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"The son of a prominent Japanese mathematician who came to the United States after World War II, Ken Ono was raised on a diet of high expectations and little praise. Rebelling against his pressure-cooker of a life, Ken determined to drop out of high school to follow his own path. To obtain his father’s approval, he invoked the biography of the famous Indian mathematical prodigy Srinivasa Ramanujan, whom his father revered, who had twice flunked out of college because of his single-minded devotion to mathematics.
Ono describes his rocky path through college and graduate school, interweaving Ramanujan’s story with his own and telling how at key moments, he was inspired by Ramanujan and guided by mentors who encouraged him to pursue his interest in exploring Ramanujan’s mathematical legacy.
Picking up where others left off, beginning with the great English mathematician G.H. Hardy, who brought Ramanujan to Cambridge in 1914, Ono has devoted his mathematical career to understanding how in his short life, Ramanujan was able to discover so many deep mathematical truths, which Ramanujan believed had been sent to him as visions from a Hindu goddess. And it was Ramanujan who was ultimately the source of reconciliation between Ono and his parents.
Ono’s search for Ramanujan ranges over three continents and crosses paths with mathematicians whose lives span the globe and the entire twentieth century and beyond. Along the way, Ken made many fascinating discoveries. The most important and surprising one of all was his own humanity."

Inhaltsverzeichnis

Frontmatter

My Life Before Ramanujan

Frontmatter

Chapter 1. Tiger Boy

I’m sitting on the couch watching Gilligan’s Island, every second-grader’s favorite sitcom. It’s the episode where the headhunters from a neighboring island attack the motley crew of castaways. As usual, the klutzy skinny first mate Gilligan accidentally saves the day, in this episode by scaring off the headhunters.

Ken Ono, Amir D. Aczel

Chapter 2. My Parents’ Generation

If you are to have a sympathetic understanding of my history, you will have to understand my roots, the story of how my parents left their families and everything they knew behind when they came to America for what was supposed to be a short visit. That short visit became a lifetime, and my parents became issei, “first-generation” Japanese immigrants to the United States of America. And as the American-born sons of my parents, my brothers and I are nisei, children of the second generation.

Ken Ono, Amir D. Aczel

Chapter 3. My Childhood (1970–1984)

Lutherville, Maryland, is a hilly network of twisted streets dotted with nearly identical 1960s-era single-family split-level homes. Our neighborhood was home to baseball legends Mark Belanger, Jim Palmer, and Brooks Robinson of the Baltimore Orioles. I loved the Orioles. Their victory over the Philadelphia Phillies in the 1983 World Series is one of the most cherished memories of my life in Lutherville. Little else from my childhood resembles anything that would have been considered normal in my neighborhood.

Ken Ono, Amir D. Aczel

Chapter 4. An Unexpected Letter

My legs are on fire. I’m fighting to spin the pedals of my svelte French Peugeot racing bicycle in a desperate effort to keep pace with Belgian cycling champion Eddy Merckx. We’re battling mano a mano, racing up the switchbacks of Mont Ventoux, the “Giant of Provence,” a cruel peak that had claimed the life of British champion Tom Simpson during the 1967 Tour de France. We’re racing for the finish line, a strip of white paint in the steep road at the summit, a desolate place marked by a decaying weather station. Merckx, known as the “Cannibal” because of his insatiable appetite for victories, sets an infernal pace. Somehow, I’m able to keep up, while one by one, all the others have fallen behind. The finish is finally in sight, and the fans are in a frenzy. Despite the overwhelming pain and self-doubt building inside me, I summon all my remaining strength. I rise out of the saddle and swing my Peugeot side to side in a furious sprint. And wondrous to relate, I leave the Cannibal in my wake.

Ken Ono, Amir D. Aczel

Chapter 5. My Escape

Ramanujan’s story, as told to me by my father, offered me, a teenager about to drop out of high school to escape a frustrating and confusing life, hope that like him, I could perhaps accomplish something in my life. I was encouraged by the fact that the dropout had achieved not only success but greatness, and I was made hopeful by the fact that the dropout’s parents continued to support him despite his troubles. Most of all, I was stunned that my father held this college dropout in such high regard; he revered this man as some kind of demigod. I found that odd, because my father didn’t believe in anything that he couldn’t see or prove, and Ramanujan seems to have had a significant mystical side to his personality. I wondered how he reconciled Ramanujan’s claim of inspiration through visions of the goddess Namagiri with his personal beliefs.

