To infinity and beyond

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A Sydney academic’s fascination with India’s mathematical genius Srinivasa Ramanujan, the subject of a new film starring Dev Patel

To infinity and beyond, that is the journey of impoverished Iyengar prodigy Srinivasa Ramanujan (1887-1920).

Srinivasa Ramanujan.Indian Link

His inspirational but heartbreaking tale began at a humble agraharam (Brahmin enclave) adjoining the Saarangapani temple in colonial Kumbakonam, where parents Komalatammal, a music teacher and father Srinivasa Iyengar, a clerk with modest means and limited ambition, nurtured similar intentions for his young lad – the path to self-sufficiency.

Little did they realise that the intuitive mathematician was ordained for greatness, albeit posthumously. Exceptionally advanced in thinking for his background, maths consumed his very existence, as he travelled from Kumbakonam to Cambridge in search of his destiny.

Ramanujan went on to become the first Indian Fellow of both Trinity College and Royal Academy in the early twentieth century, when World War One unleashed its horrors on society.

Srinivasa Ramanujan.Indian Link

The treacherous personal voyage, however, culminated in an untimely tragedy, but the young genius, who saw patterns and possibilities in the very grains of sand, had already left an indelible impression in the realm of numbers. His legacy lives on.

Carrying forth the torch of India’s robust mathematical history which dates back to the Vedic era, Ramanujan’s seminal work, often scribbled on scraps of paper, includes 4000 formulae and theorems, all of which continue to amaze and challenge mathematicians to this day. He is particularly renowned for infinite series of pi.

Srinivasa Ramanujan.Indian Link

The Man Who Knew Infinity is a moving account of the unlikely friendship between mentor and apprentice, avowed atheist and devout Brahmin, a celebrated academic and high school dropout – GH Hardy and Ramanujan – one of the greatest collaborations in mathematical history. The subject of this latest biopic has finally garnered the international attention his genius and legacy truly deserve.

Directed by Mathew Brown and featuring Dev Patel, Jeremy Irons, Toby Jones, Stephen Fry, Jeremy Northam, The Man Who Knew Infinity strives to be a sensitive and poignant representation of the man and his mathematics, winning praise from not only film critics but also the academic fraternity.

Srinivasa Ramanujan.Indian Link

“I’m certainly looking forward to the film,” Prof. Nalini Joshi, professor of mathematics at the University of Sydney, told Indian Link. “It intrigues me that, for Ramanujan, maths was a spiritual and creative endeavour. It was almost as if he dreamt up his mathematical thoughts – he allowed them to flower, and then wrote them down. His contributions continue to be incredibly important to this day, and can be found right at the leading edge, in functions to do with quantum mechanics, for instance.”

Dr Sydney Srinivas: The namesake

Indian Link’s own resident maths and science expert Dr Sydney Srinivas is a massive and unabashed fan, and has spent much time researching and writing about the man, his own namesake.

Sydney Srinivas.Indian Link
Dr Sydney Srinivas

“When the stellar British production was screened in Sydney last November as part of a British Film Festival at two houseful shows, I immediately decided that I needed to bring it to a wider audience, particularly the Indian community,” well known author, columnist, retired academic and authority on Ramanujan, Sydney Srinivas told Indian Link.

His push to deliver Ramanujan’s legacy beyond the world of academia has finally paid dividends, with two special pre-screenings of the latest film at Circular Quay and Liverpool ahead of its Australian release in early May.

“Although I was first made aware of Ramanujan’s contributions as a Year 8 student back in Bangalore, hardly anyone spoke about him in our circles,” regrets the former Deputy Head of University of Sydney’s School of Aerospace, Mechanical and Mechatronic Engineering.

Srinivasa Ramanujan.Indian Link
Srinivasa Ramanujan

“What triggered my ongoing interest was a casual lunchtime comment by Steven Armfield, Head of School at Sydney University after reading David Leavitt’s The Indian Clerk. According to the book, Ramanujan died from poisoning after eating food that he cooked in cans,” he recalled.

