My Search for Ramanujan Read online
Ken Ono and Amir D. Aczel
My Search for Ramanujan
How I Learned to Count
Ken OnoDepartment of Mathematics and Computer Science, Emory University, Atlanta, GA, USA
Amir D. AczelCenter for Philosophy & History of Science, Boston University, Boston, MA, USA
ISBN 978-3-319-25566-8e-ISBN 978-3-319-25568-2
DOI 10.1007/978-3-319-25568-2
Springer Cham Heidelberg New York Dordrecht London
Library of Congress Control Number: 2015959483
© Springer International Publishing Switzerland 2016
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To the memory of Basil Gordon and Paul Sally and to Andrew Granville
Preface
Although this book is a first-person narrative in my voice, it represents collaborative work between me and my friend and coauthor, Amir D. Aczel. This book was his idea, and without him it would never have been written. I am deeply saddened by the fact that Amir passed away unexpectedly before work on the book was complete. Amir was a passionate man who took great pride in spreading scientific ideas through his writing. I will miss him. He still had so much to give to the world.
Ever since I was a teenager growing up in a suburb of Baltimore, I have been enchanted by the story of Ramanujan. I first learned about him when my father, a prominent mathematician, received a letter from Ramanujan’s widow, sixty years after her husband’s death. Srinivasa Ramanujan Iyengar was an enigmatic Indian mathematician who, without formal education in advanced mathematics, was able to derive thousands of unproved, yet valid, mathematical formulas and identities. As a mathematician, I have spent my career extending and proving some of Ramanujan’s results, largely in an attempt to understand the soul and spirit of this genius who died at the young age of thirty-two. Along the way, I found myself and came to terms with my past.
This book is the result of my strong need to tell the world about how the story of this man and his mathematics helped transform me. I was once an emotionally frail, dispirited sixteen-year-old high-school dropout on the run from myself. Today, I am content. I have a loving family, I am a successful mathematician, and I have a rich spiritual life. As the character Jerry puts it in Edward Albee’s play The Zoo Story, “Sometimes a person has to go a very long distance out of his way to come back a short distance correctly.”
Acknowledgments
Amir and I could not have written this book without the help and support of many people. First of all, we thank our families: our wives, Debra Aczel and Erika Ono, and my parents, Sachiko and Takashi Ono, for their tough love and unwavering support. I thank my colleagues Krishnaswami Alladi, George Andrews, Dick Askey, and Bruce Berndt for their shared enthusiasm for this story. We express our deepest gratitude to SASTRA University, in India, for converting Ramanujan’s childhood home in Kumbakonam into a museum and for establishing the SASTRA Ramanujan Prize. I am indebted to Krishnaswami Alladi for playing a central role in honoring the memory of Ramanujan and for hosting me on my many trips to India. I thank Emory University and the Asa Griggs Candler Fund for their financial support, and we thank Matthew Brown, director of the film The Man Who Knew Infinity, and Pressman Films for their cooperation. The film is based on the superb book The Man Who Knew Infinity: A Life of the Genius Ramanujan, by Robert Kanigel. We are grateful to Robert for writing this exceptional biography twenty-five years ago.
We are indebted to Henna Cho, Carol Clark, Melissa Mouly Di Teresa, Danny Gulden, Robert Schneider, Marc Strauss, and Sarah Trebat-Leder, who provided many helpful comments on earlier drafts of this book. Without their help, the book would have fallen far short of its intended goals. We thank our editor, Marc Strauss, for encouraging us to tell this story. And we thank our copyeditor, David Kramer, for beautifying and polishing our manuscript. He improved our book in uncountably many ways. Finally, we thank our literary agent, Albert Zuckerman, for helping us make this book a reality.
I am one of the luckiest mathematicians in the world. I have been guided by three amazing men, without whose friendship and guidance I would certainly have had nothing to write about. We dedicate this book to them, my mentors: Paul Sally, Basil Gordon, and Andrew Granville. Sally rescued me when I was an unmotivated undergraduate at the University of Chicago. Gordon taught me how to do mathematics for its own sake. Granville taught me how to become a professional mathematician. These men reformed, transformed, inspired, and coached me, and they made me what I am today, an active, spiritually aware mathematician with a story to tell.
