My Search for Ramanujan

by Ken Ono

  Impressed by this moving display, Erika and I decided to attend a Sunday service. Although religion had played little role in our family up to that point, apart from attending services in Erika’s church of origin whenever we were in Montana, we felt a strong need to meet this congregation. It turned out that the church, Madison Christian Community, is a partnership between two congregations: Community of Hope and Advent Lutheran Church. Although the two congregations have different religious affiliations, they are partners. They have common educational and community outreach activities; they even have a joint church service once a month.

  We attended a service at the Community of Hope, an open and affirming congregation affiliated with the United Church of Christ. We were drawn by their statement of welcome:Community of Hope is an Open and Affirming community of faith where no matter who you are or where you are on life’s journey, you are welcome.

  We come together

  As people on a journey,

  Respectful of our diversity,

  Supportive of our callings and committed to learning what it means to be the body of Christ in the world today.

  We celebrate all races, abilities, creeds, socioeconomic statuses, religious upbringings and sexual orientations.

  Having grown up without religion, I was comforted by those words. We were indeed welcomed and embraced by this community on our first visit, and we realized on the spot that we had been leading lives that lacked spirituality and a sense of community.

  The congregation was led by Pastor Tisha Brown, an intelligent and vibrant woman whose weekly sermons erased my earlier fears of church: How would the congregation view heaven and hell? Was it really important to choose the right version of the Bible? How should Christians be viewed within the context of a worldwide community? How would other religious traditions be viewed? None of those questions mattered. The congregation that Tisha led was indeed open and affirming in every way.

  Tisha challenged us to deepen our spirituality and to perform work in search of justice and an improved quality of life for people everywhere. For this former tiger boy who was raised in a nonreligious kaikin home, her messages shook the foundations of my very being. Her sermons and the friends we made at the Community of Hope challenged me to rethink my purpose; they helped me develop my spirituality; and they helped me become a better person.

  In 2004, I asked Tisha to baptize me. As part of the process, I had to meet with her to discuss the church, the community, and my expected role as a future member. As a prerequisite, she asked me to explain my personal spiritual path. I came to our first meeting prepared. I brought Kanigel’s The Man Who Knew Infinity with me, and I told her about my life and the great Indian genius whose ideas came to him as visions from a goddess.

  What would it take for my parents to open themselves to the possibility of a life of the spirit? I asked at the beginning of this book. Recall that during their childhood, Emperor Hirohito, who was viewed as a god to the Japanese people, had been forced to surrender and abandon his divine status. I theorized that this event left many Japanese, like my parents, jaded and closed to any form of spirituality.

  My parents now belong to a church in Lutherville. For the past ten years, they have enjoyed their membership in a spiritual community. Although we have never talked about it, I believe that my father, like me, has learned to recognize and celebrate the things of this world and of the mind and spirit as fragments of the divine. I had run away from home so that I could be as little like my father as possible. I was surprised when Basil Gordon prophesied that I would follow in my father’s footsteps. I was even more surprised when Ramanujan emerged as the link that bound my father’s history to mine. Did he also have a role in bringing my parents to think more about spirituality and community?

  Epilogue

  My Pilgrimages

  Pilgrimages are not unique to one religion. They are retreats from normal life to focus on spiritual values or to honor a particular place or person. Because of my life story, I had a strong need to make a pilgrimage to honor Ramanujan.

  Almost fifteen years ago, around the time I moved to the University of Wisconsin from Penn State, the Dutch mathematician Sander Zwegers, in his doctoral dissertation written under the direction of Don Zagier, finally made sense out of Ramanujan’s mock theta functions, the mathematics he had conjured on his deathbed. Almost concurrently, the German mathematicians Jan Bruinier and Jens Funke developed a general theory of such functions that then made use of Zwegers’s work to show that Ramanujan had anticipated the theory of “harmonic Maass forms.”

