks contain approximately 4,000 claims, all without proofs. Most of these claims have now been proven, and like his published work, continue to inspire modern-day mathematics.

 Ramanujan had very little formal training in mathematics, and indeed large areas of mathematics were unknown to him. Yet in the areas familiar to him and in which he enjoyed working, his output of new results was phenomenal.

 Ramanujan’s level of intelligence can be understood when Hardy came up with a scale of mathematical ability that went from 0 to 100. He put himself at 25. David Hilbert, the great German mathematician, was at 80. Ramanujan was 100.

   “An equation for me has no meaning unless it expresses a thought of God.

Srinivasa Ramanujan

   On the occasion of his birth anniversary, I pay my heartfelt respects to this legendary genius who will always keep inspiring us and many more generations to come.

                            

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