Features# The Man Who Knew Infinity: A mathematician's life comes to the movies

Ramanujan had an extraordinary ability to see patterns in numbers

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. (I shall say more about the other romantic later.)

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.

Srinivasa Ramanujan. Wikimedia

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 the leading University 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 Prof Bruce Berndt and Prof 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 early 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 would have probably received a more robust and more ordinary education. 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.

The anonymous letter. Author provided

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 the self-confidence of himself and 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 give 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 very favourably Robert Kanigel’s book The Man Who Knew Infinity: A Life of the Genius, on which the movie is based.

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

**The other romantic**

The other romantic mathematician I alluded to earlier was the even more short-lived French revolutionary Évariste Galois.

Galois (1811–1832) died, aged 20, in a duel related to the famous female mathematician Sophie Germain. As the story goes, there is a note in the margin of the manuscript that Galois wrote the night before the duel. It read:

There is something to complete in this demonstration. I do not have the time.

It is this note which has led to the legend that Galois spent his last night writing out all he knew about group (Galois) theory. This story appears to have grown with the telling but his life would also make for a very interesting movie.

Jonathan Borwein (Jon), Laureate Professor of Mathematics, University of Newcastle

This article was originally published on The Conversation. Read the original article.

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