Overcome by a sense of shame at knowing so little of the tragedy, Srinivas borrowed the book. It reminded him of the Robert Kanigel classic The Man Who Knew Infinity (1991). He also read C P Snow’s foreword to G H Hardy’s famous book A Mathematician’s Apology where Snow describes the sequence of events that Hardy went through after receiving the letter from Ramanujan. (Hardy would claim famously, many years later, that he considered the discovery of Ramanujan his greatest contribution to mathematics).

Srinivasa Ramanujan.Indian Link

The chain of events set Srinivas on his own personal quest – to unravel the many mysteries of the gifted compatriot and unsung genius.

About the same time, he was asked to give a talk to youngsters by Manthana, a Sydney-based organisation run by Hindu Swayam Sevak Sangh.

“What better subject was there to choose? I naturally spoke on Ramanujan,” he quipped.

Requests to publish ensued and this led to Srinivasa Ramanujan: A Tale of Agony and Ecstasy, which was followed by a Kannada translation as well as a more detailed biography through an Indian publishing house.

In search of truth, unravelling fact from fiction, Srinivas embarked on a sacred pilgrimage. Dr Srinivas’s extensive research took him to Ramanujan’s unpretentious residence in Kumbakonam, which is now preserved as a museum. It is here that Ramanujan spent many a productive day, armed with his legendary slate and chalk-piece, scribbling away path breaking notations, unmindful of the din of everyday life.

Home of Srinivasa Ramanujan.Indian Link
Home of Srinivasa Ramanujan in Kumbakonam

In an oft-quoted incident from his childhood, Ramanujan famously questioned his Year 3 maths teacher. “If three fruits are equally divided between three people, everybody gets one each. So what happens when no fruits are divided among no one, will each still get one?”

More than a century later, Ramanujan’s room in Sannidhi Street is still intact. A framed catalogue at Ramanujan’s house proclaims that it was at the Kumbakonam school that the 15-year-old came across G S Carr’s Synopsis of Elementary Results in Pure Mathematics, a book that was to influence the young boy in ways few imagined.

Srinivasa Ramanujan.Indian Link

Retracing Ramanujan’s steps, Dr Srinivas also visited Naamakkal, Saarangapani and Parthasarthy temples, all of which were the deeply religious Ramanujan’s favourite haunts during his troubled days.

“It was a mathematical pilgrimage going to Kumbhakonam (his place of childhood, he was actually born in Erode), the town high school where he studied and the college where he continuously failed in all subjects except mathematics. Then I went to Chennai to have a look at the place where he studied (now demolished), visited his wife’s adopted son Narayanan and his wife, Vishwanathan, the grandson of Narayana Iyer, his Indian mentor.

In fact, I even visited the Namagiri Temple in Namakkal where Ramanujan offered special seva to find out whether the divine was in support of his intended trip to England. Divine permission was indeed granted,” Srinivas recounted. “My next destination was Cambridge and Trinity College in particular. I became a new person having seen all these first hand with my own eyes.”

Srinivasa Ramanujan.Indian Link

Dr Srinivas’ books on Ramanujan are now widely sold in India and have seen three or more reprints.

“This has also encouraged me to write on Albert Einstein in English and this too is going well. The next to come is Isaac Newton. In addition, I have written in Kannada about Einstein, Newton, Galileo, Marie Curie, Alan Turing, Henry Ford and Alfred Nobel. It gives a sense of pride that my books have found a place in the Wren Library in Cambridge and the National Library of Australia in Canberra,” he added.

The lives of many great scientists, poets, musicians and writers have been one of agony and ecstasy, points out Srinivas. Marie Curie and Alan Turing are good examples apart from Ramanujan. T S Elliot once rightly stated that suffering is action and out of suffering comes poetry. “Many of these geniuses have suffered and they kept the suffering to themselves. But we the posterity, enjoy the fruits of their action,” Srinivas said.

