Thursday, August 23, 2007

The Man Who Knew Infinity

Way back in the 1914 Prof G.H.Hardy, a famous British mathematician, went to see his friend, who was recovering from an illness in a hospital, in London’s Putney district. He remarked to him, that he had come in a cab which had a number 1729, and some how that number seemed, dull and unremarkable to him. To which his friend immediately replied

“No Hardy, it’s a very interesting number, it is the smallest number that can be expressed as the sum of two cubes in two different ways”.

To the mathematically challenged, it means that 1729 can be expressed as
1729= 13 + 123 or 1729= 93 + 103

This was an anecdote, which we often read as school students, and even during our mathematics classes. The friend here is of course Srinivasa Ramanujan, one of India’s greatest scientists and one of the world’s greatest mathematicians. The Man who Knew Infinity by Robert Kanigel is the story of this great genius, of which every Indian must be proud of.

The world of mathematics owes a great debt to India and Arabia, because these are the two lands from which the basic theories of mathematics have originated. Aryabhatta who contributed the number-place value system and the concept of zero, as well as calculating the area of the triangle. Bhaskara who came up the concept of the decimal system. Halayudha who provided a clear description of the Pascal’s triangle. Even in the modern age, we had great Indian mathematicians like P.C.Mahalnobis, who did pioneering work in statistics, Nobel Prize winner S. Chandrashekar, S.S.Pillai well known for his work in number theory to name a few of them.

The review is not about the book per se, but more of Ramanujan’s life and his impact. The book deals with the early life of Ramanujan, his journey to England, his relationship with his mentor Hardy. To be honest, that part of Ramanujan’s life in India, was not much interesting. It seemed more aimed at giving Western readers a view of exotic India.

Ramanujan was born into an Iyengar family, in the town of Erode, Tamil Nadu on Dec 22, 1887. His father was a clerk in a saree shop, while his mother was a devout Brahmin housewife. Theirs was a typical Tamil Brahmin household, pretty religious and orthodox. Growing up under his mother’s care and guidance, he learnt about Indian tradition and puranas. His first brush with mathematics was in 1898, in Higher Secondary School.

And that was when his prodigal talent came to being. At 11 years, he exhausted the mathematical knowledge of two college students, by 13 years he completely mastered the books on advanced trigonometry written by S.L.Loney. At 14 years he was assisting his school in the logistics of assigning its 1200 odd students to 35 teachers. When he was 17, he independently developed and investigated Bernoulli numbers and Euler’s constant up to 15 decimal places. His peers stood in respectful awe of him.

However his obsession with mathematics, made him neglect other subjects, that he often ended up failing in most of them. He dropped out of college, and pursued maths research on his own. He made ends meet, by taking up tuitions for school students. He later left for Villupuram, where he met the Dy. Collector, Mr Ramaswamy Iyer, who founded the Indian Mathematical Society, and applied for a clerical job, in the revenue department. Struck by his intelligence, Mr. Iyer, recommended him to his other friends, and his fame steadily grow. In 1912, he joined as a clerk in the Accounts Department of the Madras Port Trust. During his spare time, he would still continue his research in mathematics. He was encouraged by his boss, Sir Francis Spring and his colleague, S.Narayana Iyer.

Some of his friends like Spring, Iyer, Ramachandra Rao and Middlemast, helped him to send his work for Cambridge University, but he was rejected due to lack of formal educational qualifications. On 16 Jan, 1913, he wrote to Prof G.H. Hardy, who had the foresight to recognize Ramanujan’s skills. Hardy was especially impressed by Ramanujan’s work on continued fractions, claiming he had never seen such work before. One of Hardy’s colleagues Neville later remarked “not one of his theorems, could have been set in the most advanced mathematical examination in the world”.

Hardy requested Ramanujan to come to Cambridge, but he refused, due to the then prevailing sentiment of not going to a foreign land, strongly rooted in Indian society. For the time being, he was given a research grant at the University of Madras, where he did pioneering work on Frullani’s 1821 integral theorem. Hardy’s colleague Neville, again asked Ramanujan to come to Cambridge, and this time Ramanujan agreed. According to a popular anecdote, his mother had a dream, in which their family goddess Namagiri, commanded her not to stand in the way of her son’s progress.

From 1913-18, Ramanujan spent 5 fruitful years in Cambridge, collaborating with Hardy and Littlewood, on many research projects. While Littlewood said that “this man was at least a Carl Gustav Jacob”, Hardy remarked that he can be compared only with Euler or Jacobi. In March 1916, Ramanujan was awarded the Doctorate for his research on highly composite numbers. Hardy later remarked that this was one of the most unusual papers he had ever seen. Both of them had contrasting ways of working, Hardy followed the Western model of proof and rigor, and was an atheist. Ramanujan was a devout believer and often relied on intuition and gut feeling. It was the perfect mix of East and West.

On Oct 1918, he became the first Indian to be elected as Fellow of Trinity College, Cambridge. In 1917, he became a member of the London Mathematical Society. In 1918 he became the second Indian to gain fellowship of the Royal Society, and one of it’s youngest members. Unfortunately, his poor health, ensured he could not live long, and he died in 1919, at an age of 32. His home state of Tamil Nadu celebrates his birthday as State IT day.

Unfortunately, in his own country, he remains a forgotten person. It’s ironical that Hollywood is paying tribute to this genius with two movies, but then it took a foreigner to make a movie on Gandhi for us. Again it was a Westerner, who penned his biography. He has been referred to in movies like Goodwill Hunting as an example of mathematical genius, as well as in many novels. Its pretty sad that such an astounding genius should be a forgotten man in his own country, while the rest of the world pays tribute to him. Will we at least now start to recognize some of our real heroes, instead of idolizing fake heroes?


Kaushik K said...

I beg to differ. Mathematics is not a spectator sport. One can't appreciate genius if one doesn't understand its work. This is true of all human pursuits. But when it comes to Mathematics, people can't pretend to know what they are talking about and get away with it unlike Art or Music. Most modern "educated" Indians cannot appreciate Ramanujan because they have no idea what mathematics really is.

Geoffrey Mathews said...

"To the mathematically challenged, it means that 1729 can be expressed as 1729= 13 + 123 or 1729= 93 + 103."

Now wait a minute. Are we missing something here? It is actually:

1729 = 1728+1 = 12^3 + 1^3
1729 = 1000+729 = 10^3 + 9^3

atanu nath said...

@Geoffrey Mathews....

yes it was the actual one... and he mentioned as sum of two cubes... but din't write explicitly...

@ Kaushik K....

I don't agree... when we appreciate a business man a billionaire.. do we need to know finance?? No... we recognize a genius by the impact... by the world recognition... if the greatest mathematicians of all time praised him and praise... one doesn't need to go through mathematics again to recognize that genius... please try to understand the point the blogger wanted to make...

and I think this attitude is one reason that helped or encouraged Indian to forget Ramanujan....

and the reality is really harsh... by hero we now mean either one has to die in a war or be a hit in the bollywood or a corrupted politician...