# Infinite possibilities

How Ken Ono, AB’89, found life in and outside of math.

He had ideas that would transform mathematics, and no one to read them. So in 1911, Srinivasa Ramanujan, a two-time college dropout working as a low-level clerk in southern India, began submitting his work to local mathematics journals and, when they went largely unnoticed, writing letters to mathematicians overseas. He enclosed pages of his groundbreaking theorems and the patterns he was finding in numbers; no proofs, just bursts of mathematical insight.

In 1913 he finally got a response, from Cambridge mathematician G. H. Hardy. The renowned English number theorist saw the brilliance of Ramanujan’s work and became his mentor and champion, bringing Ramanujan to Cambridge, and his work to a wider audience.

##### Srinivasa Ramanujan (center) with colleagues, including Godfrey Harold Hardy (far right), at Trinity College at the University of Cambridge. (Public domain)

“I did not invent him—like other great men, he invented himself,” Hardy later said of Ramanujan, “but I was the first really competent person who had the chance to see some of his work, and … recognise[d] at once what a treasure I had found.”

Today mathematician Ken Ono, AB’89, the Asa Griggs Candler Professor of Mathematics at Emory University and a renowned number theorist himself, is on a hunt for those with similar undiscovered potential. His Spirit of Ramanujan Math Talent Initiative is a global search that seeks out gifted young mathematicians from modest backgrounds and pairs them with mentors and academic opportunities.

In Ramanujan, “we have a man who could have easily been lost to mathematics, and a man who has genuinely transformed the way we do mathematics,” says Ono. With the talent search, “we want to be the Hardy.”

Ono has long felt a connection and kinship with Ramanujan. As a specialist in algebraic number theory, Ono, like Ramanujan, seeks new patterns and truths in integers. He drew on the Indian mathematician’s work in his doctoral thesis and found his footing as a mathematician in part by confirming some of Ramanujan’s ideas on partition functions.

More recently, Ono, with two collaborators, found what he dubbed the “mother lode” of mathematical identities—equations that are true for any value of their variables—using two identities that were among those Ramanujan sent to Hardy in 1913. And his 2014 proof of the umbral moonshine conjecture, which has applications in fields from number theory to quantum physics, drew on work that Ramanujan furiously wrote as he was dying of tuberculosis in 1920.

Ono even helped bring Ramanujan’s story to life as the math consultant and an associate producer on the 2015 biopic *The Man Who Knew Infinity*. His on-set enthusiasm for Ramanujan was contagious, and the film companies partnered with Ono to launch the Spirit of Ramanujan Math Talent Initiative last year.

##### The 1984 letter from Ramanujan’s widow, Janaki Ammal. (Image courtesy Ken Ono)

In Ono’s corner office at Emory, framed awards placard the walls. But one frame in the middle, directly over Ono’s desk, holds something different. It’s a letter that Ramanujan’s widow wrote to Ono’s father in 1984—evidence of the Indian prodigy’s deep influence not only on Ono’s work but on his very identity.

**When Ono was growing up,** his parents often told him how, at just three years old, he had discovered infinity—when he first reasoned that there couldn’t be a largest number since there was always the possibility of adding one. Math was a part of Ono’s life as far back as he can remember; some of his favorite early memories are of sitting at a child-sized desk in the family’s home office solving problem sets while his father, the mathematician Takashi Ono, worked on his next breakthrough alongside him.

Less fond are Ono’s memories of what happened at the kitchen table where, after a less-than-perfect test score or other perceived failure, he would face a barrage of harsh criticism from Takashi and his mother, Sachiko: he was sloppy, he was unaccomplished, he was bringing shame on his family.