Srinivasa Ramanujan.Indian Link

He describes Ramanujan as an eccentric genius, a victim of his own passion. “He was brilliant in mathematics, no doubt. Yet, he did not have the common sense that mathematics alone is not sufficient to lead a good life. Many other things are also necessary. His attitude made him suffer, mostly in England. His food habits, long and erratic working hours, which he imposed upon himself, led to his untimely demise; add to this the English climatic conditions and his mother’s interference in everything including his association with his wife Janaki. A tragedy beyond words.”

Unsung hero gets his due

Quitters never win, winners never quit. These powerful words sum up the life and travails of Indian mathematical prodigy Srinivasa Ramanujan. Beset by lifelong health and financial troubles, he was a small town nobody and college dropout, with neither social standing nor connection. Yet his obsession with the magical world of numbers took him to the privileged halls of Cambridge, eventually making him a Fellow of the prestigious Royal College.

Srinivasa Ramanujan.Indian Link
Ramanujan (centre) with other scientists at Trinity College

Fuelled by self-belief and sheer determination, Ramanujan left behind a rich legacy for which he is remembered today. Even when death knocked on his doors, the humble genius kept up his tryst with numbers, working away at theorems as wife Janaki attended to his emaciated body. Ramanujan’s younger brother Tirunarayanan painstakingly compiled and chronicled the scraps of paper and handwritten notes containing significant formulae on hypergeometric series, continued fractions and singular moduli, preserving his legacy for posterity.

Srinivasa Ramanujan.Indian Link

Ahead of his time, Ramanujan’s pioneering work opened new pathways and research possibilities that are still being explored.

On the 125th anniversary of his birth, India declared his birthday as National Mathematics Day, while his home state of Tamil Nadu commemorated it as State Information Technology Day. Google honoured him on his birth anniversary with a doodle on its homepage.

“The world of mathematics saw an astonishing person who could arrive at a result most of the time by intuition. He said a Goddess wrote equations on his tongue and came in his dreams and enlightened him. He is one who is on par with Euler and such great mathematicians. He had no academic training and still was able to contribute to topics such as partitions, continued fractions, mock theta functions and many such others,” Srinivas stated in a poignant tribute.

Srinivasa Ramanujan.Indian Link

“I may point out Bruce Berndt (at the University of Illinois), Michael Hirschhorn (at the University of NSW) and many others are continuing research on Ramanujan’s mathematics. Many books and papers have been written. I am told that his theorems have found application everywhere. One in a million may not have the spark that Ramanujan had. Such people flash upon this universe – Einstein, Mozart, Beethoven and the like.”

Dr Srinivas is optimistic that modern mathematicians will be inspired to follow Ramanujan’s illustrious footsteps. “Most of the research today in engineering and science is application oriented. Pure mathematics takes a back seat. Engineers and scientists are after software that can carry out calculations, but to develop good software, mathematics and its knowledge are of paramount importance.” he said.

Srinivasa Ramanujan.Indian Link

He regrets the contemporary trend of opting for returns-based learning but is hopeful that mainstream biopics such as The Man Who Knew Infinity will nurture a renewed interest in theoretical mathematics.

Indian-origin mathematician Krishnaswami Alladi, of the University of Florida, also the Founder and Editor-in-Chief of The Ramanujan Journal says the film should inspire youngsters to pursue a subject out of pure passion and not fashion.

Prof. Joshi, for her part, hopes that the film will be able to bring out the sheer beauty of numbers, for a new generation of students. “For kids today, the main lesson from Ramanujan is that maths is not only interesting, but can actually be thought of as an art.”

