A MYSTERIOUS MIND
A well-researched novel joins the rush of attention surrounding mathematician Srinivasa Ramanujan - though at the end of it all the central character remains as enigmatic as ever, says Andrew Robinson
A DEEPLY obscure mathematician with an eccentric personal life
wins a Nobel prize. He becomes the subject of an acclaimed biography, which
forms the basis of a hugely successful Hollywood movie. Sounds familiar?
The mathematician is, of course, John Nash, who was played by Russell Crowe
in the movie
Now a similar sequence looks set to play out with the Indian mathematician Srinivasa Ramanujan. During 2007, Ramanujan's life and work have been the subject of a sold-out stage play, A Disappearing Number, at London's Barbican Centre, and no less than three rival movie projects. Two of these emanate from Hollywood: one has a screenplay by Stephen Fry, the other is based on an influential biography The Man Who Knew Infinity, by Robert Kanigel, published back in 1991. The third movie project originates from a noted director in India, Dev Benegal. Ramanujan is also the eponymous subject of The Indian Clerk, a novel by the American literature professor David Leavitt on which Fry's screenplay is based, newly published by Bloomsbury Publishing of Harry Potter fame.
While Ramanujan is slightly better known than Nash was before the movie, most of us in the US and Europe have probably yet to hear of him. In India, however, and among mathematicians everywhere, he is already a legend. In Ramanujan's own time, leading mathematicians compared him to Karl Jacobi and David Hilbert, while a recent New Scientist review article by the mathematician and computer scientist Gregory Chaitin placed Ramanujan with the all-time mathematical greats Euler and Cantor (28 July, p49). The American mathematicians George Andrews and Bruce Berndt have spent decades studying Ramanujan's notebooks, trying to prove some of his unproved theorems.
Even those who cannot grasp a line of Ramanujan's mathematics are beguiled by his life: an east-west story of rags to intellectual riches. It is almost reminiscent of the Einstein phenomenon: "Why is it that nobody understands me, yet evetybody likes me?" a genuinely puzzled Einstein once asked. Nearly everyone seems to have liked Ramanujan during his all-too-brief life in India and England. But no one, bar a handful of mathematicians, understood his revolutionary achievements in number theory and power series, most notably his theorem concerning the partition of numbers into a sum of smaller integers. Ramanujan, born in 1887, was an impoverished, devout Brahmin clerk working at the Madras Port Trust. Self-taught in mathematics, he claimed to be inspired by the Hindu goddess Namagiri. He used to say: "An equation for me has no meaning, unless it represents a thought of God." Lacking any other outlet, in 1913 he mailed some of his theorems, without proofs, to G. H. Hardy, a leading mathematician at the University of Cambridge. So transcendently original were the formulae that Hardy yanked Ramanujan from obscurity to Trinity College Cambridge, collaborated extensively with him, published many joint papers, and demonstrated that he was a mathematical genius. In 1918, Ramanujan became the first Indian to be elected a fellow of the modern Royal Society and Trinity College. After succumbing to a mysterious illness and attempting suicide on the London Underground, he returned to India to recuperate, still producing major theorems on his sickbed, and died at the age of just 32.
Long after his death, Hardy wrote of Ramanujan: "The limitations of his knowledge were as startling as its profundity... His ideas as to what constituted a mathematical proof were of the most shadowy description. All his results, new and old, right or wrong, had been arrived at by a process of mingled argument, intuition and induction, of which he was entirely unable to give any coherent account:' Kanigel, in his masterly biography, writes that "Ramanujan's life was like the Bible or Shakespeare - a rich find of data, lush with ambiguity, that holds up a mirror to ourselves or our age". He gives some fascinating examples. The Indian school system flunked Ramanujan in his teens, but a few individuals in India sensed his brilliance and rescued him from near starvation by getting him his clerk's job. In England, Hardy drove Ramanujan so hard that he may have hastened his death.
Had Ramanujan received Cambridge-style mathematical training in his early
life he might have reached still greater heights - or it might have stifled
his originality. Hardy, an atheist, was convinced
that religion had nothing to do with Ramanujan's intellectual power, but
it is at least plausible that India's loog-standing mystical attraction to
the oncept of the infinite was a vital source of Ramanujan's creativity.