Ono was recognized from an early age as a math prodigy. He was included in psychologist Julian Stanley’s well-known Study of Mathematically Precocious Youth, and his parents decided he would be a mathematician like his father. All of his time was to be spent studying. Extracurriculars, sports, television, and friends were forbidden. He doesn’t remember being hugged or hearing “I love you.” Ono’s two older brothers were raised the same way: Momaro, a gifted musician, and Santa Ono, AB’84. (Santa, not identified as a prodigy in childhood like his brothers, faced the same parental demands but without the expectations for success—ironic, says Ono, as he considers Santa, now president of the University of British Columbia, the most professionally successful of the three.)

Ono was in high school when the pressure started to become unbearable. As an outlet, and against his parents’ wishes, he joined a competitive cycling team, but it wasn’t enough. He realized he needed to get out of the house and began a months-long campaign to convince his parents to let him drop out of high school.

His ultimate success hinged on a letter that had arrived in the spring of 1984, in a rice-paper envelope from India. Janaki Ammal, Ramanujan’s elderly widow, had written to Ono’s father to thank him for contributing to a statue of her late husband. It was a short letter, but Ono had never seen his stoic father so visibly moved.

Standing in his home office, letter in hand, Takashi told Ono for the first time about Ramanujan, whose story had inspired Takashi as a struggling mathematician in postwar Japan. Takashi even had his own Hardy—André Weil, a University of Chicago mathematician who noticed Takashi’s talent at a math conference in Tokyo and secured him a position at the Institute for Advanced Study in Princeton, New Jersey, in 1955.

And so, during one of their many fights about leaving school, Ono reminded his father that Ramanujan, his idol, had been a two-time college dropout. His parents relented, and Ono became a dropout himself. Soon he was on an Amtrak train to Montreal to live with Santa, then a doctoral student at McGill University. Santa provided a couch to sleep on, a part-time job at a campus laboratory, and much-needed empathy. Less than a year later, feeling like he could breathe again, Ono started applying to colleges.

**At UChicago, Ono immediately embraced his freedom.** He joined Psi Upsilon and spent more time deejaying parties, playing foosball, and eating Harold’s fried chicken than studying. He also started competitive cycling again, which is how he met his wife, Erika (Anderson) Ono, AB’90; as a student worker in Pierce dining hall, she began setting aside bananas each Saturday morning, fuel for the kid who came in early with his racing bike.

##### Ken Ono, AB’89, and Erika (Anderson) Ono, AB’90. (Photo courtesy Ken Ono)

But at the end of his third year, a visiting math professor who was an acquaintance of Takashi told Ono that his work was subpar and he’d never be a professional mathematician. Stung and refusing to let his parents be proved right, Ono attacked mathematics with new vigor.

During Ono’s senior year, his work caught the attention of mathematics professor and “math pirate” Paul Sally Jr., who was known for mentoring students in Hyde Park and beyond. The two began meeting several times a week, to talk math or just to talk. They bonded over their untraditional paths—Sally had spent several years driving cabs and teaching high school in Boston before deciding he wanted to pursue math—and Sally helped Ono secure a spot in the mathematics PhD program at the University of California, Los Angeles.

At UCLA Ono still heard his parents’ voices telling him that he wasn’t good enough, that he would fail. He almost did fail his first attempt at a qualifying exam in his chosen field, abstract algebra, and was drifting until he took a class with Basil Gordon. Impressed when Ono offered an alternative proof in class, Gordon invited him to come talk during office hours and soon took Ono on as his final PhD student.

For his dissertation, Gordon suggested Ono pursue modular forms, a class of functions rooted in Ramanujan’s identities. It was the first time Ono realized that Ramanujan’s work had modern implications. In 1991, while Ono was at work on his doctoral thesis, biographer Robert Kanigel published *The Man Who Knew Infinity: A Life of the Genius Ramanujan *(Charles Scribner’s Sons). Ono quickly bought the book and read it from cover to cover.

