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Last Updated: Friday, 14 December 2007, 17:12 GMT
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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 20th Century Indian mathematician Srinivasa Ramanujan.

 Ramanujan died aged 32
I picked it up because I have such intense memories of my father telling me Ramanujan's story, at about the time I started secondary school, shortly after I had won a scholarship to a famous girls' school on the strength of my own mathematical promise. I even had a black-and-white photograph of Ramanujan, looking sultry and faintly like Elvis Presley, on the table at home at which I did my homework.

A humble clerk at the Port Trust in Madras, Ramanujan first came to the attention of European mathematicians in 1913, when he wrote a 10-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.

Genius

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.

Take the number two. Two is the smallest prime number. It is also the unique prime which is even, because all even numbers are divisible by two and any number apart from two which is divisible by two is not a prime, by definition.

 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 Hear Radio 4's A Point of View
So mathematicians refer to two, the only "even" prime, as the "oddest" prime.

Hardy was immediately intrigued by the extraordinary nature and complexity of the mathematics in Ramanujan's letter. But he was torn between believing that his correspondent was a crank, and wanting to recognise him as a natural mathematical genius.

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.

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 second 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.

Terror

Hardy (never much of a conversationalist) greeted the sick man abruptly with the words: "The number of the taxi-cab that brought me here was 1729. It seemed to me rather a dull number."

 Hardy and Ramanujan found a common language
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.

"Every positive integer is one of Ramanujan's personal friends," was how Hardy's friend Littlewood described it.

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.

Alarming

Last Monday the Royal Society published a "state of the nation" report on the UK's science and mathematics teaching workforce.

 I watch my adult friends back away from a simple arithmetical calculation
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".

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.

Below is a selection of your comments.

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!
Zara Smith, 2+London

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.
Tom di Giovanni, Leamington Spa, UK

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 is "Fermat's Last Theorem" by Simon Singh (I believe it was initially written as a BBC 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.
UM, UK

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.
Steve Taylor, Plymouth

This man is truly my idol
Richard Juggins, Yeovil

It has often struck me as odd that we should hide our illiteracy in shame and yet wear innumeracy 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 in it.
Jeste, Norwich

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 puzzles 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 nowadays.
Lindsay Ponting, Swindon, U! K

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.
Dave Metcalfe, Russell/New Zealand

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. Look at the Balls - Zoe isn't exactly following in her Dad's footsteps.
Richard, Bucharest, Romania

] 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.
Aisha, London

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