Ken Ono, Amir D. Aczel

The Legend of Ramanujan

Frontmatter

Chapter 6. Little Lord

Crowds ramble by on foot and rickshaw on this busy dirt road lined with small shops and peddlers seated on blankets selling vegetables, silks, tin plates, and almost anything else you might imagine. Most of the people are thin Indians clad in light, loose-fitting garments. Once in a while, a British officer or administrator passes by in a khaki uniform or formal suit. Cows and goats roam freely, eating whatever scraps and waste they can find in this hot and humid place. This is Sarangapani Street in late-nineteenth-century Kumbakonam, a town in the southeast Indian state of Tamil Nadu, Ramanujan’s childhood home.

Ken Ono, Amir D. Aczel

Chapter 7. A Creative Genius

Just like the kids I knew from Julian Stanley’s John Hopkins study of talented children, Ramanujan was identified at an early age for his gifts in mathematics. Like us, he was capable of flying through the usual mathematics curriculum. However, where we had a knack only for understanding formulas, he had a knack for creating them.

Ken Ono, Amir D. Aczel

Chapter 8. An Addiction

Imagine a college student who is so consumed by video games that he is failing all his classes. He even forgets to eat, shower, and sleep. If we replaced the video games by equations and formulas, then this would have been Ramanujan.

Ken Ono, Amir D. Aczel

Chapter 9. The Goddess

Mathematically talented children are frequently identified as such by their ability to perform very large calculations rapidly. Ramanujan was a prodigious calculator, but what set him apart was his creativity—his ability to conjure never before imagined mathematical formulas out of thin air. Where did they come from?

Ken Ono, Amir D. Aczel

Chapter 10. Purgatory

Genius often finds itself rejected when it fails to fit into the mold designed for ordinary people. Einstein, for example, was at first denied admission to the prestigious Swiss Federal Institute of Technology, in Zurich, because he failed the nonscience portion of the entrance examination. Thomas Edison’s teachers told him that he was too stupid to learn anything, and he was fired from his first two jobs for not being productive enough. Ramanujan was in good company.

Ken Ono, Amir D. Aczel

Chapter 11. Janaki

What Ramanujan’s mother had in mind was a wife for her son, and like my parents’ marriage, Ramanujan’s was to be an arranged one.

Ken Ono, Amir D. Aczel

Chapter 12. I Beg to Introduce Myself

Though he was without a college degree and had essentially no formal training in mathematics, Ramanujan had accumulated a massive collection of formulas, all recorded in his notebooks without proof. Eager to share his work with others, he began to publish some of his findings, beginning in 1911 by submitting problems to the Journal of the Indian Mathematical Society. At first, nobody paid attention, or at least no one was able to solve his problems. For example, one of the problems that he challenged readers to solve was to find the value of1+21+31+⋯. $$ \sqrt{1+2\sqrt{1+3\sqrt{1+\cdots }}}. $$ What number was represented by this infinite nested square root?

Ken Ono, Amir D. Aczel

Chapter 13. These Formulas Defeated Me Completely

And so it was that toward the end of January 1913, or perhaps in the first days of February, Hardy, over breakfast in his rooms at Trinity College, in Cambridge, received a curious letter from India containing nine pages of Ramanujan’s original mathematical work.

Ken Ono, Amir D. Aczel

Chapter 14. Permission from the Goddess

Ramanujan was elated finally to receive a positive response from England, and he promptly replied to Hardy: “I have found a friend in you, who views my labors sympathetically.” But instead of proofs of the sometimes audacious statements he was making about infinite series, continued fractions, and integrals, Ramanujan sent Hardy more theorems. Hardy received these with disbelief. How could one young man, in a country so distant from the world centers of mathematics, come up with so many ingenious mathematical results? It was a mystery. But he persisted in requesting proofs. And Ramanujan persisted in not supplying them—instead sending even more results

Ken Ono, Amir D. Aczel

Chapter 15. Together at Last

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.

Ken Ono, Amir D. Aczel

Chapter 16. Culture Shock

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 into mathematics, I think that both men, Ramanujan and my father, would have had an even more difficult time of it.

Ken Ono, Amir D. Aczel

Chapter 17. Triumph over Racism

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.

Ken Ono, Amir D. Aczel

Chapter 18. English Malaise

England’s unforgiving climate and Ramanujan’s poor diet took their toll. Ramanujan’s health continued its long decline. He had endured a variety of ailments throughout his life, and after five years in Cambridge, he was constantly ill. The doctors believed he had tuberculosis, although later findings have suggested a parasitic infection affecting his liver. Blood poisoning was also suspected. No one knew exactly what was amiss, but he suffered from fevers, stomach pains, and many other symptoms.

