What English mathematicians thought of the ‘Hindoo calculator’

On the last Tuesday in January 1913, a nondescript letter arrived at Trinity College. Enclosed in a humble brown envelope and covered with “an array of unfamiliar stamps,” this letter, addressed to Cambridge Fellow and star mathematician GH Hardy from an unknown and unschooled Indian clerk in Madras, was destined to change the history of mathematics. Initially skeptical, Hardy realised upon reading the rough theorems that this Indian might be the one to prove the Reimann Hypothesis.

The Indian Clerk, published in 2007, is American novelist and self-proclaimed Anglophile David Leavitt’s seventh novel. It begins on August 31, 1936, at Harvard, where Hardy has been invited to receive an honorary degree. When the time comes for him to give his speech Hardy launches into a lecture on the man everyone wants to hear about, his Indian protégé, “the most romantic figure in the recent history of mathematics.” The rest of the novel is a flashback to the years of their interaction, with occasional returns to the present scene in New Lecture Hall at Harvard.

Cambridge, and particularly Trinity College, just before the First World War, is of course an elitist place. Early on, we get a description of lunch in Hall with rowdy undergraduates, accompanied by fellows at the High Table, all of whom are watched over by “portraits of Byron and Newton and other illustrious old Trinitarians.” Prayers are said in Latin and waiters pour wine. Meals comprise dishes like poached turbot, dover sole or pheasant, followed by steamed pudding in a custard sauce.

Afterwards, the fellows move on to the Senior Combination Room for port and walnuts. The exclusive nature of the university is further corroborated by the existence of societies like the Apostles, which draws its members after careful vetting and mentoring. “Election was highly secretive, and, once born, the ‘embryo,’ as he was called, was made to swear that he would never speak of the society to outsiders.”

Where cultures collide

Hardy’s contemporaries at Cambridge, whether as an undergraduate or a fellow, include Bertrand Russell, John Maynard Keynes, and GE Moore. Hardy is acutely conscious of the traditions and history of the college. “Every corner of Trinity had a story to tell.” He is also very conscious of the general sense of superiority and insularity in both Cambridge and England as a whole, a sense that of course intensifies during the First World War. It is this setting that Ramanujan is invited to enter. The stage is set for a clash of two cultures that could not be more different.

From start to finish the cultural differences between the Indian and the English are constantly emphasised. Even before Ramanujan arrives in England, Hardy and his collaborator John Littlewood speak of his personal life.

“‘He’s married?’

Littlewood nods. ‘She’s fourteen.’

‘Good heavens.’

‘It’s normal over there.’ ”

Elsewhere, Alice Neville, who along with her husband first hosts Ramanujan in England, worries about his sleeping arrangements. “Back in Madras, she knows Ramanujan had no bed. Like most Indians, he and the other members of his family slept on mattress rolls that could be folded up and put away during the day. Any spare piece of floor would serve as a bedroom. And now here he is in England, where the trees are just coming into bud and, in order to sleep, he must climb up onto a bed. What must he make of it all? Does the strangeness terrify him?”

Of course it is the strangeness of Ramanujan that fascinates the English characters. Dinners are hosted so that the Trinity luminaries have a chance to meet the man they dub the “Hindoo calculator.” At one such dinner Mrs, Neville, who has arranged for a counterfeit vegetable curry, announces, “In Mr Ramanujan’s homeland, of course, we would eat with our fingers.” At the same dinner, both Alice and Hardy’s sister Gertrude watch Ramanujan closely. “It’s as if, for them, every facet of the Indian, even his genius, has an aroma as exotic and pungent as the food Alice is describing.”

No exocitisation

To his credit, Hardy notices how Ramanujan is objectified and is annoyed by it. The Nevilles, according to him, treat him “as theirs, an intelligent pet ape in the process of being trained to act like a man.” Hardy feels sympathy for the Indian perhaps because like him he too is somewhat of an outsider.

The grandson of a baker and son of teachers, Hardy has “slipped through doors that would normally have been shut to him,” and through hard work and talent, has landed up at Trinity. An atheist among Christians, he is vocally opposed to both the Cambridge tripos and the war. He is disgusted by the jingoism that surrounds him. His views of course are controversial and unpopular. As a gay man in that setting, he is further isolated. His outsider status makes him a sympathetic and sensitive character who cringes every time Ramanujan is treated like an object of curiosity.

And yet, despite his best intentions, Hardy too treats him as an exotic other. He makes a distinction between the genius of his mathematician colleagues at Cambridge and Ramanujan. Their genius, nurtured by discipline and knowledge, has a recognisable shape, but “Ramanujan’s is wild and incoherent, like a climbing rose that should have been trained to wind up a trellis but instead runs riot.”

