Wednesday, November 22, 2006

SRINIVAS RAMANUJAN

In 1913 Godfrey Harold Hardy was 36 years of age and an established mathematician. He belonged to the field of pure mathematics. He was already a Fellow of the Royal Society and was with Cambridge University. His name appeared not only in every Mathematical Journal of the time but also in the journal of Medicine. He had propounded the Hardy-Wienberg law, which states,
‘dominant traits would not take over and recessive traits would not die out’.
His future was secure and life fixed. Then with one letter from India, by someone called Srinivas Ramanujan, it all changed.
‘Sir,
I beg to introduce myself as a clerk in the Accounts Department... I have no University education... I have not trodden through the conventional regular course... but I am striking out a new path myself. I have made special investigation... and the results... are termed as startling by local mathematicians’.

And then he had rattled off some of his results. Hardy had never seen anything of this kind. It is then as Hardy would say later,
‘The romantic incident of my life began'.

The two men were exact opposites. If they had anything common, it was Mathematics. Ramanujan was intuition incarnate; Hardy was the Apostle of proof. Ramanujan was so firm in his faith in God that an equation for him had no meaning unless it was expression of a thought of God. Hardy thought mathematics proved otherwise. Ramanujan did not have a good schooling and no education after it. Hardy got the best of education; Public school then Cambridge University. ‘THE MAN WHO KNEW INFINITY A Life of the Genius Ramanujan by Robert Kanigel (Published by Rupa & Company) is the story of Ramanujan. It is the story of Hardy as well; and what they meant to each other.

 Srinivas Ramanujan - photo courtesy Wikipedia

Ramanujan was a child prodigy. No one including his teachers understood him. One day when he was in class 3, his teacher was explaining, a number divided by itself is one. You distribute 3 mangoes amongst 3 persons each will get one. Ramanujan asked, ‘Is zero divided by zero also one. If no mangoes are distributed among any one - will still each get one?’ He was talking about the ‘Indeterminate’. Something which even today is not very well understood by anyone in school years. While he was still in school that he discovered that trigonometric functions, instead of being related to the ratio of the sides of a right angle triangle, are an expression of a series. The mathematical world had discovered it 150 years ago. He did not know. He discovered it himself. Unlike common belief, Ramanujan had stood first in the district in his primary examinations and had passed school with flying colours. It is only in college that he left all subjects except mathematics. He breathed and dreamt of nothing but mathematics. It is this, which led to his failure. He could not pass college examination.

It is surprising that how many, apart from Ramanujan's mother and Hardy, have had a small but significant role to play in his life. Hardy was a cricket fan. He was in College, when Ranjit Singh the great Indian Cricketer, was in his prime. He had something to do with the removal of Hardy's prejudices against a native. Ramanujan had initially refused to go to England. Hardy recommended a scholarship for him in India. Madras University debated on whether it should be given or not. It was opposed. It could only be given to someone with the Master's degree. Ramanujan, at that time, did not even have the Bachelor's degree. It was only the persuasive arguments of Chief Justice PR Sundaram Aiyar, the then Vice-Chancellor that carried the day. He said ‘The preamble of the act establishing the University showed the prime object was to promote research. And Ramanujan had proven ability for the same’. It is only then that the University awarded the scholarship.

Hardy was once asked, what was his greatest discovery. ‘Ramanujan’ he firmly answered. At another time he said,
‘I did not invent him. Like other great men he invented himself.’
At the end of his life when Hardy would give an explanation for irrelevance of pure mathematicians to a common man's need in ‘A mathematician's apology’, a classic and still remembered for its mesmerising hold on readers, he would console himself.
‘I have done one thing... (that pompous people) have never done... (It) is to have collaborated with... Ramanujan on something like equal terms.’

Ramanujan was original and intuitive. He could feel the results. Hardy believed in logic. For him nothing was true unless proved. May be they complemented each other. It is for this reason that they got off well. And Hardy even after Ramanujan's death, at a very young age, went on to write papers on the mathematics of Ramanujan. It is often said what would have happened if Ramanujan, instead of learning mathematics himself would have learnt it traditionally. Hardy answered it in 1927,
‘he would have been a greater mathematician... discovered more that was new... (But) he would have been less of a Ramanujan and more of a European Professor and the loss might have been greater than the gain.’
About half a century later another man in another field - physics, known as Richard Feynman, would do the same. Unlike Ramanujan, he would go to college but bunk his physics classes, would rebuild college physics himself. And in that process, solve the problem of Quantum Electrodynamics in such a radical way that he could write down the answers straight away without using any mathematics. Apart, in their many traits, both were self-taught and originality was their first and their last virtue.

No article about Ramajunan can be complete without that incident about the Taxi number. Ramanujam was ill and admitted in a hospital in London. Hardy would visit him there on weekends. On one of his visits Hardy noticed the Taxi number 1729. On reaching the Hospital he mused that if it was a dull number and being a multiple of thirteen (13x133) may be bad omen. Pat came the reply from Ramanujam,
‘No, it is a very interesting number. It is the smallest number, which can be expressed as the sum of two cubes in two different ways. 1729 is equal to 123 +13 and 103+93.’

‘The man who knew infinity’ is a book, which is gripping and well written. It is one of the finest biographies ever written. It is the story of a poor but self-confident young man. It is a story of scientific achievement in adversity. It not only talks about the achievements but also narrates the psychology and cultural differences of that time. The book deals with the mathematics that Ramanujan did; the equation that he loved. They are explained in a simple way. Even if one does not understand them one can skip them. This does not affect the rhythm. The book undoubtedly will inspire young readers to emulate the great man and who knows might produce future Ramanujans. He is a source of great pride to all of us.
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