Ono and Gordon held long, intense work sessions on Saturdays, taking breaks to walk up the beach or talk about literature. Gordon could quote long passages from memory; Ono vividly recalls him reciting the opening of *Moby-Dick*. “I was mesmerized by his ability to make mathematics beautiful by making analogies with classical art, literature, and music,” Ono wrote after Gordon died in 2012. Gordon viewed math as an art form, a way of understanding—and embracing—the world around him. From him Ono learned for the first time to truly, as he says, “do mathematics.”

Ken Ono, AB’89, and Erika (Anderson) Ono, AB’90. (Photo courtesy Ken Ono)

As he was closing in on his doctorate, Ono drove to Erika’s hometown of Missoula, Montana, to present at a math conference. His talk covered Galois representations, a part of modern number theory related to modular forms. But Ono, wanting to impress his audience, made the mistake of preparing lectures that were too technical. The audience couldn’t follow, and one professor berated him afterward for wasting his time. His parents’ recriminations came rushing back. Ono felt he’d failed in abstract number theory, a subfield in which he thought he was making real progress, in front of mathematicians he deeply admired, and in a city where word might reach his new wife’s family. On the last day of the conference, Ono was driving on a rainy Montana highway, devastated and alone except for the critical voices filling his head. An oncoming truck came into view, and, seeing a way out, he yanked the wheel and steered his car over the center line.

**Ono doesn’t remember how** he found the other side of the road and brought his car to a stop, only that he sat shaking, terrified. “I couldn’t believe what I had almost done,” he later wrote. “I had never had suicidal thoughts before. … It was an impulsive act that I will never fully understand.”

For almost 20 years, he didn’t tell anyone what happened on that highway, but the following week he had to tell Gordon how the conference had gone. The response buoyed him. Gordon told Ono he hadn’t failed and hadn’t disappointed him. Math, he reminded Ono, is about taking risks, voyaging into the unknown, and occasionally overreaching. Delving too deeply into his topic was a symptom of transforming into a mathematician. It was exactly what Ono needed to hear.

In 1997, at a math conference honoring Gordon’s 65th birthday, Ono’s banquet speech started simply, and without hyperbole: “I thank Basil Gordon for saving my life.”

Ono successfully defended his thesis on Galois representations in 1993. He secured positions at the University of Georgia and then the University of Illinois at Urbana-Champaign and cowrote what he calls a “semi-important paper in representation theory.” Despite these successes, voices of disapproval still rang in his head. He identifies it now as impostor syndrome—the persistent belief that one’s success has been unearned, that it’s only a matter of time until one is exposed as a fraud. “When I first started, I was grateful that anyone would come hear a lecture that I would give,” he says. At some point, he feared, other mathematicians were going to validate his parents’ criticism.

Those voices finally started to subside when Ono received an appointment at the Institute for Advanced Study in Princeton, an echo of his father’s achievement four decades ago. It was the first time Ono had been recognized solely for his own ideas. “These guys had actually heard of me and knew some of my theorems,” he says. “That was the first time I actually recognized that nothing else matters if you work hard and you have faith and have some luck.”

##### Ken Ono, AB’89, and Erika (Anderson) Ono, AB’90. (Photo courtesy Ken Ono)

Later, a breakthrough in partition functions while he was an assistant professor at Penn State led to international acclaim and fellowships from the Alfred P. Sloan Foundation and the David and Lucile Packard Foundation (see “Partition Revelation”). In 1999 Ono received the Presidential Early Career Award for Scientists and Engineers from president Bill Clinton. His parents attended the White House ceremony, and afterward Takashi presented Ono with the fateful letter from Ramanujan’s widow. Now, he said, he considered Ono the letter’s rightful owner. He added, “I am so proud of you.”

Ono’s relationship with his parents has slowly continued to improve. His professional successes, including appointments at the University of Wisconsin–Madison and then at Emory, ended their criticism, making room for new ways of connecting. His parents now send cards for birthdays and holidays, events that weren’t celebrated when Ono was growing up. Ono, for his part, has come to understand better why they applied the pressure they did on their children. In his memoir he reflects on the traditional Japanese ideas about child-rearing that his parents brought with them to the States, and how the racism the family encountered in postwar America focused their attention even more intensely on hard work and achievement.

