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Mathematicians of India - Srinivas Ramanujan

Ramanujan The teacher was asking some simple questions in arithmetic. The class was learning the simple operation of division. When the teacher asked how many bananas would each boy get if three bananas were divided equally among three boys, someone had an answer. One each. Thousand bananas divided equally among thousand boys? The answer was still the same. One. The class was progressing thus, questions being asked by the teacher and answers being provided by the student. But there was a boy who had a question. If none of the bananas was divided among no boys, how much would each boy get? The whole class burst into laughter at what the students thought was a fast one or a silly question. But the teacher seemed to have been impressed. He took it upon himself to explain to the boys that what the student had asked was not a silly question but rather a profound one. He was questioning the teacher about the concept of infinity. A concept that had baffled mathematicians for centuries, until the Indian scientist Bhaskara had provided some light. He had proved that zero divided by zero was neither zero nor one, but infinity.

The student was Srinivas Ramanujam, the genius who introduced the concept of zero to the world. Ramanujam was born Erode in Tamil Nadu on December 22, 1887. His mathematical genius began to show at a very early age and soon senior students began to haunt his house for clarifying doubts. When he was merely thirteen years of age, he mastered a book on Trigonometry. So taken by the subject was he that he launched his own research work. He put forward theorems and formulae that had been discovered earlier by great mathematicians but were not covered in the book.
Srinivas Ramanujan

The real turning point that triggered off his own creations came two years later, when a friend introduced the book Synopsis of Elementary Results in Pure and Applied Mathematics by George Shoobridge Carr to Ramanujam. Where any other person at the age of fifteen may have recoiled from the book, Ramanujam became delighted at the introduction. He began solving problems given in the book. With the floodgates now open, ideas began to pour forth. Such was the gush of ideas that Ramanujam found it difficult to write them all down. Can you hazard a guess on the number of papers that Ramanujam required per month for jotting his ideas? Two thousand! He scribbled his results in loose sheets and notebooks. In fact, before he went abroad for pursuing his studies at the Cambridge University, he had filled three notebooks with his jottings, which later came to be known as Ramanujam’s Frayed Notebooks.

Ramanujam’s father, a clerk, however, could never fathom the boy’s obsession for numbers. Although the boy had secured a first class in his matriculation examination and had also been awarded the Subramanyan scholarship, he had failed in his first year college examinations. This was because, being obsessed with mathematics, he had neglected all other subjects. Desiring to bring his “mad” son back on the course of “normalcy”, the worried father got him married to a young girl of eight!

This put Ramanujam in real dilemma. He needed to find money to support self, wife and buy paper for his jottings. Oh yes, marriage did not distract him from his magnificent obsession. Driven to desperation, he began reusing papers, now writing on them in blue and rewriting over it in red so as to be able distinguish between two trains of thoughts. Ramanujam approached several offices and applied for a clerical job, displaying his now famous frayed notebooks and papers and claiming that he was good in mathematics. However, nobody could follow his work and he was turned away. Luckily for him, he came across one Francis Spring, who did seem to understand what was in the notebooks and who appointed him at the Madras Port Trust where he (Spring) was the Director. Soon after, some educationists took up the cause of Ramanujam and in May 1913, the University of Madras awarded him a fellowship although he had no formal degree.

In the meantime, Ramanujam had approached the great mathematician G. H. Hardy and presented to him a set of one hundred and twenty theorems and formulae. A part of it was the Reimann series, a topic in definite integral in calculus. Ignorant of Reimann’s original work, Ramanujam had reproduced the work all over again.

Yet another intriguing portion of the collection sent to Hardy was Ramanujam’s interpretation about the equations called “modular”. It was later proved that Ramanujam’s conjectures were indeed correct. The collection also included a formula in hypergeometric series, which later came to be named after him.

Hardy and his colleague, J. E. Littlewood, recognised the genius in Ramanujam and made arrangements for him to travel to Cambridge University to study. Hardy was amused to find that Ramanujam was an unsystematic mathematician, who played with maths much as a child played with toys. His mathematical truths were not explained and it was left to other mathematicians to prove them.

Ramanujam was elected Fellow of the Royal society in February 1918. He was the second Indian to be honoured with this fellowship and the first Indian to be elected Fellow of the Trinity College, Cambridge. His contributions to the field of mathematics included the Hardy-Ramanujam –Littlewood circle method in number theory, Roger-Ramanujam’s identities in partition of integers, list of highest composite numbers and some work on the algebra of inequalities and the number theory.

Unfortunately, Ramanujam fell victim to tuberculosis and had to be sent home to India. Fighting pain and death, Ramanujam kept himself pre-occupied by playing with numbers. He succumbed to the illness at the tender age of thirty-two. Within the short life span, Ramanujam had earned repute as an astrologer and an orator too.

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