  Armed with these advances, Kathrin Bringmann and I proved a number of theorems on Ramanujan’s mathematics that earned us many invitations, one of which came from India. I was invited to speak at the 2005 SASTRA University conference on number theory. SASTRA University, located in Ramanujan’s hometown of Kumbakonam, had decided to establish an award in honor of Ramanujan, a prize to be bestowed on mathematicians not exceeding the age of thirty-two who have made outstanding contributions to areas of mathematics influenced by Ramanujan. I was invited by SASTRA to give an address at the inaugural SASTRA Prize Conference.

  My dream had finally come true. I was offered the opportunity to make a pilgrimage to India, to seek Ramanujan, to see his home, his temple, and his schools. Krishnaswami (Krishna) Alladi, a number theorist at the University of Florida and the founding editor of the Ramanujan Journal, kindly facilitated our visits to these special places. My travel companions were the SASTRA award winners, my friends Sound and Manjul Bhargava. This would be my first of many trips to India.

  After final exams at the University of Wisconsin in December 2005, I boarded a plane at the Dane County airport. Forty hours later, I was in India, in Chennai, the city where Ramanujan had written his deathbed letter on mock theta functions eighty-five years earlier. This is the city where he passed away tragically at the age of thirty-two with Janaki by his side.

  Chennai was not the final destination. I still had the long journey to Kumbakonam, Ramanujan’s childhood home and the site of the SASTRA conference. SASTRA University arranged a private minivan, barely large enough to accommodate the American mathematicians attending the conference, which included Sound, Manjul, Manjul’s mother, Krishna, and my doctoral student Karl Mahlburg.

  My arrival in Chennai had been delayed by a winter storm in Europe, which left almost no time to relax before the long bus ride. Manjul graciously offered his hotel room for a quick shower, after which we departed for Kumbakonam straightaway.

  Although Kumbakonam is only 180 miles from Chennai, the drive took over six hours. At first, we poked along in the ridiculous congestion that defines Chennai traffic. Imagine inching along in a sea of bicycles, small cars, cows, goats, motorcycles, and rickshaws—stoplights being mere suggestions. I assumed that the traffic conditions would improve once we escaped the city. In some ways, they did. Our speed improved outside the city, but the driving conditions deteriorated. The roads narrowed, and they had been severely damaged by recent flooding, which had scoured out deep potholes. That preposterous ride rivaled the most extreme turbulence I have ever experienced in an airplane, and it went on and on and on for nearly thirty miles. I had no idea that a 180-mile drive could be so physically demanding. We arrived in Kumbakonam after dusk, and we were greeted by the staff of the hotel, who draped lovely garlands around our necks and imprinted red tilaks on our foreheads. They kindly offered glasses of delicious rose water, perfect elixirs after such a grueling ride, and then they massaged our feet.

  Our hotel, the secluded Sterling Resort, was a collection of carefully restored nineteenth-century buildings that had been an abandoned rustic village. The grounds were complete with a small farm, livestock, large sculptures of Hindu gods, and a museum.

  The next morning, I took a short stroll around the grounds. It seemed as though we had somehow taken a journey back in time. After a breakfast of masala dosa, one of my favorite south Indian dishes, we boarded the minivan for the short
drive to SASTRA University, the site of the “Conference on Number Theory and Mathematical Physics” and home of the Srinivasa Ramanujan Centre. The day began with the presentation of the first SASTRA Ramanujan Prize, awarded jointly to my friends Manjul and Sound. The dazzling ceremony included the lighting of a tall polished brass lamp, traditional Indian songs, and a passionate speech by the executive director of the Indo-US Science and Technology Forum, an organization that promotes collaboration in science, technology, engineering, and biomedical research between the United States and India.

  After a full slate of lectures, the invited speakers were driven to two sacred sites: Ramanujan’s childhood home and the Sarangapani Temple. We first visited Ramanujan’s home, a one-story stucco house that sits inconspicuously among a row of shops. This house, which had deteriorated and was in a dilapidated condition for several decades, was purchased and beautifully restored by SASTRA University. At SASTRA’s invitation, India’s president, Abdul Kalam, visited the home in 2003, and he was so impressed that he declared it a national museum.