Ken Ono, Amir D. Aczel

Chapter 19. Homecoming

In hospitals, sanatoriums, halfway houses, through declining health, Ramanujan kept up his work. He continued to produce groundbreaking theorems about partitions, identities, infinite series, integrals, and more, though now—in contrast to his work five years earlier—with a proof of every result. He had learned how to do mathematics in the modern style in which every assertion must be demonstrated using rigorous argumentation.

Ken Ono, Amir D. Aczel

Chapter 20. The Tragic End

As Ramanujan approached the end of his life, he was surrounded by domestic strife. His wife and mother were constantly arguing with each other over even the most trivial matters. Anything would send one of them, usually the mother, into a tirade against the other. But Janaki was now twenty years old and no longer a child. She had her husband at her side, who would often support her against the unreasonableness of his mother. Ramanujan’s maternal grandmother had also joined the household, and she would frequently add her two cents to the domestic arguments. It was not an environment conducive to healing.

Ken Ono, Amir D. Aczel

My Life Adrift

Frontmatter

Chapter 21. I Believe in Santa

My parents dropped me off at Baltimore’s Penn Station, and I was now standing alone on the platform waiting for the Amtrak train to New York, where I would change for the “Adirondack” to Montreal. I had my backpack, my Peugeot bicycle, and my large suitcase. My parents were on their way home, and there was no turning back. Like Ramanujan, who ran away to Vizagapatnam after he flunked out of college, I was running away having dropped out of high school. Of course, we had different reasons for running. Ashamed of having lost his scholarship, Ramanujan had simply disappeared. I was fleeing my pressure-cooker of a life, but I had left with my parents’ knowledge and consent.

Ken Ono, Amir D. Aczel

Chapter 22. College Boy

I arrived at the University of Chicago in September 1985. Its campus, constructed largely in the collegiate Gothic style, occupies a two-hundred-acre site on Chicago’s south side. The northern and southern parts of the campus are separated by the Midway Plaisance, a broad mile-long park that was constructed in 1893 for the Columbian Exposition. Whether by chance or design, I was assigned to Santa’s former residence, Burton–Judson Courts, just south of the Midway. I had a room in a first-floor corner suite in Dodd–Mead House, one of the six houses that constitute Burton–Judson. The neo-Gothic architecture, the leaded windows, the view across the Midway to Harper Library, all enhanced my already overbrimming confidence in my success as a college freshman. Several of the older students remembered Santa, and I was delighted to learn that my hero astrophysicist Carl Sagan had lived in the same dormitory in the 1950s, a few doors from my own suite.

Ken Ono, Amir D. Aczel

Chapter 23. Erika

I had moved out of Burton–Judson at the end of my freshman year and was now living in Shoreland Hall, a building dating from the 1920s, when it opened as the luxury Shoreland Hotel, a place where Al Capone held “business” meetings and Jimmy Hoffa kept a room. Another famous resident was the economist Milton Friedman. But nothing lasts forever (except eternity), and by the 1970s, the Shoreland had come down considerably in the world. Needing another dormitory, the university bought the hotel and converted it into a residence hall. That incarnation lasted until 2009, when it was sold to a private developer and renovated into luxury apartments. I had a room on the sixth floor with a breathtaking view of Lake Michigan.

Ken Ono, Amir D. Aczel

Chapter 24. The Pirate Professor

UChicago’s Department of Mathematics is located in Eckhart Hall, a distinguished neo-Gothic building on the main quadrangle across the street from Alpha Delta Phi, a rival fraternity. Many famous mathematicians have taught in this building, including André Weil, the man who discovered my father in 1955 in Tokyo. The department’s history and the imposing nature of the building intimidated me from day one.

Ken Ono, Amir D. Aczel

Chapter 25. Growing Pains

Ramanujan’s story had offered me hope in 1984, when I was a depressed tenth-grader, that I could find my own path in life, and so I dropped out of high school and left home. My path was still crooked and uncertain, but on it, I had found emotional and intellectual support, first from my brother Santa in Montreal, and then in Chicago from college friends, fraternity brothers, my cycling mentor Tom Kauffman, and professors such as Paul Sally. Then in 1988, just as I was nearing the end of a half-hearted math major at Chicago, Ramanujan helped me a second time. The television documentary about his life reinvigorated my feeling of hope, and it inspired me to work hard my senior year. The documentary had caught me off guard, and it knocked some sense into me. I focused on mathematics my senior year and impressed Professor Sally enough that he helped get me into UCLA.

Ken Ono, Amir D. Aczel

Finding My Way

Frontmatter

Chapter 26. My Teacher

I finally passed my remaining qualifying exams, and on paper, I had earned the right to advance to candidacy in the UCLA doctoral program. This may have been true on paper, but in reality, I had no idea what I was supposed to do next. I was poised to drift through the program or else drift right out of it. I needed direction.