It is Hardy’s own awareness of his prejudices that causes some internal conflict. When he first receives Ramanujan’s letter, Hardy has this memory. “Years before, when he was a child, his school held a pageant, an Indian bazaar, in which he played the role of a maiden draped in jewels and wrapped in some Cranleigh school version of a sari. A friend of his, Avery, was a knife-wielding Gurkha who threatened him… he realises that this paste and colored-paper facsimile of the exotic east, in which brave Englishmen battled natives for the cause of empire, is the image his mind summons up every time India is mentioned to him.” This self-reflection comes not from Hardy – that we know of – but from the author David Leavitt, who is an avid reader of Indian literature and wary of exoticising people from the Subcontinent.

Despite the differences between the two cultures, what ultimately draws Hardy and Ramanujan together is their love for mathematics. Love might be putting it too mildly. Obsession may be a more suitable word.

Much of the novel’s narrative tension arises from the question of whether or not Ramanujan will in fact solve the Reimann Hypothesis, which involves the arrangement of prime numbers. Hardy and Littlewood spend sleepless nights over these primes. Hardy recalls early in the novel how, as a young boy, he distracted himself in church on Sunday mornings by breaking down the numbers of the hymns into their prime factors. While others around him were contemplating the mysterious ways of God, the young Hardy was beguiled by the secrets of mathematics.

“He remained preoccupied with the primes. Up to 100 – he counted – there were 25. How many were there up to 1000? Again he counted – 168 – but it took a long time. At Cranleigh he had replicated, on his own, Euclid’s astonishingly simple proof that there was an infinity of primes. Yet when he asked his maths master at Winchester if there was a formula for calculating the number of primes up to a given number n, the master didn’t know. Even at Trinity, seat of British mathematics, no one seemed to know.”

I confess to having skimmed over the longer sections with formulae and equations. But somehow Leavitt succeeds in making his characters’ fascination with numbers contagious. He does this by immersing readers into the inner worlds of these celebrated mathematicians.

One example is the scene where Ramanujan tells Neville, Hardy and Littlewood that he has lately become interested in composite numbers, what he calls “a sort of anti-prime.” As he proceeds to explain what he means, we get a flurry of numbers. Then Ramanujan finds a piece of chalk with which to scribble on the blackboard.

“And he’s off. At the blackboard, any self-consciousness he might feel about speaking English leaves him, just as Hardy’s discomfort evaporates. They’re lost now, and when, an hour later, Alice Neville peers down from the top of the stairs, she sees four men she hardly recognises, speaking a language she cannot hope to understand.”

The epigraph to the novel, which is a quote from GH Hardy’s well-known essay A Mathematician’s Apology, states that “languages die and mathematical ideas do not.” If anyone has a shot at immortality, according to the essay, it must be a mathematician. Perhaps that is why, at the lecture at Harvard, Hardy makes an attempt to rekindle memories of his protégé. The Indian clerk died young, but his mathematical legacy can and will live on.

Ramaunjan’s untimely death is a cause for much regret. Hardy wonders if he neglected him or failed to protect him, or worse still, if he perhaps caused the death by inviting him to England. Hardy’s lecture to the American audience in 1936 is an attempt to explain Ramanujan, and in so doing, perhaps explain himself and try to purge himself of any feelings of guilt. But of course, Hardy fails to do the former. How can he explain someone he never knew?

But where’s Ramanujan?

If the book has a weakness it lies in the fact that while there are multiple sections from the point of view of different English characters, we get only one tiny glimpse of what’s going on in Ramanujan’s head, in the scene when he’s cooking rasam. And we barely hear him speak. He is typically quiet, and is characterised by a peculiar waggle of the head.

The strict vegetarian in him has a great deal of trouble with food, especially during the war. He sleeps on top of the coverlet in the dead of winter because he does not know he should get under them. He is not only odd, but also inscrutable, like many Indian characters in English novels of the time. No one quite knows what he’s thinking or feeling.

He is only perceived through the English, who must interpret him as best they can. In allowing them to interpret Ramanujan for readers, the book ends up objectifying the Indian further. In the West, he is to be stared at, marveled at, and talked about, both during his life and decades following his death. But, in the end, perhaps that reflects the reality of Ramanujan’s experience.

Hardy famously called his interaction with Ramanujan “the one romantic incident of my life.” The repeated use of the term “romantic” is interesting in a book that deals largely with mathematics. By “romantic” what Hardy really means perhaps is exotic.

This book is about the romantic university town of Cambridge, whose peace is disturbed by the First World War. It is about the romantic dalliance of Littlewood and his mistress Anne, Hardy’s own tryst with a young soldier, and Alice Neville’s infatuation with Ramanujan. It is even about the romance of war, a subject that Cambridge undergraduate Rupert Brooke, who appears in these pages, wrote poems about. But most of all, it’s about the romance of numbers.

The book is not really as much about Ramanujan as it is about Hardy and his friends. It is their emotions that are fully realised and evoked with touching insight. This is a fictive biography where the author admits to have taken some liberties for the sake of drama.