In 2014 Takashi and Sachiko traveled to Atlanta for the high school graduation of Ono’s daughter, Aspen. She and her younger brother, Sage, are now both undergraduates at Emory. They’re talented students but Ono talks up Aspen’s figure skating and Sage’s swimming (he was recently named UAA Men’s Rookie Swimmer of the Year and an NCAA National Champion, Ono says proudly). Ono has raised them to follow their passions and to love themselves as much as he loves them—including their imperfections. Aspen has close to a perfect 4.0 GPA, says Ono, “so I tell her, go get a B and learn that it’s okay.”

**In 2016 Ono published a memoir,** *My Search for Ramanujan: How I Learned to Count* (Springer), detailing his winding life path and how it kept leading to the Indian mathematician. (The book is dedicated to his mentors.) It “was good for him,” says his wife, Erika, “to unpack his mental closet.” But Ono also wrote it to help those who might be struggling like he was.

Ono likes to tell his undergraduate classes at Emory that he barely got any As in math during his first three years of college—drawing laughs when he adds, “But believe me, I am totally able to teach this class.”

“They need to hear that,” says Ono, especially from someone as successful as him. He frequently encounters students he can tell are under heavy parental pressure to get top grades and then go into the profession their families favor. “Every class I teach, I will end up having to talk to four or five kids who are not sure about what they are meant to do or be,” he says. “And it’s shocking how often it’s related to, ‘Well, my parents think I should do this.’”

##### Ken Ono with *StarTalk Radio* host Neil deGrasse Tyson (left) and cohost Eugene Mirman (right). Ono made a guest appearance on an episode of the show last fall to discuss Srinivasa Ramanujan. (Photo courtesy Ken Ono)

Life beyond college is even a part of Ono’s course syllabi. For years the last question on every final exam he gives has been, “What are you going to do to make the world a better place?” He’s so well known for it that many students write and print out their answers ahead of time and bring them in to staple to the test.

For several years Ono has given an address to freshman parents during Emory’s Family Weekend that includes a bit of his life story. Last fall that talk drew explicitly on his memoir. (Santa has also made use of his life story to help his students; he publicly revealed in 2016 that he battled depression as a young man and has continued to talk about his own experiences while president of UBC as a way to destigmatize mental illness on his campus and encourage students to seek help when needed.)

##### Ken Ono. (Photography by Bryan Meltz, courtesy Emory University)

Ono currently has seven graduate students, who share a workspace down the hall from his office. He’s in there frequently, to check in but also to ask one about her marathon training, or to earnestly tell another that she should really consider Hawaii for her honeymoon.

But in front of a chalkboard working through a problem with one of them, he’s quiet and focused, shaping formulas with rapid-fire questions and rapid-fire encouragement. Ono’s devotion to his students’ work and ideas is effective—and remembered. “When you are working on something day in and day out, it is easy to lose sight of the big picture and the excitement, and he can give that to you,” his former student Robert Lemke Oliver told *Emory *magazine. “I would not be the mathematician I am today if I’d had almost any other adviser.”

What Ono loves is “watching someone achieve something they don’t think they are ever going to be able to do.” When that happens he delights in saying he told them so. “Nobody likes hearing that, except in this case.” He finds working with students both a joy and a duty, and feels he owes it to his own mentors—and to Ramanujan—to be the best Hardy he can be for the next generation.

**In 2014 Ono got a surprise email from Matthew Brown,** the writer and director of *The Man Who Knew Infinity*, based on the 1991 Kanigel biography of Ramanujan. Brown’s team needed help ensuring the accuracy of documents that were going to be reproduced for the biopic. Impressed by Ono’s deep knowledge of Ramanujan’s work and life, Brown invited Ono to be the movie’s math consultant.

