Friday, August 10, 2007

Book Review-- Maths-S Ramanujan

Ramanujan: Letters and Commentary (History of Mathematics, Vol 9)-- by Bruce C. Berndt, Robert A. Rankin

It is lonely at the top

Shivanand Kanavi

"I beg to introduce myself to you as a clerk in the accounts department of the Port Trust Office at Madras .... ". Thus started the most famous letter in 20th century mathematics, written by Srinivasa Ramanujan to Godfrey I-tarold Hardy.

Was Ramanujan, afraid that proofs of his theorems may be stolen by the dons at Cambridge or was he afraid of being ridiculed for his intuitionistic methods? Was he really afraid that he will be "polluted" by going to England or was he pressured into refusing to go by other orthodox Brahmins, and so on are among the many questions that are raised by this latest collection of Ramnaujan letters, edited by two mathematicians, B.C.Berndt and R.A.Rankin.

Ramanujan's method of stating an important result and providing some 'hand waving' arguments as the basis of the result rather than give rigorous proofs was unique and mathematicians like MJ.M.Hill dismissed his genius. One of the reasons for the cryptic nature of his proofs was his notation which he very much kept to himself and the other was that many a time his "proof" will involve leaps that could not be bridged by rigorous mathematics. Nevertheless G.H.Hardy recognised the genius and endeavoured successfully to get him to come to Cambridge. In fact the collection contains a letter written by Bertrand Russel to one of his women friends wherein he mentions, "I found Hardy and Littlewood in a state of wild excitement, because they believe they have discovered a second Newton, a Hindu clerk in Madras".

But actually, Hardy's close associate J.E.Littlewood thought otherwise, in a letter he told Hardy that, he placed Ramanujan on par with Jacobi (important Hungarian mathematician, but not up to the stature of Newton). He also thought Ramanujan was not disclosing his proofs because he probably feared that English mathematicians might "steal" his results! Ramanujan expressed his pain on reading the same allusion in Hardy's reply to his first letter, but surprisingly did not disclose any more information regarding his methods. Instead he wrote, "I am already a half starving man. To preserve my brains I want food and this is now my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship either from the University or the government", and added a few more results in his famous second letter. Considering his economic plight and the craving for professional peer recognition and even critique and considering the plundering of India in the hands of Britain his unexpressed fears are understandable.

A misconception cleared by the collection under review is regarding Ramanujan's orthodoxy that. prevented him from accepting the invitation to go to Cambridge. In a letter to Hardy, Ramanujan explained that when the offer was made by C.E.Mallet of India Office, London, it was too vague and besides it brought visions of having to appear for a civil service examination. This made him hesitate and mean while, his boss, an orthodox Brahmin, who was accompanying him, intervened and categorically told mallet that Ramanujan cannot go due to religious reasons. It is clear from the letters that Ramanujan was actually looking forward to meeting the best mathematical minds of Europe.

The letters also bring out the loneliness he suffered during his illness first in England and then in India. However being extremely conscientious and grateful for the fellowship he kept sending new results despite severe illness.(The illness which was never diagnosed properly has now been diagnosed as amoebiasis of the liver according to the authors). In fact Hardy's letter to J.J.Thompson (Nobel Laureate physicist and president of the Royal Society) shows that fearing the worst and aiming to give some incentive to Ramanujan to fight the illness, Hardy lobbied for the early award of the Fellowship of the Royal Society.

Though after his death his family members engaged in a sordid exhibition of greed and propensity to cash in on respect and sympathy for Ramanujan, he himself exhibited his generosity by asking his family to actually give some money for scholarships to poor students.
The collection is a valuable addition to the growing literature about Ramanujan's life and work. The editors have taken particular pains to add fairly detailed biographical notes on all the individuals that are mentioned in the letters, thereby giving a flavour of associates and friends of Ramnaujan. They have also given extensive mathematical notes on the history and evolution of each of Ramanujan's propositions as they appeared in his letters. On the whole it is an enjoyable reading for mathematicians as well as lay public interested in the Indian genius.

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