"Was Ramanujan's life a tragedy of unfulfilled promise? Or did his five years
in Cambridge redeem it?" asks Kanigel. "In each case, the evidence [leaves]
ample room to see it either way.
Leavitt is alive to these ambiguities, and has clearly done detailed research on Ramanujan, Hardy, the world of Edwardian Cambridge -wranglers, homosexuality, the Apostles, Bertrand Russell's pacifism and so forth - and the home front during the first world war. Leavitt respects historical facts where they are known, but also admits to inventing important chunks of plot from the scantiest of evidence, or even no evidence.
For example, it is known that Hardy - whose fictional confessions form the
spine of the novel - was gay. Yet there were no obvious homoerotic elements
in his relationship with Ramanujan, and there exists no clear evidence (nor
even much gossip) to prove that Hardy practised sodomy - unlike some other
members of the Apostles, such as John Maynard Keynes and Lytton Strachey.
Nonetheless, Leavitt harps throughout on Hardy's sexuality, inventing a subplot
in which Hardy seduces a wounded soldier, and a far-fetched encounter with
a handsome London policeman who humiliates Hardy for being "queer". There
is absolutely no evidence for these episodes, as Leavitt frankly admits.
The result is a book that does not convince overall, but is never less than engaging and intelligent. It smoothly integrates the mathematics with the effects of war on Cambridge and London, atmospherically evoked: Trinity College's Great Court is turned into a hospital; a zeppelin raid on London strikes Ramanujan as divine punishment for his lapse from strict vegetarianism. One thing Leavitt lacks is a feel for crucial nuances of the imperial relationship; he is no E. M. Forster and lacks Kanigel's obvious affection for south Indian culture.
How close was the real Hardy - who never visited India - to Ramanujan, beyond their twin obsession with mathematics? Could Hardy's well-known reserve, verging on indifference to others, have contributed to Ramanujan's fatal illness? Judging from Hardy's actual letters and writings, which reveal his ignorance of Ramanujan's home culture, the two were certainly not intimate. Leavitt seems to accept this when he writes of Hardy at the very end: "He was too old to believe any longer that he bad touched more than a fragment of that vast, infernal mind:' Yet within the novel he has Hardy dwell implausibly on the mores and motives of Ramanujan's caste-bound mother and child wife in far-away India.
The Indian Clerk begins with a lucid quotation from A Mathematician's Apology, Hardy's melancholy 1940 memoir about his fading mathematical powers, which Graham Greene hailed as "the best account of what it is like to be a creative artist". The real Hardy wrote that "Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. 'Immortality' maybe a silly word, but probably a mathematician has the best chance of whatever it may mean." Leavitt's fictional Hardy goes on to speak in a very different voice, and to my mind this mismatch diminishes our understanding of the real Ramanujan and the reasons for the growing fame he commands long after his death.
Andrew Robinson is the author of The Story of Measurement and The Lost Man Who Knew Everything
The Indian Clerk by David Leavitt,Bloomsbury £16.99 $24.95 ISBN 9780747581680
The beauty of maths
A POINT OF VIEW
By Lisa Jardine
The story of an Indian clerk with an extraordinary talent for mathematics should inspire young people to see the beauty that lies in numbers.
I have been thinking recently about the way in which stories we are told when we are young shape our adult lives. I am reading with great enjoyment a new novel entitled The Indian Clerk, by David Leavitt, based on the life of the early twentieth-century Indian mathematician Srinivasa Ramanujan.
Ramanujan died aged 32.
A humble clerk at the Port Trust in Madras, Ramanujan first came to the attention of European mathematicians in 1913, when he wrote a ten-page letter to the Cambridge mathematician and fellow of Trinity College, GH Hardy, which contained over 100 statements of theorems on infinite series and number theory.
Number theory is a fascinating field of mathematics. It consists of the study of the properties of whole numbers or integers. Among these, primes or prime numbers hold a special charm for number theorists, because of their peculiar power among the naturally occurring numbers.
A prime number is a number divisible only by itself and the number one (which is itself a prime, but for reasons I won't go into here is usually omitted from the list). The primes under 20 are two, three, five, seven, 11, 13, 17, and 19.