  Sound and Manjul in front of Ramanujan’s boyhood home (photo by Krishnaswami Alladi)

  The house is devoid of any striking features. In the front, there is a small porch, one of Ramanujan’s favorite places to do mathematics. We took many photos of the porch, and we tried to imagine Ramanujan as a young boy, performing his calculations there on his slate. I spent the next half hour pacing through the diminutive house, which consisted of two small rooms and a kitchen.

  The very small bedroom is found immediately on the left as you enter the front door, and its only distinguished features are a small window facing the street and an old-fashioned bed occupying nearly half the floor space. The museum’s exhibits, which include a bust of Ramanujan decorated with garlands, are lovingly displayed in the main room. On the day we visited, there was a beautiful kolam in front of the bust, an intricate, symmetric floral design on the brick floor created out of rice flour. In the rear part of Ramanujan’s house there is a tiny courtyard with an old well.

  Two blocks away, the Sarangapani Temple towered over Ramanujan’s neighborhood. There, Ramanujan and his family regularly offered prayers to the Hindu god Vishnu, one of whose epithets is Sarangapani, the bow-carrier. Ramanujan used to work on his mathematics in its great halls, sheltered from the heat and humidity by its stone walls. I tried to picture Ramanujan working out his mathematics on his slate with his notebook by his side.

  The Sarangapani Temple (photo by Krishnaswami Alladi)

  The brilliant orange of the sun’s rays formed a corona around the colossal structure, which beckoned us as we stood on the porch of Ramanujan’s house. The temple, built mostly between the thirteenth and seventeenth centuries, was constructed from stone brought from north India by elephant. The temple is tetragonal, and its outer walls are completely covered with colorful ornate carvings depicting countless Hindu legends.

  Immediately beyond the gopuram, the temple gate, dozens of bats circled above us against the darkening sky. A few steps away, we could see cows eating hay. The interior of the temple is a stunning labyrinth of sculptures, stone columns, brass walls, flickering lights and candles, and brass pillars. The walls are completely covered with ornate metalwork and stone carvings. Following Hindu tradition, we stepped barefoot over the stone floor in a clockwise direction, passing dozens of kolam floor designs. The air was warm and muggy, and heavy with the scent of incense. The main central shrine is a monolith resembling a chariot drawn by horses and elephants. Beyond the monolith we found the inner sanctum, protected by a pair of ancient bulky wooden doors covered with bells. The inner sanctum, bursting with silver and bronze vessels, is considered the bronze-walled resting place of Lord Vishnu. Krishna and his cheerful wife, Mathura, called us into the inner sanctum and made offerings of coconuts and vegetables to Lord Vishnu, placed by sweaty bare-chested Hindu priests clad in holy white robes. I understood that Krishna had arranged for us to be blessed in this impassioned pooja, or ceremony of propitiation.

  As we made our way back toward the gate of the temple, I came upon a small set of steps that led to a small cubbyhole holding the statue of a Hindu god flanked by melted candles. Its ancient stone walls were covered with numbers scrawled in charcoal and carved in stone. Ramanujan’s temple had special numbers! Sound’s father explained that it is not unusual for Hindus to etch important numbers when making offerings. Some numbers appeared to be birthdays, while others appeared to be telephone numbers and street addresses. I excitedly searched for numbers made famous by Ramanujan, such as Hardy’s “taxicab” number (to be described later). I didn’t find any. However, to my great surprise, I found 2719 prominently etched at eye level. For me, this number is special. It is the largest odd number that—as Sound and I had proved with near certainty—is not represented by Ramanujan’s ternary quadratic form x 2 + y 2 + 10z 2. I was delighted to see it near where Ramanujan might have been writing in his notebook a century ago. I have now visited India several times, and I always make it a point to check on my sacred 2719 etched delicately in a niche in Ramanujan’s temple.