Ken Ono
Amir D. Aczel
Atlanta, GABoston, MA
December 2015
Prologue: My Happy Place
I cannot sleep. I have a lot on my mind. It is 5:30 a.m. on May 28, 2015, and I am sitting on the lanai of an oceanview room at the Makena Beach and Golf Resort on the island of Maui. The doves are cooing. The gentle ocean breeze and the soothing sounds of waves crashing on the white sandy beach below define this heavenly moment. I am waiting for the first hint of the sun’s rays in what I expect will be an absolutely glorious sunrise, with the Haleakala volcano as a backdrop.
I have never been happier.
Last night, I enjoyed a lovely evening with my wife, Erika, complete with a delicious sunset dinner at a fancy Italian restaurant on the beach in Kihei. This week we are celebrating our twenty-fifth wedding anniversary, doing many of the things we love most: mountain biking in the Makawao Forest Preserve, scuba diving in search of manta rays and green sea turtles, hiking the lava fields that formed this gorgeous island, surfing the waves at Kalama Beach, among other activities that define our active lives. Our teenage children, Aspen, who is an undergraduate at Emory University, and Sage, a rising junior at Centennial High School, in Roswell, Georgia, are home alone, enjoying ten days of freedom from their parents. They are great kids; we couldn’t be more proud of the young adults that they have become.
With Erika on Maui (May 27, 2015)
Although the last twenty-five years seem to have passed by in a blur, Erika and I are blessed in that life has not passed us by. We have spent much of this week reminiscing about the path we have taken—our college years in Chicago, our years in Los Angeles, where I earned my doctorate, my postdoctoral tour of America, the birth of our kids, and so on. We have been leading rich lives. We have traveled the world, and we have many good friends. We are at peace with who we are as a couple, as parents, and as individuals. I am a successful mathematician, a professor at Emory University, and I am considered a leader in my field. I am a
well-known mentor of young mathematicians. To borrow an overused phrase, “I’m living the dream.”
How have I been lucky enough to get to where I am today?
That is the question that keeps me awake. It is a question of grace and gratitude, a question that I ask every day in wonder, almost out of fear that I will be awakened from this lovely dream to discover that none of my life has actually happened. It is a question that will haunt me for the rest of my life. Erika knows this about me. But even she will be surprised when she reads some of the details of the story I am about to tell, events that I haven’t shared with anyone before.
It wasn’t that long ago that my waking thoughts, the parental voices in my head, were about inadequacy and fear of failure. There was a time when I couldn’t even imagine wanting to live long enough to witness my thirty-second birthday. In a moment of weakness and despair twenty-three years ago, when I was twenty-four, I came within seconds of taking my own life. In a torrential rainstorm, I veered over the double yellow line of a Montana highway, near a place called Ronan, with the intention of driving headlong into an oncoming logging truck. I swerved back into my lane at the sound of the trucker’s frantic horn, and I pulled over and came to a stop on that lonely strip of asphalt in the middle of a vast wilderness. I sat there alone, with the engine running, protected from the driving rain, for an eternity, trying to figure out what I was going to do with the life I had just failed to destroy. The harrowing voices, the product of my confusing and frustrating childhood as one of three sons of tough-loving, hard-driving Japanese-American parents, had nearly dragged me to my death.
Most of my current acquaintances know nothing of my past. I have done my best to erase my childhood by pretending to myself that my life began when I was sixteen years old. I ran away from my former life, and I have successfully managed to live my adult life in self-imposed amnesia. I almost never talk about my life before college; the memories are too painful. Instead of coming to terms with the past, I dumped it into a black hole, a massive part of my history from which memories could not escape.
I was so tortured by those voices that I dropped out of high school in the naive hope that I could escape my feelings of inadequacy. I have spoken to not more than one or two of my former classmates and friends since that day over thirty years ago. I didn’t return phone calls from former friends who were wondering what had become of me. I made a clean break. I simply abandoned my former self. Although I didn’t understand it at the time, I now feel that I was committing a metaphorical ritual suicide, what the Japanese call seppuku.
I was raised by “tiger parents,” a term applied to Asian-American parents who raise their children in an overly strict way (by Western standards) with the goal of fostering an academically competitive spirit. This form of upbringing is intended to direct a child toward success, and it has one goal—to raise extraordinarily successful children, conquerors of their fields. Tiger parents set high academic standards, and they severely restrict nonacademic activities with this long-term goal in mind. That is how my parents showed their love for me, by demanding nothing less than the best. But the cost was enormous. It almost killed me.
My professional success confirms, and perhaps even justifies, the merits of this philosophy. There is certainly much truth to the undeniable fact that my parents fostered qualities in me that have been essential for my success. I am ambitious and competitive. I am restless, anxious to take on the next challenge. I thank my parents, whom I love deeply, for instilling these qualities in me.
