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Ramanujan – The Man Who Knew Infinity

Tuesday 23 February, 2016

by Jonathan Borwein (Ontario & Jesus 1971)

The Man Who Knew Infinity

The movie The Man Who Knew Infinity is about Srinivasa Ramanujan, who is generally viewed by mathematicians as one of the two most romantic figures in our discipline - the other being Evariste Galois (1811–1832).

Ramanujan (1887–1920) was born and died, aged just 32, in Southern India. But in one of the most extraordinary events in mathematical history, he spent the period of World War I in Trinity College Cambridge at the invitation of the leading British mathematician Godfrey Harold (G. H.) Hardy (1877–1947) and his great collaborator John E. Littlewood.

To avoid having to issue spoiler alerts, I will not tell much of Ramanujan’s story here. Suffice to say that as a boy he refused to learn anything but mathematics, he was almost entirely self-taught and his pre-Cambridge work is contained in a series of Notebooks.

The work he did after returning to India in 1919 is contained in the misleadingly named Lost Notebook. It was lost and later found in the Wren library of the leading college for mathematics of one of the leading Universities in England. While in England Ramanujan became the first Indian Fellow both of Trinity and of the Royal Society.

A Man of Numbers
Ramanujan had an extraordinary ability to see patterns. While he rarely proved his results he left a host of evaluations of sums and integrals. He was especially expert in a part of number theory called modular forms which is of even more interest today than when he died.

The lost Notebook initiated the study of mock theta functions which are only now being fully understood. Fleshing out his Notebooks has only recently been completed, principally by American mathematicians Bruce Berndt and George Andrews. It comprises thousands of printed pages.

An old Indian friend, Swami Swaminathan, oversaw the Ramanujan Library in Madras over half a century ago. He commented that had Ramanujan been born ten years earlier he would have been unable to receive the education and financial assistance that made his pre-Cambridge work possible.

Swaminathan went on to say that had Ramanujan been born ten years later, he probably would  have received a more robust and more ordinary education in India. In either case our version of Ramanujan would not exist.

Ramanujan and Me
Ramanujan has been part of my life for as long as I can remember. My father David was a student of one of Hardy’s students. In our house “the bible” referred to Hardy’s masterpiece Divergent Series.

In 1962 on the 75th anniversary of Ramanujan’s birth the envelope (below) arrived at my parents' house. A kind stranger had put the franked stamps on the back.

In 1987 I was fortunate enough to speak with my brother at the major centennial conference on Ramanujan, held at the University of Illinois. We had become experts on, and had extended, Ramanujan’s work on Pi.

Highlights at the conference included the Nobel prize winning astronomer Subrahmanyan Chandrasekhar, who described how important Ramanujan’s success in England had been to his self-confidence and that of the founders of modern India including Jawaharlal Nehru, who became the first prime minister of independent India in 1947.

In 2008 David Leavitt published a novelised version of Ramanujan’s life entitled the Indian Clerk. While Leavitt captures much beautifully, as a novelist, he takes some sizeable liberties. In particular, he dramatically embellishes Hardy’s (closeted?) homosexuality. I prefer my novels as fables and my biographies 'straight'.

In 2012 on the 125th anniversary of Ramanujan’s birth the Notices of the American Mathematical Society published eight articles on his work. This suite forcibly showed how Ramanujan’s reputation and impact continue to grow.

Gifted with Numbers
There is one famous anecdote about Ramanujan that even a non-mathematician can appreciate. In 1917 Ramanujan was hospitalised in London. He was said to have tuberculosis but it is more likely this was to cover a failed suicide attempt.

Hardy took a cab to visit him. Not being good at small talk all Hardy could think to say was that the number of his cab, 1,729, was uninteresting.

Ramanujan replied that quite to the contrary it was the smallest number expressible as a sum of two cubes in two distinct ways:

1,729 = 12^3 + 1^3 = 10^3 + 9^3

This is now known as Ramanujan’s taxi-cab number.

Mathematicians in the Movies
There has been a recent spate of books, plays and movies, and TV series about mathematicians and theoretical physicists: A Beautiful Mind (2001), Copenhagen (2002), Proof (2005) and last year’s Oscar winning movies The Imitation Game about Alan Turing and The Theory of Everything on Stephen Hawking.

When I have read the book on someone’s life, I frequently avoid the movie. As writer Michael Crichton put it:

All professions look bad in the movies […] why should scientists expect to be treated differently?

Such movies – even biopics – have to compress a life of the mind into 90 to 120 minutes and offer a flavour of genius to the rest of us. Even more than the books on which they are based, they have to make the character more exotic (Turing) or better redeemed (John Nash in A Beautiful Mind) than in the book let alone real life.

So I tend to avoid the movies and to be satisfied with my own knowledge and the corresponding book which can take 500 pages and more if it needs to.

The Man Who Knew Infinity
But I do intend to see the movie of The Man Who Knew Infinity. Ramanujan’s presence has been too much a part of my life (intellectually and personally) for me to miss it.

In the movie Hardy is played by Jeremy Irons while Stephen Fry plays Sir Francis Spring who was an early advocate of Ramanujan in India. Twenty-five year old Dev Patel, who acted in Slumdog Millionaire (2008), is Ramanujan.

I reviewed for Science very favourably Robert Kanigel’s 1991 book The Man Who Knew Infinity: A Life of the Genius, on which the movie is based.

The film has the brilliant Canadian-born Fields Medalist and Princeton professor of mathematics Manjul Bhargava as primary technical advisor. Bhargava, also an expert tabla player, works in fields well aligned with Ramanujan’s opus. This augurs well for the movie’s accuracy.

The movie is in general release in the spring of 2016. Most of my mathematician friends who attended previews were well pleased.

Jonathan Borwein (Jon) (Ontario & Jesus 1971) read MSc and DPhil Maths and is Laureate Professor Mathematics at the University of Newcastle, Australia. He also regularly blogs: This post was originally published entitled: 'The Man Who Knew Infinity: a mathematician’s life comes to the movies' in 'The Conversation' on November 18, 2015.

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