My Search for Ramanujan

by Ken Ono

  Hardy also interceded on Ramanujan’s behalf to convince the Indian authorities to support such a move. He described Ramanujan’s exceptional abilities in letters to Indian officials at the University of Madras, whose help he needed to secure funding to match what he could garner in England, so that Ramanujan’s travel and stay in Cambridge could become a reality. The word spread like wildfire throughout the academic community of south India: a professor of the highest rank in Cambridge, a Fellow of the Royal Society, believed so strongly in Ramanujan that he wanted to bring him to England.

  Ramanujan had no such interest. He wrote to Hardy, “What I want at this stage is for eminent professors like you to recognize that there is some worth in me.” And now he clearly had obtained the recognition he so badly craved—and everyone in Madras knew it.

  Soon, other offers came his way, offers that were much closer to home. Everyone wanted him, everyone hoped that he would stay in his native India and help make it great in mathematics. On April 12, 1913, Ramanujan was granted a generous scholarship as a research student at Presidency College, in Madras. There were no obligations, just that he should pursue his researches in any way he wanted, that he should do the mathematics that he loved with absolutely no other responsibilities. This was truly a dream come true. Hardy’s interest in his work had finally won him not only recognition, but the financial independence that would allow him to do mathematics and would grant him also the possibility of receiving—finally, after twice failing to do so—an academic degree that could secure his future. Ramanujan was on top of the world. He had no reason to go anywhere.

  When all of the arrangements for his fellowship at Presidency College had been made, he was joined by his mother and his wife, and they found a pleasant apartment near the college. This was perhaps the happiest period in his life. He was with his loving mother and wife, and he was free to pursue his research. He was now famous all over south India as the amazing genius whom even the great professors in England admired.

  But Neville continued to nudge him toward Cambridge, at Hardy’s urging. It soon appeared, however, that the ocean was an insurmountable obstacle. Brahmins live by very strict laws that govern everything they do in their lives. Ramanujan was a strict vegetarian, and more than that, he could accept food only if made by a trustworthy fellow Brahmin. In addition, there was a prohibition against Brahmins crossing the ocean. They could travel within India—but not over the sea to England. Many, of course, did go. Britain has had a considerable number of Indian students in its universities, many of them Brahmins, but those who went did so by breaking the rule against travel by sea.

  And now, finally, Ramanujan was soaring. His renown increased as he created ever more new mathematical formulas and theorems. He was respected and admired by everyone. What more could he have asked for? Yet one day, Neville came to him and they talked about mathematics, and about England, and to his surprise, he found that Ramanujan was not absolutely averse to accepting Hardy’s invitation. He understood that in Cambridge, among prominent mathematicians, he would thrive. He would be able to aspire to loftier goals, to do better mathematics, than was possible in the relative isolation of Madras.

  The minor problems were soon resolved: Ramanujan was prepared to break the religious prohibition against travel—promising that he would adhere strictly to his dietary rules even across the seas. But he would not leave India without his mother’s blessing. But the mother objected, and the problem was the goddess.

  Komalatammal maintained that the goddess Namagiri had told her that she was against her son’s leaving India. Ramanujan tried to convince his mother that she had no way of knowing the goddess’s wishes, but his mother knew better. After a few more months of wrangling, Komalatammal suggested to her son that perhaps he should try to obtain Namagiri’s permission on his own.

  And so it was that in December 1913, Ramanujan, accompanied by two friends, set out for the city of Namakkal, eighty miles west of Kumbakonam. Their destination was a rocky promontory on which an important ancient temple dedicated to the goddess Namagiri was perched. After a trek up to the temple, they set up camp on its floor and meditated. Ramanujan and his friends remained at the temple for three days and three nights, and on the third night, Ramanujan had a dream in which Namagiri spoke to him and granted him permission to leave India for England.

  According to another version of this story, while Ramanujan did in fact make the pilgrimage to Namakkal, it was his mother who obtained Namagiri’s permission for her son to leave India. In this telling, Komalatammal had a dream in which Namagiri told her to allow her son to leave. Dream or no dream, wishful thinking or chicanery, Namagiri seemed to be on board, and Ramanujan was free to pursue his destiny.

  On March 17, 1914, Ramanujan set out for England aboard the SS Nevasa, of the British India Lines. Janaki had asked her husband to take her with him, but he refused her request, saying that she would be a distraction from his work. Now he was standing on deck, clearly with mixed feelings—excited to go where leading mathematicians could help him advance his mathematical career, but worried about being alone in a strange, cold country. England was indeed cold compared to south India, where it is always warm, even hot, and practically never even cool. And he was also worried about maintaining his strictly vegetarian diet.

  © Springer International Publishing Switzerland 2016

  Ken Ono and Amir D. AczelMy Search for Ramanujan10.1007/978-3-319-25568-2_15

  15. Together at Last

  Ken Ono1 and Amir D. Aczel2

  (1)Department of Mathematics and Computer Science, Emory University, Atlanta, GA, USA

  (2)Center for Philosophy & History of Science, Boston University, Boston, MA, USA

  The Nevasa made it to the mouth of the Thames almost exactly a month after leaving Madras. Ramanujan disembarked and was taken to London, where he stayed for several days at a center that welcomed Indian students on their arrival in England. Neville arrived home in England around this time, and Ramanujan spent his first few months in Cambridge living with Neville and his wife in their house near Trinity College.