After that, primes occur increasingly far apart, sporadically and apparently unpredictably. For centuries, a great deal of mathematical effort has been expended on trying - unsuccessfully - to predict some patterned way in which large primes occur.
Let me try to give you something of the flavour of the way in which prime numbers seem intriguing to someone with a passion for numbers in general.
So mathematicians refer to two, the only "even" prime, as the
Having worked through some of the material in the letter with his fellow-mathematician and collaborator JE Littlewood, however, both men became convinced of Ramanujan's unusual ability and, after some initial difficulties, Hardy contrived to get him to Cambridge.
As a child, I found the whole story of the brilliant, self-taught Indian clerk who solved some of the most difficult problems in number theory and died so young, extremely romantic.
There followed an extremely productive five-year collaboration between Ramanujan and Hardy. The two perfectly complemented one another's abilities: Hardy was a great exponent of rigour in analysis, while Ramanujan arrived at his results by what Hardy described as "a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account".
Through his work in Cambridge, Ramanujan achieved the recognition he had sought when he first approached Hardy, and in 1918 he was elected a Fellow of the Royal Society (the first Indian to be so honoured).
The British climate, however, took its toll on his health. In 1917 he collapsed with a mysterious stomach complaint and was rushed into hospital, where doctors feared for his life. By late 1918 his health had slightly improved and in 1919 he returned to India. But his health failed again, and he died the following year at the age of 32.
As a child, I found the whole story of the brilliant, self-taught Indian clerk who solved some of the most difficult problems in number theory and died so young, extremely romantic. But it was one specific anecdote about Ramanujan that particularly captivated me.
Ramanujan was recovering from his first bout of serious illness in a nursing home in Putney and Hardy had gone there by taxi to visit him.
To which Ramanujan replied without hesitation: "Not at all, Hardy! It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways."
1729 can indeed be represented as 1³ + 12³ and as 9³ + 10³, and is the lowest integer for which such a combination is possible.
What intrigued me about the story was that someone could have such a familiarity with the integers that he would spontaneously recognise an attribute of an apparently "dull" or unprepossessing number as being susceptible of expression in a (for a mathematician) attractively patterned way.
Hardy and Ramanujan found a common language
Caring deeply about numbers and their properties may in part at least be something that runs in families. At the age of four, my eldest son used to wake in terror from a recurrent nightmare. He was on a wide sandy beach at low tide.
"I had to count the grains of sand," he would tell me, tearfully, "and I knew that I just wouldn't be able to do it."
Even at that age, numbers mattered to him intensely enough for him to dream about them. But just as in some families, fear of spiders is passed on to the children who witness their parents' alarm at an arachnid in the bath tub, so terror of mathematics can be passed on from generation to generation.
The role of good maths teachers in schools to encourage pupils in this area, is particularly important, to overcome openly-displayed anxiety on the part of parents about dealing with maths homework.
The report concluded that there is a crisis in the provision of qualified specialist maths and science teachers in our schools, of which the government is largely unaware.
This shortage is particularly alarming, the report goes on, because "the skills, knowledge and understanding that come from learning and enjoying science and mathematics at school and college prepare young people for jobs in a demanding workplace and life in the modern world".
I watch my adult friends back away from a simple arithmetical calculation
The shortage of well-qualified and committed teachers in maths has, I suggest, a particularly unfortunate effect in girls' schools, where it amplifies an existing inclination among many girls to insist that they simply do not like doing maths.
A London inner-city girls secondary school of which I am a governor recently received a dazzling Ofsted report for its achievement across the board. The only area in which there was even a hint of criticism was in maths teaching at key stage four.
When a small group of us discussed the inspection report in detail with the head teacher, she was quick to explain that the problem was a rapid turnover in teachers and serious difficulty in recruiting well-qualified maths teachers at all.
But several people round the table inevitably also mentioned the likelihood that girls simply did not feel comfortable with maths, or even, could not do maths. It was not surprising, was it, if the school had difficulty getting all of them to succeed when it came to numbers and equations?
Thinking back to my own upbringing I feel sure that the problem lies elsewhere. All too often I watch my adult friends back away from a simple arithmetical calculation with the words "I never could do maths".