This style of parenting, however, especially when carried to the degree that I experienced, has the potential of crushing a child’s spirit. Children can grow up emotionally unfulfilled and starving for recognition. Those voices in my head that nearly drove me mad, my despair and feelings of worthlessness, all attest to that fact.
What vanquished those voices and gave me back my soul? The answer involves a mysterious genius from India, a man whose story inspired me at my lowest points, and whose ideas have powered my career.
Let me tell it to you as I remember it.
Makena Beach, Maui, HI
May 2015
Contents
Part I My Life Before Ramanujan
Chapter 1 Tiger Boy
Chapter 2 My Parents’ Generation
Chapter 3 My Childhood (1970–1984)
Chapter 4 An Unexpected Letter
Chapter 5 My Escape
Part II The Legend of Ramanujan
Chapter 6 Little Lord
Chapter 7 A Creative Genius
Chapter 8 An Addiction
Chapter 9 The Goddess
Chapter 10 Purgatory
Chapter 11 Janaki
Chapter 12 I Beg to Introduce Myself
Chapter 13 These Formulas Defeated Me Completely
Chapter 14 Permission from the Goddess
Chapter 15 Together at Last
Chapter 16 Culture Shock
Chapter 17 Triumph over Racism
Chapter 18 English Malaise
Chapter 19 Homecoming
Chapter 20 The Tragic End
Part III My Life Adrift
Chapter 21 I Believe in Santa
Chapter 22 College Boy
Chapter 23 Erika
Chapter 24 The Pirate Professor
Chapter 25 Growing Pains
Part IV Finding My Way
Chapter 26 My Teacher
Chapter 27 Hitting Bottom
Chapter 28 A Miracle
Chapter 29 My Hardy
Chapter 30 Hitting My Stride
Chapter 31 Bittersweet Reunion
Chapter 32 I Count Now
Chapter 33 The Idea of Ramanujan
Chapter 34 My Spirituality
Epilogue
Afterword
Part I
My Life Before Ramanujan
© Springer International Publishing Switzerland 2016
Ken Ono and Amir D. AczelMy Search for Ramanujan10.1007/978-3-319-25568-2_1
1. Tiger Boy
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
Lutherville, Maryland (1976–1984)
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.
I really should be doing the geometry problems that my parents assigned me, but they aren’t home, and I love Gilligan’s Island. If my parents find out, I’ll be in super big trouble. But I’m prepared. I have a washcloth and a small pink plastic basin filled with ice water. The TV is on low enough that I will be able to hear my parents pull into the driveway, which will give me just enough time to turn off the TV and cool the back of the set with the ice-cold washcloth.
My second-grade portrait
Does this seem over the top?
In her book Battle Hymn of the Tiger Mother, Amy Chua, a Yale law professor, writes about what she calls tiger parenting, a traditional strict form of child-rearing popular in Asia and among Asian-American families. This “tiger mom” ideology accurately describes the approach of my Japanese immigrant parents, Sachiko and Takashi Ono. Like other tiger parents, they believed that their children could be “the best” students and that academic achievement is a reflection of successful parenting. Indeed, if their children are not at the top of their class, then the parents aren’t doing their job. My parents went a step further. If I wasn’t the best student, then I would bring shame on my family. It was understood that it was my duty to be “the best.”
My parents in 1999 (photo by Olan Mills)
I emerged from my early childhood with the voices of my parents in my head that continually rebuked me for my inadequ
acy and my inability to live up to their unrealistic expectations:Ken-chan, your parents are disappointed in you. You are embarrassment. Look at that professor’s children. Unlike you, they study all of time, and they what you should be. You sloppy. You spoiled. Your mother sacrificed her life for you, so you do your part. What wrong with you? You want play all of time?
Those voices told me that my parents would love me only if I was both a star student and a brilliant musician. Those voices told me that it was wrong to relax and have fun and hang out with friends. When I did those things, those voices made certain that I suffered tremendous pangs of guilt.
I now understand that many children today hear similar voices. Tragically, some of these children will succumb to those voices and take their own lives. Moreover, those suicides often occur in clusters, a phenomenon that has recently become a source of concern in communities like Palo Alto, where elevated academic expectations are rampant and such parenting is common.
Those voices are symptoms of an anxiety disorder that has been the focus of considerable recent study by clinical psychologists. Their research suggests that children of tiger parents are often burdened with anxieties that last a lifetime. The research also offers a possible biological explanation for this phenomenon.