  Soon would come the test whether Ramanujan had made the right choice in coming to England. Having worked in isolation his entire life, he welcomed the chance to have a mentor and friend who understood the beauty that he saw in mathematics. And he now had the hope of receiving validation for his years of lonely labor from the top men in English mathematics.

  One can only imagine the first meeting between Ramanujan and Hardy. Not long after their first conversations, Hardy declared, “He possesses powers as remarkable in their way as those of any living mathematician. His work is of a different category.”

  Trinity College Courtyard at Cambridge University

  Eventually, Ramanujan was assigned rooms at Trinity, very close to Hardy’s own rooms. The two men met almost every day for several years, poring over Ramanujan’s amazing formulas. Hardy had already received more than one hundred formulas in letters from Ramanujan, and Ramanujan had brought many more with him. Looking at his claims, Hardy could see that many of them were remarkable innovative breakthroughs in mathematics. How could this man have produced them entirely on his own? That was an enigma that Hardy, even with Ramanujan by his side, could not resolve. What does one do with an answer like, “Namagiri, our goddess, presented them to me in my dreams”? Mathematicians would be contemplating the mystery for the next century.

  At one point, Hardy described Ramanujan’s amazing achievement by saying that in India, he had been working under “an impossible handicap, a poor and solitary Hindu pitting his brain against the accumulated wisdom of Europe.” I find this image both deeply moving and highly descriptive of the life of this towering mathematical figure, a unique genius.

  In working with Ramanujan, Hardy saw two immediate aims he must try to achieve. First, he wanted to establish complete and rigorous proofs of as many of Ramanujan’s claims as possible. The two of them worked together, proving many of the results, and those deri
vations were subsequently published by the two of them in academic journals. Other results would take many years to prove—by them or by other mathematicians, including my colleagues and myself. A small fraction of the claims turned out to be false. But in those cases, the results still presented interesting methods that could be used to crack other difficult problems and that shed important light on mathematics itself and how it is pursued.

  Hardy’s second aim was to bring Ramanujan up to speed on modern mathematics. Ramanujan had done all his previous work without the benefit of an advanced mathematical education, like what was available at Cambridge. He thus encouraged Ramanujan to sit in on classes and lectures. That effort was not an unqualified success, because by then, Ramanujan was set in his ways. He had done mathematics according to his own methods and was reluctant to change them. But he did learn how to construct rigorous proofs of theorems.

  © Springer International Publishing Switzerland 2016

  Ken Ono and Amir D. AczelMy Search for Ramanujan10.1007/978-3-319-25568-2_16

  16. Culture Shock

  Ken Ono1 and Amir D. Aczel2

  (1)Department of Mathematics and Computer Science, Emory University, Atlanta, GA, USA

  (2)Center for Philosophy & History of Science, Boston University, Boston, MA, USA

  Like my father, who came to America in the late 1950s, Ramanujan had accepted the invitation of a leading mathematician to work in a foreign land. Both men struggled to fit into an alien culture with different languages and customs. In a way, Ramanujan and my father were both fugitives. My father fled the desperate conditions of postwar Japan, and Ramanujan fled a life in which he was intellectually hampered. I believe that my parents responded to the effects of racial prejudice, and in particular anti-Japanese sentiment, by enforcing kaikin, isolationism, in our home in Lutherville. Ramanujan, as a foreigner in England, was similarly isolated, separated from virtually everyone apart from Hardy and a few friends. If it were not for their shared absorption in mathematics, I think that both men, Ramanujan and my father, would have had an even more difficult time of it.

  Ramanujan would work for hours at a time. Often, he would start late at night, when the world was quiet, and work until dawn. He would then cook breakfast for himself, then sleep much of the day, seeing very little sunshine—both because Britain is notoriously gray and because he largely kept to his rooms. The only other place he frequented was Hardy’s rooms, where they would work together. Unlike Hardy and other Fellows of Trinity College who regularly played sports, such as tennis and cricket, Ramanujan’s life was completely sedentary.

  He was having a difficult time adjusting to life in England. The customs were completely different from what he was used to. The English were formal and cold—unlike the smiling, warm south Indians, ever interested in how you felt and what you were up to. He hated having to give up his long hair for a European cut. The collar of his stiffly starched shirts hurt his neck, and his feet never got used to the pressure of Western shoes. He longed for his carefree life in sunny India, wearing Indian dress, eating the spicy and vibrant food of his childhood, feet unbound.

  And since as a Brahmin he could not trust the cooking at the Hall at Trinity, where everyone else ate, he was forced to buy his own foodstuffs and cook for himself in his rooms. This had the effect of depriving him of the important social contact that took place in the dining halls of the college, for much of the social interaction among faculty, fellows, students, and others at Trinity took place in the dining halls. Ramanujan was mostly alone.

