Tuesday, October 18, 2016

DVD: The Man Who Knew Infinity

The Man Who Knew Infinity tells the amazing story of Srinivas Ramanujan, a very gifted mathematician who made astonishing contributions to the analytical theory of numbers in the field of mathematics. The movie is based on the book, The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel. In the movie, Ramanujan is portrayed by actor Dev Patel (Slumdog Millionaire).

Ramanujan was born December 22, 1887 in Erode, Madras Presidency in the British Raj. When Ramanujan was a small child he did not like attending school. He became interested in mathematics while attending Town High School where he came across a book, Synopsis of elementary results in pure mathematics by G.S. Carr. He was able to teach himself mathematics using this textbook. In 1904, Ramanujan attended Government College in Kumbakunan on a scholarship. However he lost his scholarship the following year because he devoted all his time to the study of mathematics and very little to other subjects. Eventually he left Government College and in 1906 he entered Pachaiyappa's College in Madras with the intention of passing the First Arts Examination so that he could attend the University of Madras. He failed the examination because he was only able to pass the mathematics portion of the exam and dropped out of school. Despite this, Ramanujan continued to work on mathematics; in 1908 he worked on continued fractions and divergent series and in 1911 he published a paper on Bernoulli numbers in the Journal of the Indian Mathematical Society. This paper gained him the reputation as a mathematical genius in the Madras area. At this time in his life Ramanujan was struggling to survive as he had no paying job. He had married a ten year old girl, Jannaki Ammal in 1909 but they did not live together for several years.

Ramanujan was well known to many mathematicians in the Madras area and he was finally able to obtain employment as clerk in 1912 at the Madras Port Trust. In fact, the Chief Accountant for the Madras Port Trust was a trained mathematician and he clearly recognized Ramanujan's abilities. Eventually Ramanujan's work came to the attention of  G.H. Hardy, a resident at Trinity College, Cambridge when he received a letter from him in early 1913. Ramanujan had contacted various other professors in England without much success. However Hardy was most interested. Ramanujan's letter contained a long list of unproven theorems and Hardy wanted some proofs. Ramanujan desperately wanted to travel to England but he required a scholarship to do so. With Hardy's help he was able to obtain a scholarship for two years from the University of Madras and travelled to England from India in 1914.

Srinivas Ramanujan
The Man Who Knew Infinity picks up Ramanujan's story in 1914 just before he leaves Madras for England. Dev Patel is cast as Ramanujan and G. H. Hardy is played by Jeremy Irons. This casting gives viewers the sense that Hardy was a much older mentor to the younger Ramanujan but in fact there was only ten years between the two men. The film beautifully portrays the gradual friendship and mutual respect that develops between these two men from vastly different cultures over the span of five years. In fact it is this wonderful capturing of the deep relationship between these two brilliant men that makes this movie so rewarding. At the beginning, Hardy is somewhat gruff and professional and it is the kindly encouragement of Hardy's colleague, John Littlewood that helps Ramanujan. But Hardy's open mindedness and his willingness to recognize the genius of Ramanujan and to help him, form the basis of a deep friendship and working partnership. Despite their common love of theoretical mathematics, Ramanujan and Hardy were very different. Ramanujan was a deeply religious man, a Brahmin who was a vegetarian. In contrast, Hardy was an atheist, who states in the movie that he doesn't believe in anything he can't prove. In a scene from early in the movie, Ramanujan questions Hardy for walking with an umbrella in bright sunshine. Hardy responds that "God and I don't exactly see eye to eye." but Ramanujan tells him "No sir. You believe in God. You just don't think He likes you." When asked by Hardy (and others) where he got his ideas, he often stated that they came from God. "You want to know how I get my ideas? God speaks to me...An equation for me has no meaning unless it represents a thought of God." Hardy works tirelessly to get Ramanujan elected as a Fellow of the Royal Society and as a Fellow of Trinity College Cambridge. When Ramanujan decides to return to India and they say goodbye, Hardy tells Ramanujan he wants a letter each week with a new idea. The two men are now close friends and Hardy seems at a loss over Ramanujan's departure. Overlaying this scene is a sense that Hardy will never see him again in this life.
Ramanujan (centre) with fellow Trinity students.

The film portrays Hardy's efforts along with his colleague John Edensor Littlewood (who is played by Toby James) to give Ramanujan the mathematical training he needs. Hardy is seen relentlessly insisting that Ramanujan must provide proofs of his theorems. Meanwhile, Ramanujan seeming to sense he is running out of time, is determined to see his work published.

In fact as World War I dragged on and the vegetables Ramanujan often ate became scarce his health began to suffer. Ramanujan had previously been ill in India and in 1917 he became seriously ill in England. In the movie, he is seen frequently visiting the medical tents set up on campus for the injured soldiers sent back from the front in Europe. The film suggests that Ramanujan was thought to have tuberculosis, although the diagnosis of exactly what was wrong with him was never fully determined.

The Man Who Knew Infinity captures the historical period well, providing viewers with a sense of the obstacles Ramanujan faced upon arriving at Trinity, and the struggles his fellow mathematicians had in understanding and accepting him. Two mathematicians, Ken Ono and Manjul Bhargava were involved in the making of the film to ensure the mathematics was accurately portrayed. The movie was ten years in the making and premiered at the 2015 Toronto Film Festival. Well worth the wait and definitely worth viewing.

This short biography of Srinivasa Aiyangar Ramanujan from the MacTutor  History of Mathematics website is worth reading.

As shown in the movie and stated near the end, Ramanujan left a number of books and manuscripts containing his ideas and theorems, all of which have since been proven. Work on his ideas continues to this day as this article from Science Daily explains. This more recent article from + plus Magazine: Living Mathematics 2015 is also quite interesting.

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