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The Man Who Knew Infinity: A Life of the Genius Ramanujan

Washington Square Press
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Kanigel’s biography of Ramanujan has by now become the standard account of one of the more romantic mathematical lives of the last century. It was very well received, chosen for the Book-of-the-Month Club (at the time a significant force in middlebrow American culture), shortlisted for several awards, and strongly recommended by the MAA for all undergraduate mathematics libraries. It’s interesting to look at the book again, more than 20 years later.

The great virtue of this biography is that it places Ramanujan very firmly in the context of his native South India. Kanigel works overtime to give us a sense of what life was like for Ramanujan as a young boy in Kumbakonam and then a young man in Madras. He tells us what the weather was like, what kinds of food were eaten, what family life was like. He also emphasizes the religious side of India, the large role that temples and meditation played in everyday life. The account is vivid and convincing, though I am sure anyone from South India will find things to disagree with. (See, for example, Alladi’s review of the book in his Ramanujans Place in the World of Mathematics.) 

South India helped form the personal side of the young man who later would find England strange and ultimately inhospitable. He was sociable and likeable, used to warm temperatures and strongly-flavored food. As a Brahmin, he was vegetarian, bore the “sacred string,” wore Indian clothes, and had his hair in a kutumi, a bunched-up knot at the back of the head..

Kanigel’s Ramanujan discovered mathematics and went through a period of almost exclusive concentration on its mysteries. As a result, he failed a crucial school exam and was denied the opportunity to attend university. This crucial event in Ramanujan’s life parallels the early life of other brilliant mathematicians, with Galois in particular coming to mind. Galois, however, seems to have moved from an obsession with mathematics to an obsession with revolutionary politics, while Ramanujan stayed focused on mathematics for the rest of his short life.

The other huge difference between Ramanujan and Galois was the lack of an active mathematical community in Madras. In Paris, Galois was disliked and misunderstood, but still had access to textbooks, journals, and even lectures. In Madras, the few local mathematicians were unable to assess Ramanujan’s work, which was both incredibly original and nonstandard in presentation, and they were unwilling to bend the rules for this young man without a formal degree of any kind. This explains Ramanujan’s decision to appeal to mathematicians in Britain, which eventually led, after some failures to communicate, to his famous letter to Hardy.

Hardy comes off as insightful, dedicated, and vigorous. He saw what others had not: here was a mathematician of genius, even if untrained and exotic. He decided to help, and in particular to bring Ramanujan to England. He made things happen.

The positive response from Hardy seems to have caused a fundamental change in the attitude of the Indian mathematicians around Ramanujan: attestation from a well-known mathematician from the “center” served to convince the “periphery” of the value of Ramanujan’s work. One senses, at this point, that Kanigel feels that staying in India would have been a better option for Ramanujan, that perhaps the research fellowship he had received in Madras would have allowed him to grow and mature and live a long and productive life. But as we know, it was not to be. The objections of his mother were overcome, he had a Westernizing makeover, and he set out for England.

The story from that point on is fairly well known from the accounts of Hardy and others. Moving to England turned out to be both bane and blessing: the close daily interaction with Hardy (and, to a lesser extent, Littlewood) was the most exciting intellectual adventure of Ramanujan’s life, but living in England during World War I turned out to be lonely, cold, depressing, and ultimately deadly. Kanigel calls our attention to the fact that this was not at all unusual for Indian students at Oxford and Cambridge, citing a report from the period that was concerned with how to improve their experience.

From then on, the reader knows where the story is going and looks on with something like horror. Ramanujan fell ill and got a chance to sample medicine in the 1910s — scary stuff. Going back to India in the middle of a war was too dangerous. The doctors fumbled around, not quite knowing what was wrong, unable to help him get better. The letters from home dried up. There was no energy for doing mathematics. Finally the war ended and Ramanujan returned to India. He improved a bit, but family relations had degenerated and complicated the attempts at treating his sickness. He produced some significant mathematics, but soon got worse. He died in 1920, thirty-three years old.

Given the emphasis on the Indian context, it is not surprising that Kanigel spends some time discussing Ramanujan’s attitude towards religion. It is well known that he attributed some of his insights to revelations from the family goddess, Namagiri of Namakkal. Hardy claimed that Ramanujan’s attitude was simply a respect for ritual without any intellectual commitment (which may well reflect a Westernized idea of what it is to be “religious”, putting theological commitments above practical devotion). For Kanigel, Ramanujan never felt any of the Western anxieties about religion, continuing to balance intellect and spirit throughout his life. If he tells us he received revelations, well, maybe he did.

Kanigel also attempts to convince us of the importance of Ramanujan by tracing some of the impact of his work. This is probably the weakest chapter in the book, full of name-dropping and ultimately unconvincing, most likely because Kanigel does not really have a good understanding of the mathematics. At other points in the book, he makes valiant attempts to explain Ramanujan’s ideas, but clearly cannot go very deep. He does, I think, successfully convey the conflict between intuition and rigor that must have characterized the interactions between Ramanujan and Hardy.

The text mostly reads well. At times the narrative gets repetitive, giving me the feeling that there is not all that much evidence to discuss and that the author hopes that many words will be sufficient to convince. There are lots of notes (arranged by page, without note markers in the text itself). At times one wonders whether there isn’t a bit too much mind-reading, as in “Even if he didn’t always let his mind wander back home, there were times when the small, familiar things of South Indian life insinuated their way into his awareness” (page 244, with no note to explain how Kanigel knows what was in Ramanujan’s mind).

Finally, there is the weird business of the photographs. At several points in the book, Kanigel discusses photographs of Ramanujan, interpreting them for clues to his feelings and attitudes. For example, discussing the awarding of Ramanujan’s Cambridge B.A. “by research,” in 1916:

In the early afternoon of March 18, Ramanujan posed for a photograph to mark the occasion with a group of students in their academic robes outside the Senate House. The shortest and stockiest of the lot, he stood squarely at attention, like an army recruit in boot camp, his mortarboard sitting flat atop his head. His trouser legs were a couple of inches too short. His suit bulged, its buttons straining. (page 234)

These descriptions help make the person real to the reader, but strangely the photos themselves are not included. Lots of other photographs are: of Ramanujan’s family, of his Indian mentors, of Cambridge professors, of locations in both India and Cambridge. But there are only two images of Ramanujan himself: the famous passport photo and the Indian stamp based on it. Readers who want to see the pictures Kanigel describes will have to find them in Ramanujan: Letters and Commentary, edited by Bruce Berndt and Robert Rankin.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME.

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Tuesday, May 27, 2014
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Tuesday, May 27, 2014