Book Review: The Man who knew Infinity

Till a few days back, to me, Srinivasa Ramanujan was a well known and eccentric Indian mathematician. Now, after reading Robert Kanigel's  'The Man Who Knew Infinity', I am better informed. Ramanujan was  one of the most original mathematicians of the 20th century.  More specifically, he is acknowledged to be a great formalist comparable in skills to the all time greats - Gauss, Euler and Jacobi. And Robert Kanigel's biography of Ramanujan is the one of the best biographies I have read, and one has that has made a lasting impression on me. 

Ramanujan's story is a most extraordinary one. He arrived from nowhere and cast his genius on the mathematical world in a short, dazzling life (1887-1920). Born in the Kumbakonam town, Tanjavur district of Tamil Nadu in the Kaveri delta, he spend a childhood in tight financial conditions, yet not in penury. However, given his Brahmin roots there was an emphasis on education. He did very well in school in all subjects, excelling in Maths and was given a scholarship for the Government College, Kumbakonam. Around this time he developed a fierce appetite for mathematics. The turning point came with Carr's 'A Synopsis of Elementary Results in Pure and Applied Mathematics'. This was basically a book for preparation to Cambridge's Tripos exam, so it basically listed results and hints to get to them. A totally unremarkable book, that may be despised as one of those 'exam guides'. However, he had little access to mathematical texts and this book hooked him to mathematics. He lost all interest in all other subjects. He proved results in Carr's book by developing his own methods, finding his own ways through the mathematical maze, totally immersing himself in mathematics. The book proved influential to Ramanujan's style of mathematics which as Hardy said was a "curious mix of reason, intuition .." Today, Carr is famous only because Ramanujan read his book. As a result, Ramanujan flunked other subjects and lost his scholarship to college. He spent a few years in wilderness, with no income and just about sustaining himself. He tutored a few students to support himself. He got another scholarship, but the temptation for mathematics would again lead him to ignore other courses. He spent a lot of time at home or being supported by his friends. Yet, he continued his mathematics and started maintaining notebooks of his results. which were to subsequently become the famous Ramanujan notebooks. He was so hard pressed that he didn't have any money for paper, and did the proofs on slate and chalk transferring results to paper later. In this manner he ended up "rediscovering a century of Western mathematics and added his own astounding finds". His mathematical skills of no use, he spent very harsh days barely surviving and working on Maths. Through his friends, he got a monthly stipend from a wealthy benefactor and finally a decently paying job at Madras port trust as a clerk. 

In Madras, people started noticing his mathematics, and he was encouraged by his boss. He was soon publishing in the Indian Mathematical Society. But no one really understood his maths, and he needed validation of his work from a more established authority - so that he could be justified of his achievement, so that he could support himself while doing maths. He sent letters to Cambridge mathematicians, one of which was to Prof. Hardy. This event was to change his life. Hardy soon recognized that it was the work of a great mathematician. With Hardy's stamp of approval, the Madras University made an exception for him and made him a research fellow though he did not have a Bachelor's degree. But Hardy was not satisfied, and wanted to bring Ramanujan to England. Ramanujan was not ready given the caste restrictions on travelling to foreign lands and concerns about food given his strict vegetarian needs. Finally he relented, supposedly after a commandment in a dream from the family deity Namagiri.  His stay in England was most fruitful, where in collaboration with Hardy he made significant contribution to partitions, prime number theorem. However, the alien conditions took their toll on Ramanujan, both physically and mentally. He attempted suicide once, and returned home in poor health. He was now however an FRS and Fellow of Trinity, and was given a generous research grant with which he could live comfortably with his family. In spite of failing health, he continued to work and in the last year of his life did some pathbreaking work on mock-theta functions. 

His is a story of true determination and integrity as much as it is a story of genius. Against all odds, in a society where there was no particular place for his mathematics and with no mathematical pedigree in his family, how did a genius like Ramanujan arrive? A writer best described him as 'svayambhu' - 'self-born'. As Kanigel says - "He was self-willed, self directed and self-made. Indeed, some might conceivably label him as 'selfish' for his preoccupation with doing the mathematics he loved without any concern for the betterment of his family or country. Ramanujan did what he wanted to do, went his own way." It was his unshakable confidence in himself that carried him so far. He found his own methods and stuck to them. When the whole of Europe was moving towards a maths based on rigor where intuition seemed to have little place, Ramanujan displayed his brand of mathematics which was "a curious mix of intuition and evidence".  

Kanigel's biography is a great effort that goes beyond Ramanujan, the legend to discover Ramanujan, the man. Kanigel has done excellent reseach in understanding the culture of South India prevalent at that time. His attempt to describe South India, its geography, landscape, its people and culture is admirable. Given that the book is written for a western audience, it is a very beautiful account of a part of the world for readers who don't know about it.  A lot of what we know about Ramanujan is due to Hardy, and Kanigel rightly delves deep into the story of Hardy. It is almost as if the book contains a mini-biography of Hardy within. As Hardy himself has acknowledged - it was his good fortune to be associated with Ramanujan and Littlewood. Kanigel paints a picture of English middle class at that time, of the Cambridge culture. Its seems eerily similar to ours today - the focus of parents on education then, the Tripos exams - which is the equivalent of the JEE today, the coaching culture. Truly, history repeats itself. 

But Ramanujans occur but so rarely.