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Kumbakonam, his hometown, flanked by the Cauvery and one of its tributaries, lay in the heartland of staunchly traditional South India, 160 miles south of Madras, in the district then known as Tanjore. Half the district’s thirty-seven hundred square miles, an area the size of the state of Delaware, was watered directly by the river, which fell gently, three feet per mile, to the sea.
The Man Who Knew Infinity PDF Book by Robert Kanigel
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Spreading its rich alluvial soil across the delta. The Cauvery conferred almost unalloyed blessing. Even back in 1853, when it flooded, covering the delta with water and causing immense damage, few lives were lost. More typically, the great river made the surrounding land immune to year-to-year variation in the monsoon, upon whose caprices most ofthe rest oflndia hung.
In 1877, in the wake oftwo straight years of failed monsoons, South India had been visited by drought, leaving thousands dead. But Tanjore District, nourished by the unfailing Cauvery, had been scarcely touched; indeed, the rise in grain prices accompanying the famine had brought the delta unprecedented prosperity.
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No wonder that the Cauvery, like the Ganges a thousand miles north, was one of India’s sacred rivers. India’s legendary puranas told of a mortal known as Kavera-muni who adopted one of Brahma’s daughters. In filial devotion to him, she turned herself into a river whose water would purify from all sin. Even the holy Ganges, it was said, periodically joined the Cauvery through some hidden underground link.
So as to purge itself of pollution borne of sinners bathing in its waters. Dakshin Gange, the Cauvery was called-the Ganges of the South. And it made the delta the most densely populated and richest region in all of South India. The whole edifice of the region’s life, its wealth as well as the rich spiritual and intellectual lives its wealth encouraged, all depended on its waters.
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The Cauvery was a place for spiritual cleansing; for agricultural surfeit; for drawing water and bathing each morning; for cattle, led into its shallow waters by men in white dhotis and turbans, to drink; and always, for women, standing knee-deep in its waters, to let their snaking ribbons of cotton or silk drift out behind them into the gentle current.
Then gather them up into sodden clumps of cloth and slap them slowly, relentlessly, against the water-worn rocks. Today, Town High’s cluster of handsome white buildings occupies an oasis of tropical charm insulated from the noisy street out front by a sandy field shaded by tall margosa trees.
At the time Ramanujan attended, however, the first block of classrooms, with its roof of densely layered red clay tiles and porch overhangs of palm leaf thatching, had gone up just a few years before. Its classrooms were laid end-to-end, making for a building one room wide, with windows on both sides to catch any hint of breeze. The Man Who Knew Infinity PDF Book
The windows would have caught any adolescent clamor, too, but there was probably little to carry. Years later an alumnus would recall the long coats and turbans ofthe teachers and the respect they commanded among the students. Headmaster during Ramanujan’s time, and for twenty-two years in all, was S. Krishnaswami Iyer, a severe-faced man partial to impromptu strolls between classes.
The tapping of his walking stick would alert both teachers and students to his coming. Sometimes he’d step into a class, take over from the teacher, question students, and teach the rest of the class-with enough flair, it seems, that when he taught Grey’s “Eton College” one student imagined little Town High as Eton, the irrigation ditch crossing the campus as the Thames.
The school, which stood about a five-minute walk from Ramanujan’s house, drew the cream of Kumbakonam youth and launched them into college and career. Alumni would later recall it with genuine fondness. And it nourished Ramanujan for six years, bringing him as close as he’d ever come to a satisfying academic experience. The Man Who Knew Infinity PDF Book
Even allowing for the retrospective halo that sees in every schoolboy exploit of the famous a harbinger of future greatness, it’s plain that Ramanujan’s gifts became apparent early. Ramanujan entered Town High’s first form at the age of ten, corresponding to about an American seventh grade. And already while he was in the second form, his classmates were coming to him for help with mathematics problems.
Soon, certainly by the third form, he was challenging his teachers. One day, the math teacher pointed out that anything divided by itselfwas one: Divide three fruits among three people, he was saying, and each would get one. Divide a thousand fruits among a thousand people, and each would get one. So Ramanujan piped up: “But is zero divided by zero also one?
If no fruits are divided among no one, will each still get one?” As brahmacharya, you are a student, learning the spiritual and intellectual ropes. As grihasta, occupying the longest span, you are a householder, with responsibilities to home and family. As vana prastha, or “inhabitant of the forest,” you begin to throw off the bustle offamily life and seek solitude, introspective calm. The Man Who Knew Infinity PDF Book
Finally, as sanyasi, you relinquish everything-family, possessions, attachments-in pursuit of spiritual fulfillment. At his wedding, in heading off for Benares, Ramanujan had ritually opted for this last stage. But in fact, he was now a grihasta. He had responsibilities now. He had a wife. His father was pushing fifty. No longer was he a free spirit, left “ranging with delight” through mathematics, happily on his own.
It was time that he assume the mantle of adulthood. But now a medical problem intervened. Some accounts later found it more delicate to refer vaguely to “kidney trouble,” but in fact Ramanujan had developed a hydrocele, an abnormal swelling of the scrotal sac. “Hydrocele” is a physical finding, not some particular illness. A subtle, and otherwise harmless, imbalance in the rate of absorption ofscrotal fluid can cause it.
So can filariasis, endemic in South India, an infection of the lymph system by mosquito-borne parasites. So can other infections, among them tubercular. Usually, there are no symptoms, not even sexual; men sometimes carry a small hydrocele around with them for years. Only when one reaches the size of, say, a tennis ball, does sheer mechanical inconvenience make it a problem and demand surgery. The Man Who Knew Infinity PDF Book Download
The operation is simple; an incision is made in the scrotal sac to release the blocked fluid. Because the area is so rich in blood vessels, healing is normally rapid, and infection rare, even under poor sanitary conditions. There was one problem; the family had no money for the operation. Komalatammal asked friends for help, but none was forthcoming.
