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Portable protégé

The Indian Clerk by David Leavitt

Seelye Martin 27 March 2011

www.lablit.com/article/655

Detail from the cover

He is not happy: he can’t get familiar food, his feet hurt, the climate and society are terribly unfamiliar

In 1913, the British mathematician G. H. Hardy (1877-1947), a legendary figure in number theory, receives a 15-page letter from an Indian clerk named Srinivasa Ramanujan (1887-1920), who works for the Port Trust Office in Madras. The letter discusses various existing mathematical results in number theory, and states new results without proofs. Hardy reads the letter, is intrigued, and discusses it with his Trinity College collaborator John Littlewood. Thus begins the David Leavitt’s novel, The Indian Clerk (2008), about the discovery by Hardy of the Indian mathematical prodigy Ramanujan, the effort expended in bringing him to Cambridge, Ramanujan’s collaboration with Hardy and his trials and tribulations in England. The story of Ramanujan and his discovery by Hardy as a self-taught mathematical genius in Madras is a mathematical legend (the 1995 movie Good Will Hunting is a modern analogue), and serves as the basis for a well-researched and interesting novel.

The book has several narrators, including Hardy, Littlewood and Alice, the wife of Neville, a junior mathematics faculty member at Trinity. Interleaved throughout the book are chapters describing Hardy’s thoughts at the 1936 Harvard Tercentennial, where he was invited to give a series of talks on Ramanujan, which allow him some perspective on the events that occurred during Ramanujan’s visit, and to present information on Ramanujan’s early life. If you decide to read this book, the paperback is preferable, because as the author notes, many of the mathematical and historical errors in the hardback are corrected in the paperback.

Hardy and Littlewood work closely together. Hardy is gay; he has crushes on a variety of Cambridge undergraduates and moves in the gay society of Trinity College, where in the book at least, gay issues and gay sex figure prominently; he is also haunted by the ghost of a former lover. In contrast, Littlewood is having an affair with a married woman, whom he meets about once a month in London. Leavitt has done a great deal of research on Cambridge of a century ago; from his description, pre-war Cambridge appears to be as mysterious as India of that time. As an example, as part of their graduation requirement, all Cambridge mathematics students must take an examination called the Mathematical Tripos. The form of this examination was set in the late 18th century, is based on Newton’s Principia, and uses Newton’s archaic form of the calculus, rather than the usual Leibnitz form. To pass the Tripos, the students must undergo a year of intense tutoring in Newton’s work. Hardy is bitter and dismissive about this archaic exam; the German mathematicians make fun of it, until finally in 1910 Hardy manages to replace the Tripos with an examination based on modern mathematics. The combination of the Apostles, the state of the Tripos examination, and the strong class system gives an archaic flavor to Cambridge of a century ago.

One of Hardy’s goals in inviting Ramanujan to England is his desire to solve an important theorem in number theory, the Riemann hypothesis, which at this writing remains unproved. The Riemann hypothesis is based on the conceptually simple zeta function and involves the determination of the location of its zeros in the complex plane – Leavitt does a credible job explaining it in the novel.

Real-life fellow mathematician Stanislaw Ulum, who met Hardy at least twice, once in Cambridge, England and once in Cambridge, Massachusetts, describes him as “known for his eccentricities” – and Leavitt describes many of these. Hardy did his best to avoid being photographed, and would cover the mirrors in hotel rooms where he stayed. His strangest behavior occurs during a boat trip to Copenhagen. On the return, it is very stormy, and Hardy worries that the ship might go down. To cover himself and before getting on the ship, he sends out a number of postcards to friends on which he writes that he has proved the Riemann hypothesis. His assumption is that because the mathematician Fermat wrote that he had proved Fermat’s last theorem in the margin of a textbook before he died, that God would permit such an event to happen only once, so that Hardy would survive the trip.

Equations relevant to number theory are sprinkled throughout the book. Some of them such as the definition of the zeta function are informative, others are simply wallpaper. Given the importance of number theory to Hardy’s life, and his feeling that his work is without application, let me give two examples of the use of number theory in the real world. First, when I pay for my purchases at the grocery store with a cash card, before transmission of the debit to my bank, the information is encrypted with an algorithm based on prime numbers. Another application occurs in the recording of Brian May’s anthem, “We Will Rock You”. Here, the sound of the repeated stomp-stomp-clap was generated by superposition of the individual stomps or claps with audio delays proportional to the prime numbers 2, 3, 5, 7, 11, 13, 17…, so that each composite stomp and clap is distinctly non-harmonic. The resultant clap or stomp sounds as if it were centered on the listener. (Find out more in this interview with Brian May).