This is not an excuse they would dream of making publicly with regard to reading.
Perhaps, just as we try so hard to instil a love of great writers in successive generations, we should be looking for more stories like that of Ramanujan, to inspire all our young people with a lasting love for the beauty of numbers.
--------------------------------------Add your comments on this story, using the form below. ------------------------------------------
I loved this article, this is what the youth of today (and I
am one of those) is missing - passion in a subject. I love maths, it's great
as it's the only thing in life which is constant. 2+2 is always 4 even if
your having a bad day!
I had a brilliant maths teacher at school - a guy called Simon
I'Anson. He enjoyed maths and taught me to do the same. It was mainly because
of his inspiration that I went on to study maths at university. It's hard
to overemphasize the importance of maths as a subject. It's not just that
it teaches you to put numbers together (important though that is); mathematics
teaches people to think logically and rigorously. It's a disgrace that we
accept "I can't do maths" as an excuse. Mr I'Anson wouldn't.
I do agree with the author of the article; stories that we
read or hear when we are young influence our lives forever. I know lots of
people that read "A Brief History of Time" and went on to study physics.
I personally prefer maths to physics, and one book that I found really inspiring
Last Theorem" by Simon Singh (I believe it was initially written as a
documentary). If you are looking for a good Christmas present, get "The
Indian Clerk" or "Fermat's Last Theorem". If you are kids are slightly interested
in science, they might get inspired for life.
I went to school in Barnsley in the 70s. My maths tutor was
very passionate about his subject which rubbed off on me. I thoroughly enjoyed
maths, but after leaving school aged 16 there was never an avenue to pursue
this passion (leave school, get a job etc.). University at that time seemed
out of reach, but I do believe that outlet is much more available now. I
still enjoy maths and it is always my intention to undertake further studies.
This man is truly my idol.
It has often struck me as odd that we should hide our
in shame and yet wear
as a badge of honour. What else do we allow ourselves to be poor at without
any embarrassment? Several areas- languages, geography, science, cooking,
singing, etc.. Coming last in cross-country is far more shaming than being
bottom of the class in technology. What worries me is that the list gets
longer and literacy could soon become another casualty of our casual approach
to standards in education for an increasing proportion of the population.
There are areas outside the school curriculum where we permit ourselves to
be hopeless - caring for the environment, parenting teenagers, politics,
citizenship, manners. We can allow people to fail but not to take a pride
Perhaps the problem lies with getting children to be good at
arithmetic before they get on to maths. The fact that they don't even teach
them times tables nowadays is a major backwards step as they are very useful
in later life. I am good at arithmetic including mental arithmetic. However
in the first year at grammar school the "maths" teacher was actually a rather
bad tempered woodwork teacher who frightened the life out of me, and I never
caught up. I love
and was good at algebra, treating it as a puzzle to be solved, but nobody
ever explained what it could be used for. At the time I was at school there
(1958-65) there was a Certificate in Proficiency in Arithmetic, which I took
instead of maths GCE, and it proved very useful indeed. A young shop assistant
even had to use a calculator to deduct 10p from a wrong total the other day,
and that is an appalling reflection of the state of teaching on this subject
Great story! When I was at school Scunthorpe Grammar - 1964
to 1969) we had a Mathematics Teacher called Mr Holmes... he was very strict
(almost Victorian in approach) but he taught us to believe in "the beauty
of mathematics". I will never forget, and I do "love" mathematics as
a result... what a great man! If only every teacher could do that for their
subject. Merry Christmas to all back in UK.
A very charming story. Maths and science lack relevance today.
There is no lack of mathematicians and scientists. There are no skills shortages
whatsoever in these areas. I wouldn't encourage children to do maths or science
- there is no fun, no reward and no gain to be had - and maths and science
teachers know it.
at the Balls - Zoe isn't exactly following in her Dad's footsteps.
This is an inspiring story. My own fascination for Maths began
very young and had something to do with my father being a Science and Maths
teacher. He had a wonderful way of explaining how to do calculations and
made it look so easy that everything just clicked. Had it not been for his
influence in my life I am sure I would have become one of the "I never could
do maths" of society. God bless you Dad.
15 December 2007 Newscientist