  He worked at night, cooked early in the morning, went shopping for food later in the day, slept, saw Hardy for an hour or two, ate dinner, and worked again. It was an unhealthy life, with few breaks or rewards—other than the mathematics. He had a small gas stove in an alcove in his rooms, and there he would cook his vegetables. He missed the delicious raitas and spicy rice dishes of south India. Here he had to make do with what he could find.

  © Springer International Publishing Switzerland 2016

  Ken Ono and Amir D. AczelMy Search for Ramanujan10.1007/978-3-319-25568-2_17

  17. Triumph over Racism

  Ken Ono1 and Amir D. Aczel2

  (1)Department of Mathematics and Computer Science, Emory University, Atlanta, GA, USA

  (2)Center for Philosophy & History of Science, Boston University, Boston, MA, USA

  Like my father, Ramanujan dealt with racial prejudice. Japanese-Americans like my parents suffered the effects of racism in America largely because of World War II. Ramanujan suffered as a dark-skinned Indian living under British imperialism. Both men were able to overcome prejudice through their important mathematical contributions.

  Ramanujan’s theorems stunned the British mathematical world. Nothing like his magical legerdemain had ever been seen. There was no question but that he was realizing the potential that Hardy had recognized in his letters.

  In March 1916, Ramanujan was awarded a bachelor’s degree from Trinity College for his contributions to mathematics made during his time at Cambridge. The doctoral degree was not commonly given for mathematics during that period, and later, when mathematics PhDs began to be awarded, his degree would be upgraded to a doctorate.

  Ramanujan at Cambridge (Ramanujan center and Hardy standing at far right)

  Hardy felt strongly that Ramanujan deserved to be elected a Fellow of Trinity College, as he himself had been. So he began to lobby with the other fellows to have Ramanujan thus honored. But he was surprised by the strong resistance that he encountered. He should not have been. To begin with, the relationship between Britain and India was that of colonial power over a conquered people. Part of what makes it possible for one people to colonize another is a belief in the colonizer’s superiority. In this case, that sense of superiority had a strong racial element: “Take up the white man’s burden” is the notorious refrain of a poem published by Rudyard Kipling in 1899.

  As overlords of a subjected people of an “inferior” race, the English rulers of India consciously isolated themselves from the masses they ruled. They lived apart from them; they didn’t socialize with them; they worked with them only to the extent necessary. Even the most refined and educated Brahmin could not socialize as an equal with the lowliest British civil servant stationed in India.

  Indian students came to Britain in modest numbers, and they were formally welcomed there. But nobody embraced them, just as my father was welcomed to the United States in the 1950s but was not considered a true member of American society.

  When Ramanujan’s name was proposed for election as a Fellow of Trinity College, one of the English fellows responded that he would “not have a black man as fellow.” This defeat depressed Ramanujan greatly: he could be the most gifted mathematician around, but he would be seen in this land as a “black man,” unworthy of recognition.

  When my father first told me about Ramanujan thirty years ago, he made it a point to stress the injustice that Ramanujan experienced as an Indian in England. That bigotry evoked powerful images of my parents’ lives as Japanese-Americans living in the United States in the 1950s and 1960s, and of course, to a lesser extent, it reminded me of the bigotry that I had encountered in my own life.

  Another reason why Hardy failed in his attempt to have Ramanujan elected a Fellow of Trinity College had to do with World War I. The “Great War” erupted in 1914, and Cambridge almost emptied of students as they joined the effort to defeat the Germans. Many professors, including Littlewood, also headed to the battlefields of France and Belgium. Hardy remained, as did Ramanujan.

  Hardy was opposed to war, even while he understood the necessity to defend Britain and the Continent from German aggression. Although he was not a conscientious objector, he voiced his opposition to how such objectors were being treated. Then at some point during the war, he supported antiwar statements made by the eminent Cambridge logician Bertrand Russell, and that was enough to tar him with the pacifist brush. He was thus politically weakened and could not effectivel
y fight for Ramanujan.

  Ramanujan, humiliated and upset by the defeat of his nomination to become a fellow, also suffered physically. It was at this point that the wartime scarcity of fresh fruits and vegetables—the main staples of his vegetarian diet—began to affect his health adversely. He became desperately ill. Naturally heavy, he now lost weight. He talked less, even meeting his only main contact with the world, Hardy, less frequently. One day, in London, he threw himself in front of an oncoming subway car. Miraculously, an operator saw him fall to the tracks just in time to throw the electric switch, cutting power to the trains and thus saving Ramanujan’s life.

  Despite such adversity, Ramanujan continued to do mathematics—but his health continually declined. He now required frequent hospitalizations, and Hardy began to fear for his life. Hardy then decided that he would try another way to get Ramanujan the recognition he deserved, and so he put him up for election to the Royal Society. If Trinity rejected him, Hardy reasoned, the more hallowed Royal Society might take him. The Royal Society heard the case for Ramanujan, and also considered—something Hardy brought to their attention—that his health was declining and that if he were not elected that year, there might be no future opportunity to recognize his achievements. And so in 1918, Ramanujan became a Fellow of the Royal Society, the second Indian to be awarded this high recognition, and one of the youngest fellows ever. Ramanujan was vindicated.