However, it also offers interesting insights into Ramanujan’s life while at Cambridge. Ultimately, the novel can and should be read as a record not of how the Indian clerk felt, but of how he was perceived by the English even as his brief presence in England forever transformed their lives.

What The Author Says

David Leavitt is a professor in the Department of English at the University of Florida in Gainesville. He is an excellent cook and is very partial to Indian recipes. Excerpts from an interview:

What made you interested in the story of a mathematician from India?

I happened upon Ramanujan while researching the Reimann Hypothesis for my book on Alan Turing (The Man Who Knew Too Much: Alan Turing and the Invention of the Computer, published in 2006). Instantly I knew that I had to write a book about this man, about Hardy, about their friendship. I wasn’t sure why I felt compelled to write such a book. I suppose I wrote it in order to find out.

In retrospect I think that what appealed to me about Ramanujan and Hardy was that in different ways each saw himself as an outsider. One of the questions the book asks is what happens to an artist’s creative drive when he is accepted by the very institutions that have rejected him and, in rejecting him, instilled in him the impetus to prove his worth; what happens to your sense of yourself as a rebel when the force you are rebelling against embraces you.

What kind of research did you have to do for this book so strongly based on historical fact? What were some of the challenges?

I read a lot of books and articles and dug up as much primary material as I could find. I met and talked with a lot of mathematicians. (By a stroke of luck the chair of the mathematics department here at UF turned out to be South Indian and an authority on Ramanujan.)

I went everywhere that my characters spent time – London, Trinity College, Cambridge, Chennai, Kumbakonam – and did my best to absorb the atmospheres of these places. I tried to immerse myself in World War I England to the point that I could get some approximate sense of what it felt like to have lived in that time and place – not the degree of familiarity, obviously, that comes of experience, but close enough to allow me to write with confidence. (This involved, among other efforts, tracking down an early twentieth-century British vegetarian cookbook.)

I always get quite anxious about research and getting some tiny detail wrong. Do you worry about that when writing a book like this? I read a review of the book in The Guardian that mentioned a few factual errors. How important is stuff like this? What advice do you have for newer writers regarding research?

Errors are an occupational hazard of this kind of writing. You simply have to accept their inevitability. Plus you can rest assured that reviewers and readers, having spotted them, will never let you forget that you made them. (Several of the more obvious errors I was able, thank God, to correct in the paperback edition!)

Most of the errors in The Indian Clerk are entirely my own fault. One – the misdating of the Battle of Hastings – was a typo. The errors in the mathematical equations were the fault of the typographer, whom I cannot really blame. Such equations are very difficult for a non-mathematician to transcribe.

In your epigraph you write, “languages die and mathematical ideas do not.” The quote implies that math is greater than languages (and literature) and has a better chance at immortality. As a writer do you believe this is true? Were you ever very interested in math? I’m asking because I always hated it and I know many other writers who do as well. You also wrote the book about Turing. How do you make math accessible to readers and also a suspenseful plot device?

I only really got interested in mathematics when I wrote the Turing book. This interest took me completely by surprise. In high school I hated math. (In retrospect I realise that the reason I hated it was probably the way it was taught, and continues to be taught, in most American high schools.)

In order to explain the interest in mathematics that Turing awakened in me (and that persists to this day) I would draw a comparison to music. Though I am tone deaf and cannot play an instrument (I can read music, sort of), I have never doubted my capacity to listen to – and talk about – a Mozart symphony, say, or a Chopin prelude. This is how I approach mathematics, as an art I can appreciate even if I have no gift for it.

Regarding the epigraph, Hardy is really talking about the truth value of mathematics. His point is that mathematical assertions, once proven, are true in a way that virtually nothing else is. Their truth is immutable. It is bedrock.

In your novel Ramanujan is a mysterious figure that no one can quite read. His life in India is shadowy to the English characters. Was this intentional?

Early on I made a conscious decision not to try to enter into Ramanujan’s point of view. (In the end I broke my own rule, but only in one very short chapter.) This decision was in part structural – I wanted The Indian Clerk to be a “stranger comes to town” novel, with Ramanujan as the stranger. The other part of the decision was fear.

Quite simply, I didn’t feel that I knew enough about Hinduism (particularly Hinduism as practised in Tamil Nadu) to enter into the mind of a man whose mathematical discoveries so often took the form of religious visions. RK Narayan could have written the story from Ramanujan’s point of view. At that point, at least, I felt I could not.

I’ve always enjoyed a special kinship with you based on your affection for Indian writing and Indian food! Can you talk a little about your relationship with India and interaction with it?

Why does one love a place, a country, a culture, a literature? It’s hard to say. The word that comes to mind is “affinity.” Whenever I am in India I am fascinated, overwhelmed, bewildered, confused, happy.