  The next day provided another full program. My student Karl gave a superb talk on his thesis research, which would earn him a postdoc at MIT and the Proceedings of the National Academy of Sciences “Paper of the Year Award.” I then gave my lecture on my work with Kathrin on mock theta functions and Maass forms. Kathrin would win a SASTRA Ramanujan Award a few years later in large part because of these results.

  At 3:00 p.m., we boarded the minivan for further sightseeing. We visited Government College, the first college to dismiss Ramanujan, and Town High School, where he excelled before becoming addicted to mathematics. At Government College, I had hoped to see the original copy of Carr’s book, the one that awakened Ramanujan’s genius. Unfortunately, the book was lost.

  After the short visit to Government College, we made our way to Town High School, the site of Ramanujan’s first academic successes. We arrived after classes had ended for the day. The school was an impressive two-story building with arched balconies and a lush tropical courtyard. We were greeted by A. Ramamoorthy and S. Krishnamurthy, two of the school’s teachers. They kindly gave us an entertaining tour of campus, which included a stop in Ramanujan Hall, a cavernous room dedicated to the memory of Ramanujan. The teachers also proudly displayed copies of awards that Ramanujan had won as a top student. I was deeply moved by the pride with which they shared their campus and their devotion to the story of Ramanujan. Their passion confirmed to me that Ramanujan is still treasured in India.

  Near the end of our visit, Mr. Ramamoorthy revealed to us that he teaches English, and as a student was never very good at math. He timidly asked whether I could explain any of Ramanujan’s work to him, and from the look on his face, it was clear that he didn’t think that I could. I accepted the challenge. We found a chalkboard, and I explained Ramanujan’s work on partitions. I explained the partition numbers to him, and then told him that Ramanujan proved that every fifth partition number, beginning with p(4) = 5, is a multiple of 5. My new friends were delighted by the simplicity of the result, and they promised to share it with their students the next day. Mr. Ramamoorthy thanked me, and he joked, “You are not Mr. Ono, you are Mr. Oh-Yes.” Although I would have hated hearing this as a high-schooler, somehow in Kumbakonam it was music to my ears.

  The conference ended the next day, on December 22, 2005, Ramanujan’s birthday. Manjul delivered the Ramanujan Commemorative Lecture, a fascinating look at his work with Jonathan Hanke on quadratic forms. Manjul fittingly noted that in his 1916 paper on quadratic forms, Ramanujan had already anticipated some of the most difficult problems in the subject. Manjul’s final slide was about my joint work with Sound, our result that proved (modulo the generalized Riemann hypothesis) that 2719 is the largest odd number that is not of the form x 2 + y 2 + 10z 2. That slide was for me a poetic conclusion to the conference and my pilgrimage: the number 2719 appearing at the end of the final
lecture and echoing from a small cubbyhole in the great halls of Ramanujan’s temple a few miles away.

  Three years ago, I had the chance to visit many of the other sites that are important to Ramanujan’s history. The president of India had proclaimed 2012 a “National Year of Mathematics” to honor the 125th anniversary of the birth of Ramanujan. The Indian government provided the financial backing for the documentary The Genius of Srinivasa Ramanujan.

  Nandan Kudhyadi, the director, asked me to appear in the film as one of the experts on Ramanujan’s work, along with my friend A. Raghuram, the coordinator of the mathematics program at the Indian Institute of Science Education and Research, in Pune, India. I spent several weeks in October 2011 with a small film crew visiting sites in south India that played an important role in Ramanujan’s life. I visited Ramanujan’s birthplace in Erode. We visited Namakkal, a town that dates to the seventh century. Namakkal is home to the Namagiri Temple where Ramanujan had his vision that allowed him to accept Hardy’s invitation and travel across the seas to Cambridge. We filmed at various locations in Madras, including the hostel where Ramanujan lived before flunking out of college and the neighborhood where he spent the last months of his life.