Finally, in January 1910, a certain Dr. Kuppuswami volunteered to do the surgery for free. As the chloroform was being administered, a friend later recalled in wonder, Ramanujan noted the order in which his five senses were blocked. For a time, Ramanujan was left prostrate. One day, hurrying onto his legs again too soon, he walked with his friend Anantharaman to a village a few miles out of town.
The wound began to bleed. But soon, recovered, fueled by the new resolve a long rest can bring, Ramanujan began to go out to the wider world beyond the pial. Spring had just learned that the university was prepared to set aside ten thousand rupees, equivalent to more than six hundred pounds, or enough for two years in England. The Man Who Knew Infinity PDF Book Download
But the decision hinged on higher approval. And here, he said, “His Excellency may perhaps be able to interfere with advantage.” “The best gentleman and by no means the worst brain we ever sent to India,” it was once said of Lord Pentland. Born John Sinclair, he was a slim, slight man with a full mustache who had graduated from Sandhurst, the British West Point, and served eight years in the Royal Irish Lancers.
Then he’d turned to politics, most recently serving as secretary for Scotland under Prime Minister David Lloyd George. Only the previous October he’d come to Madras as governor of Fort St. George, in which capacity he ruled over forty million people. He believed that the state’s function, according to one who knew him.
Should be “to secure for all its members the best procurable conditions for the full development of personality.” Now, in the case of Ramanujan, he had the chance to act on it. He had already gone to bat for Ramanujan once when, the year before, he had consented to his special research scholarship. Now he was ready to “interfere with advantage” again. The Man Who Knew Infinity PDF Book Free
“His Excellency cordially sympathizes with your desire that the University should provide Ramanujan with the means of continuing his researches at Cambridge,” his secretary wrote back to Spring, “and will be glad to do what he can to assist.” On January 24, 1918, the names of Ramanujan and 103 other candidates were read out at a meeting ofthe society.
If past experience applied, only a few of them would be elected. There was no question in Hardy’s mind, or Littlewood’s, or anyone else’s, that Ramanujan merited the honor. Still, few candidates made it the first time out, and by normal practice his nomination was premature. Hardy had been thirty-three years old when elected in 1910.
Littlewood himselfhad made it only the previous February, also at age thirty-threemore than a decade, and dozens of notable mathematical papers, beyond his early glory as a Senior Wrangler. Ramanujan, still twenty-nine at the time of his nomination, had contributed to European mathematics for just a few years and still had a modest publication record, at least in number. The Man Who Knew Infinity PDF Book Free
But Hardy’s concern for Ramanujan’s health moved him to press his claim with unusual urgency. J.]. Thomson, discoverer of the electron, winner of the Nobel Prize in 1906, and then president of the Royal Society, had asked him to outline the circumstances surrounding Ramanujan’s candidature.
“If he had not been ill I would have deferred putting him up a year or so,” Hardy admitted: “not that there is any question of the strength of his claim, but merely to let things take their ordinary course. As it is, I felt no time must be lost.” This is what Ramanujan’s identity, suitably interpreted, revealed: two seemingly distinct mathematical subworlds fused together in a single unifying relationship.
In volume 2 of his book Combinatory Ana(ysis, which came out in 1916, MacMahon devoted to it and the other identity a whole chapter, “Ramanujan’s Identities.” He verified it by reams of hand calculation as far as any reasonable person could, “so that there is practically no reason to doubt its truth; but,” he added, “it has not yet been established” through formal proof. The Man Who Knew Infinity PDF Book Free
But it had been, in a paper twenty years before. One day in 1916 or 1917 Ramanujan was rummaging through the 1894 volume of the Proceedings ojthe London Mathematical Society when there, near the bottom of page 318, he saw it. It was entitled “Second Memoir on the Expansion of Certain Infinite Products,” and two of those infinite products were just the identities he thought he had discovered.
Before MacMahon’s book came out, Hardy had shown Ramanujan’s identities around. Did anyone know proofs for these marvelous theorems? Could anyone furnish any? No one could. Yet here, in black and white, like a specter from the past, was evidence that someone already had.
“I can remember very well his surprise, and the admiration which he expressed” for the older work, Hardy would say of Ramanujan. As for any loss, or even bittersweet ambivalence, that he may have also felt, Hardy said nothing. The man who anticipated Ramanujan was Leonard James Rogers, a remarkable character if ever there was one. The Man Who Knew Infinity PDF Book Free
Born in 1862, in Oxford, where his father was an economist, he had not only done well on the Oxford equivalent of the Cambridge mathematical Tripos, but had earned a bachelor of music degree in 1884. He was a fine pianist, an exceptional mimic, liked to affect a broad Yorkshire accent.
Ramanujan’s career, just because he was a mathematician, is of unique importance in the development of relations between India and England. India has produced great scientists, but Bose and Raman were educated outside India, and no one can say how much of their inspiration was derived from the great laboratories in which their formative years were spent and from the famous men who taught them.
India has produced great poets and philosophers, but there is a subtle tinge of patronage in all commendation of alien literature. Only in mathematics are the standards unassailable, and therefore of all Indians, Ramanujan was the first whom the English knew to be innately the equal of their greatest men. The Man Who Knew Infinity PDF Book Free
The mortal blow to the assumption, so prevalent in the western world, that white is intrinsically superior to black, the offensive assumption that has survived countless humanitarian arguments and political appeals and poisoned countless approaches to collaboration between England and India, was struck by the hand of Srinivasa Ramanujan.