After introducing us to Cambridge and to Littlewood, the novel shifts to Hardy and Littlewood’s efforts to bring Ramanujan to England. Correspondence ensues between Hardy, Littlewood, the British India Office in London and the British in India. Given the letters from Hardy/Littlewood, the British/Indian officials realize that they have a prodigy on their hands, so Ramanujan is offered a research fellowship at a university in Madras. Because the newly married Neville and Alice are going to India for Neville to give a series of lectures, Hardy asks Neville to negotiate the details of Ramanujan’s visit to Cambridge. Difficulties ensue: Ramanujan’s religion forbid him to travel over water, and he is also concerned that the source of his mathematical ideas is the Goddess Namagiri, and that if he leaves India, she will cease to provide them. He has married a 12-year-old girl, where the marriage will not be consummated until she turns 18, who will not travel with him. His mother, however, urges him to go, and Neville is able to raise the necessary funds for his travel. As soon as Ramanujan has a dream that the gods have given him permission to travel over water, in April 1914, he travels to Cambridge.

Once in England, Ramanujan wears a western suit and shoes, both of which are too tight. The college community knows him as the “Hindoo Calculator.” Ramanujan is not happy: he can’t get familiar food, his feet hurt, the climate and society are terribly unfamiliar, and he is concerned that his wife back home is being abused by his mother. And then, World War I begins, and because of the German submarine blockade, Ramanujan can’t go home.

The book, previously sad in tone, becomes very dark. Littlewood enlists in the Army as a second lieutenant and is posted to Woolwich Arsenal to work on ballistics. Hardy and Neville are pacifists, and remain at Cambridge. All healthy English students leave Cambridge and enlist. The Cambridge common becomes a drill field; the college high tables become officers’ messes; the college lawns are filled with hospital tents with a cumulative length of three-quarters of a mile. Because the British medical establishment is fixated on fresh air as a curative, the tents are open to the weather.

As a pacifist, Hardy feels strongly that the international community of mathematicians is of greater importance than the war. During the war, he writes a paper by mail with a Hungarian mathematician that is published in Sweden. He works to free a German mathematician from an internment camp in Britain. He publishes in journals based in neutral countries. He becomes secretary of the Cambridge branch of a group called the Union for Democratic Control, which lobbies for a just peace settlement. The group is extraordinarily unpopular; Neville, who is also a member, loses his Trinity fellowship, and Hardy’s cat is poisoned.

One problem with the novel is the disconnect between the description of the importance of Hardy’s and Ramanajan’s work, and the lack of information about its actual content and relevance. Between 1914 and 1919, Hardy states that he had written 50 papers, but without describing their content. The work that Ramanujan does in England is sufficient to have him elected both a Fellow of the Royal Society and the first Indian fellow of Trinity College. In these elections, because of the unpopularity of Hardy’s antiwar stance and Littlewood’s army service, Littlewood does most of the work in getting Ramanujan these honors. Again, there is little information on the details of Ramanujan’s accomplishments and publications used in these elections. The book would have been improved by the addition of a scene where Littlewood and Hardy discuss which publications of Ramanujan’s should be used to qualify him for these honors. Instead, Hardy only states that Ramanujan is the best mathematician in 400 years.

During this period, Ramanujan becomes seriously ill. Hardy behaves impeccably; he tries to obtain the best medical care for Ramanujan and sends him away to a country hospital, but it’s a grim place, where Ramanujan is forced to do all his mathematical work in the only heated building, a small toilet. Ultimately, his illness increases, and he becomes suicidal as the story heads for its dark conclusion. And afterwards, Hardy is unable to shake his guilt for his part in his protégé’s fate.

Ramanujan, both before and after his death, was lionized in India, with scholarships and prizes named after him. In England, Trinity College currently offers a three year Ramanujan Research Studentship in mathematics for Indian students. Despite its less-than-happy ending, Ramanujan’s story and his interaction with Hardy have become a part of mathematical and popular culture.