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Reflections-By Dr Rajan Philips

( This motivational article was published in Oman Observer , one of the leading Newspapers in Oman. The article is reproduced with the permission of the author )

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An oriental mathematical wizard


HE was a self taught Indian mathematical genius, who made remarkable contributions to various branches of maths. The world of Mathematics hails him as an all-time great on par with the likes of Leonhard Euler, Carl Friedrich Gauss, and Carl Gustav Jacobi.

We are talking about S Ramanujan whose birth anniversary falls today, 22 December. Hence it is but apt that we take a brief look at this prodigy and his phenomenal contributions in a very short life span of 32 years Srinivasa Iyengar Ramanujan was born in 1887 at Erode, a town in the southern Indian state of Tamilnadu in an ordinary orthodox Brahmin family. His father was a salesperson in a cloth store and his mother a housewife, who was greatly attached to him.

Ramanujan did fairly well at studies and passed his primary school examinations in November 1897. Then he enrolled at the Kumbakonam Town Higher Secondary School where his tryst with formal mathematics began. By 11, he had a thorough grasp of the mathematics courses of two college students who were lodgers at his home. Later, some one lent him a book on advanced trigonometry written by S L Loney. He completely mastered this book by the age of 13 and went on to formulate sophisticated theorems on his own. He would complete his maths exams in half the allotted time.

When 16, Ramanujan came across the book A Synopsis of Elementary Results in Pure and Applied Mathematics by George S Carr. It was a collection of 5,000 theorems, and it stirred Ramanujan’s mind even further. Next year, he independently investigated and developed Bernoulli numbers and calculated Euler’s constant up to 15 decimal places.

At his high school graduation in 1904, the headmaster, Krishnaswami Iyer, awarded him a special prize and remarked that he deserved scores higher than the maximum! Next, he studied at Pachaiyappa’s College in Madras. He excelled in mathematics, but performed poorly in other subjects. Thus he never got to complete his college degree but he carried on independent research in mathematics, despite living in poverty and desperately hunting for a job.

The situation eased a bit when he tutored a few college students and landed the job of a clerk at the Accountant-General’s office in Madras. With the support of a few well wishers he managed to have his work published in the Journal of Indian Mathematical Society.

In 1912, his friends encouraged him to send samples of his theorems to three mathematicians at the University of Cambridge. The first two, H F Baker and E W Hobson, returned Ramanujan’s papers without comment. Only the third, G H Hardy, sensed the brilliance of his work, though he too was baffled initially. Hardy had his colleague, J E Littlewood, take a look at the papers. He too was amazed by the originality of the work.

Subsequently, Hardy invited Ramanujan to come over to Cambridge and work with him. However, there was an unusual hitch. His orthodox parents were against the idea of their son leaving his country to ‘go to a foreign shore’. So Ramanujan took up research work at the University of Madras for the next two years.

In due course, fortunately, his parents’ resistance vanished after his mother had a dream in which the family goddess advised her to let Ramanujan undertake the trip as it would lead to greater things in life. That was indeed a turning point in his life. Ramanujan thus boarded the S S Nevasa and left Madras at 10 am on 17 March 1914, to arrive in London on 14 April. Soon after, he began his research with Littlewood and Hardy that lasted nearly five years. They found his ‘notebooks’ packed with theorems many of which were amazingly original.

Ramanujan was awarded a BA degree by research (which was later renamed PhD) in March 1916 for his work on composite numbers, which was published in the Journal of the London Mathematical Society. In December 1917, he was elected to the Society. He became a Fellow of the Royal Society in 1918. On 13 October 1918, he became the first Indian to be elected a Fellow of Trinity College, Cambridge.

A popular anecdote about Ramanujan relates to the number 1729, a taxicab number that Hardy mentioned as rather uninteresting. Spontaneously, Ramanujan disagreed and stated that it was the smallest number that can be represented in two different ways as a sum of two cubes.

1729 = 13 + 123 = 9 3 + 10 3
Plagued by poor health all through his life, Ramanujan’s health deteriorated in England. He was diagnosed with tuberculosis and a severe vitamin deficiency and was confined to a sanatorium. He returned to India in 1919 and died on 26 April 1920 at the age of 32.

G H Hardy once said that his greatest contribution to mathematics was ‘discovering Ramanujan’. In his rating of mathematicians on the basis of pure talent, Hardy gave himself a score of 25, to J E Littlewood 30, David Hilbert 80 and Ramanujan 100. Such was the awe that Ramanujan inspired in other mathematicians.

That it has taken many decades since his death to understand and appreciate the full implications of some of his original theorems, speaks eloquently of his incredible genius. All his phenomenal contributions came in a shockingly short life span of 32 years, weighed down by financial insecurity and severe ill health. These circumstances make his achievements all the more amazing and invaluable.

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