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Book Review, © Copyright 1999, Jim Loy
This book is subtitled, "A life of the genius
Ramanujan." This is an interesting book, about an incredibly interesting
person. Srinivasa Ramanujan Iyengar, usually called S. Ramanujan or just
Ramanujan, was among the greatest of all mathematicians, perhaps the greatest
in some ways, in all of history. His picture, from a postage stamp, is on the
left.
He was born in India, on December 22, 1887. He was of the Brahmin caste. His family was poor. He lived much of his life in Madras. He was mostly a failure at school, as mathematics is all that he would do. Several times he failed to get into college in India. In 1903, he found the mediocre book, A Synopsis of Elementary Results in Pure and Applied Mathematics by George Carr. While mastering this book, Ramanujan began discovering mathematical formulas which were not in the book. And he wrote these down in notebooks. He got a job as a clerk. He traveled around India showing his notebooks to mathematicians, trying to get into college. In 1913, he wrote letters to mathematicians in England. Only one of these men took an interest. Ramanujan's letter to G. H. Hardy (perhaps the most respected mathematician in England at the time) began like this:
Dear Sir,
I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras on a salary of only £20 per annum. I am now about 23 years of age. I have had no University education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at Mathematics. I have not trodden through the conventional regular course which is followed in a University course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as "startling."
And he included several pages of formulas. To Hardy, some of these made sense. Some were already known from other sources. Some made no sense or were wrong. And some were intriguing beyond measure. Hardy said of some of these formulas: "They must be true because, if there were not true, no one would have the imagination to invent them."
Because of Hardy's support, Ramanujan received a scholarship at Presidency College in Madras. This gave him what he needed most, enough money to live, and the time to do mathematics. Hardy tried to get him to come to England, to study at Trinity College, Cambridge. In 1914 Ramanujan sailed to England, leaving his 13 year old wife in India. World War I (the Great War) began.
Ramanujan sharpened up his knowledge and technique. And he collaborated on papers with Cambridge mathematicians, mostly with Hardy. And Ramanujan became world famous among mathematicians.
In 1918 Ramanujan got sick, apparently with tuberculosis, and published fewer papers. He tried to commit suicide. In 1918 he was elected to the Royal Society. World War I ended. In 1919 he returned to Madras. His mother tried to destroy his marriage. His illness got worse; he wasted away. Near the end he produced some of his most interesting work. On April 26, 1920, Ramanujan died at the age of 32.
Ramanujan was creative and original, more so than perhaps any other mathematician in history. He was fairly weak in some areas, especially in proving his interesting conjectures. As a result, a few of his conjectures are false. Others of his conjectures and papers are still producing new results, 80 years later.
G. H. Hardy did original mathematics all of his life. But he is best known for his support of and collaboration with Ramanujan.
In India (and worldwide) Ramanujan is an inspiration, a tragedy, and a reminder that education for most is inadequate or nonexistent. Will future Ramanujans remain undiscovered?
To order this book, click Amazon.com (goes directly to this book).