Maths, Ramanujan style

  • 1729 is called the Hardy-Ramanujan number, after a famous encounter between the British mathematician GH Hardy and Ramanujan in 1918. Hardy had ridden in taxi cab number 1729 and remarked that the number seemed to be rather a dull one. ‘No,’ Ramanujan replied. ‘It is the smallest number expressible as the sum of two cubes in two different ways: 1729 = 13 + 123 = 93 + 103.’ It triggered an interest in numbers that are the smallest number that can be expressed as the sum of two cubes inn distinct ways, and are now called “taxicab numbers
  • A remarkable result of the legendary six-year-long Hardy-Ramanujan collaboration was a formula for the number p(n) of partitions of a number n. A partition of a positive integer n is just an expression for n as a sum of positive integers, regardless of order. Thus p(4) = 5 because 4 can be written as 1+1+1+1, 1+1+2, 2+2, 1+3, or 4. Leonard Euler initially found a formula for the generating function of p(n) (that is, for the infinite series whose nth term is p(n)xn). While this allows one to calculate p(n) recursively, it doesn’t lead to an explicit formula. Hardy and Ramanujan came up with such a formula (though they only proved it works asymptotically, German-American mathematician Hans Rademacher proved it gives the exact value of p(n) in 1937, validating Ramanujan’s earlier supposition.
  • Ramanujan identified several efficient and rapidly converging infinite series for the calculation of the value of ?, some of which could compute 8 additional decimal places of ? with each term in the series. These series (and variations on them) have become the basis for the fastest algorithms used by modern computers to compute ? to ever increasing levels of accuracy (currently to about 5 trillion decimal places).

Source: Story of Mathematics

Maths on the film set

He may have played a young Ramanujan, India’s greatest mathematician, but for 26-year-old actor Dev Patel, mathematics as a subject in the school curriculum was always a scourge.

“I was terrible at mathematics,” Dev revealed recently. “It was worse because my father is an accountant.”

Ramanujan notwithstanding, all Indians are not good at maths, so stop stereotyping, readers!

Srinivasa Ramanujan.Indian Link

To get Dev to understand his character better, young director Matt Brown, it is believed, worked very closely with contemporary mathematicians Ken Ono and Manjul Bhargava (who won both the Fields Award and the Padmashree) in cracking the formula to get it all down pat.

“I was involved because they wanted to get their mathematics right,” Japanese-American Ono said in a statement. “Before I knew it, I was on the sets in England, helping out with so many different things. It was, of course, difficult to explain how to be a mathematician to someone who is not a mathematician.”

He added, “My favourite scene in the film is where Dev Patel completes a complex mathematical formula on the blackboard and one can see that he has done it in real time. My challenge was to select a formula that he could remember easily and complete it in the sequence,” Ono added.

“They worked for a long time, exactly on the formulas and how they were written, how partitions were done. Much attention was given to each aspect of the film to bring the realistic quality forward,” executive producer Swati Bhise said.

Tamil film Ramanujan (2014)

National award winning director Gnana Rajasekar’s eponymous Tamil film Ramanujan (2014) first introduced movie goers to the world of mathematical genius. Biopics of trailblazing individuals are becoming quite the norm these days, with cinematic representations clearly grabbing eyeballs where biographies have sadly languished.

Mathematics nevertheless is no easy task to portray on celluloid. Featuring debutant Abhinay Vaddi (grandson of golden couple Gemini Ganesan and Savithri) and Bama (Janaki Ammal), Nizhalgal Ravi as father and Suhasini Maniratnam as domineering but doting mother, the Tamil film is almost archetypal Indian – how we repeatedly fail to recognise a genius, heaping ridicule at signs of brilliance and often equating it to madness.

Srinivasa Ramanujan.Indian Link

The personal tragedy of Srinivasa Ramanujan makes for an inspiring story but the film has been criticised for failing to resonate deep within. Nevertheless, it won kudos for being able to recreate the epoch with brilliance.

Besides a great soundtrack that blends Carnatic and western melodies, beautifully laid out frames and deep insight into customs and beliefs of the time help convey the poignant message that Ramanujan tragically was a victim of the prejudices and attitudes prevalent at the time.

Apart from the classical numbers that have already struck a chord with listeners (including Vani Jayaram’s comeback piece, the ‘Zero to One’ composition in the film is unique – a musical metaphor of Ramanujan’s mind, which was always preoccupied with complex layers of calculation, according to music director.