Ken Ono, Amir D. Aczel

Chapter 27. Hitting Bottom

Basil Gordon had awakened me. I had been dangerously adrift at UCLA, and his mentoring coaxed me back into the life I was meant to lead. Like Ramanujan, I had developed an addiction for mathematics. I was in love with mathematical beauty. I had a passion for doing mathematics. Yet I had no idea how things might turn out for me professionally. Desire does not always lead to fulfillment. Would my theorems be good enough for anyone to care about? Might I have a thesis in me but not much else?

Ken Ono, Amir D. Aczel

Chapter 28. A Miracle

I didn’t tell Erika very much about the seminar and the conference. I couldn’t bring myself to admit to her that all our hopes had been dashed. I couldn’t tell her how badly I had failed. I also dreaded my next meeting with Gordon. I had let him down. I had imagined a triumphal march down Palisades Avenue to Gordon’s house to the sound of cheering crowds and popping champagne corks. In our time together, we had already had much to celebrate—mastering a difficult research paper, completing the proof of a theorem, the acceptance of a paper for publication. But there was nothing to celebrate now. I had pain to share, and I wanted to spare him, and myself. On the day of our usual meeting, I walked down Palisades Avenue accompanied by no sound but my beating heart. I reached the house and stepped up onto the porch, and then I froze. I must have stood for five full minutes staring at the heavy oak door before I could muster the courage to press the doorbell. I felt as if I had arrived at my own funeral. What was I going to say?

Ken Ono, Amir D. Aczel

Chapter 29. My Hardy

I moved to Athens, Georgia, in August 1993. It was only a one-year position, and after that, the future was as uncertain as ever. But I had done it. I had completed my PhD. I was now Dr. Ken Ono, mathematician. To get this far, I had not traveled an easy path, but inspired by Ramanujan and guided by caring mentors such as my brother Santa, Paul Sally, and Basil Gordon, I had achieved an important milestone. I had hoped that my accomplishment would have elicited the recognition and praise from my parents that I had long sought and now felt I merited. After all, earning a doctorate was part of the formula that my parents had laid out for me long ago. It was a major accomplishment, and I had come through. But I received no acknowledgment from them. I didn’t bother to go to my graduation ceremony, assuming that they wouldn’t want to attend. My father had advised a number of PhD students, and I would have thought that he would appreciate what it meant to end one’s apprenticeship and set forth into the world as a certified member of the profession. I suppose he viewed obtaining a doctorate as just one more chore that was expected of you, like brushing your teeth or walking the dog.

Ken Ono, Amir D. Aczel

Chapter 30. Hitting My Stride

Hardy had judged Ramanujan worthy and had invited him into the community of professional mathematicians. Eighty years later, Andrew Granville extended such an invitation to me, and like the earlier pair, we collaborated on research. When we had completed our one joint project, Andrew encouraged me to take aim at some well-known unsolved problems. My year at UGA was an important transition, one that I like to think of as somewhat analogous to Ramanujan’s first days in Cambridge. We both had a lot to learn about the world of professional mathematics, and we both had mentors to guide our way.

Ken Ono, Amir D. Aczel

Chapter 31. Bittersweet Reunion

Shortly before we moved to Penn State, my parents made the drive from Baltimore, where my father was still teaching at Johns Hopkins, for a weekend visit. I had arranged for them to be reunited with André Weil, who was now 91. My parents had not seen Weil since the 1970s, and they didn’t know what to expect. They were nervous. However, the reunion was important to them. They needed to thank him for his generosity, for having made their lives possible.

Ken Ono, Amir D. Aczel

Chapter 32. I Count Now

Aspen, Erika, and I moved to State College, Pennsylvania, home of Penn State, in July 1997. To celebrate my appointment, George Andrews and I organized the conference “Topics in Number Theory in Honor of Basil Gordon and Sarvadaman Chowla.” The meeting was held from July 31 to August 3 at the Penn State Hotel. George and I wanted to honor the memory of Chowla, a longtime member of the Penn State faculty who had passed away in 1995, and we wanted to celebrate Gordon’s sixty-fifth birthday.

Ken Ono, Amir D. Aczel

Chapter 33. The Idea of Ramanujan

How have I been lucky enough to get to where I am today?

Ken Ono, Amir D. Aczel

Chapter 34. My Spirituality

I am often asked whether I believe that Ramanujan’s findings truly came to him as visions from a goddess. I didn’t believe this for most of my life. Perhaps if I were a Hindu, I would have had an easier time subscribing to such a view. Instead, I wish to offer my opinion on a simpler question: was Ramanujan’s mathematics divine in origin?

Ken Ono, Amir D. Aczel

Backmatter

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