##### Ono and actor Jeremy Irons, who played G. H. Hardy, on the set of *The Man Who Knew Infinity*. In October Irons joined Ono at the White House for a screening of the movie and a panel discussion on math education. (Photo courtesy Ken Ono)

On set in England, Ono went to work checking and perfecting all the math that appears on screen. He was present during rehearsals and filming to explain math concepts as needed and to help the lead actors, Dev Patel and Jeremy Irons, develop gestures and use inflections that fit both the characters and the math discussed in the movie.

Ono was even able to help when the movie’s prop coordinators, looking for a sample of Janaki Ammal’s handwriting, asked him if he knew of anything, anywhere, that might have Ramanujan’s wife signature on it.

When he saw that Ramanujan’s story was really striking a chord with Brown and others working on the movie, Ono was thrilled. He and the producers began brainstorming ways to help *The Man Who Knew Infinity* have a lasting impact. “We thought, this film isn’t going to be *Batman v. Superman*, but for us it’s important,” says Ono. “And so we decided that we should have the film mean something.”

##### Ono and actor Dev Patel, who played Srinivasa Ramanujan, on the set of *The Man Who Knew Infinity*. (Photo courtesy Ken Ono)

Last spring Ono, Pressman Film, and IFC Films launched the Spirit of Ramanujan Math Talent Initiative. The project builds on math outreach work that Ono has done for years, and the goal, he says, is to find and support “the brilliant outliers”—young people like Ramanujan who have the potential to make significant contributions to math but have few resources or mentors.

The Spirit of Ramanujan’s mobile-friendly online math and logic quiz directs high scorers to an application. The American Mathematical Society, the Templeton Foundation, and other organizations are also helping promote the initiative, and during its inaugural round, more than 8,000 applications flooded in. The four winners received financial support and connections with professional mathematicians in their fields. Tenth-grader Kendall Clark of Baltimore will study applied mathematics with Johns Hopkins professors this summer, and 13-year-old Ishwar Karthik works every week with a number theorist at Texas A&M’s Qatar campus.

Ono discovered the most recent winner in December during a trip to Kenya. After Ono finished a lecture on his recent work at the University of Nairobi, a young man stood up in front of 500 audience members to offer a correction based on a Hans Rademacher proof from the 1930s. Ono later met with the questioner, Martin Irungu , and discovered he wasn’t an advanced graduate student, like Ono had thought, but a recent high school graduate. Unable to afford the University of Nairobi’s tuition, Irungu had been spending his free time on campus, poring over math books from the library. “He was reading material that a second- or third-year PhD student at a top school would be reading,” says Ono.

In less than 48 hours, Ono managed to secure Irungu a visa to travel to Emory. He spent a week on campus working with Ono’s graduate students and will return for the summer. Irungu also met with other mathematicians from around the country who were in town for a conference. “I ended up introducing him to professors at Harvard and MIT and Berkeley,” says Ono, “and now they’re competing for him.”

Ono is confident the Spirit of Ramanujan Math Talent Initiative will continue to identify similarly gifted students. “They’re out there,” he says, and he’s going to do everything he can to find them.

**It was in London, on the set of The Man Who Knew Infinity,** that Ono was struck by an insight that turned out to be a major step forward in proving the umbral moonshine conjecture. Being outside his office and part of a different kind of creative process made the difference, he thinks—and standing face-to-face with Ramanujan (as played by Patel) didn’t hurt either. Ever since his walks on the beach with Gordon, Ono has done some of his best work outside Emory’s stately white-stone Mathematics and Science Center, whether on a simple walk or training for a triathlon (he’s represented Team USA in several recent World Cross Triathlon Championships).

He also likes to work at home on his sofa, in a meditative state, as he thinks through new patterns or ideas. This can look a lot like dozing off, says Erika—fortunately Ono has socks that read, “Don’t wake me, I’m working,” to prevent misinterpretation. The look of contentment is often a giveaway too.

## Partition revelation

Ono’s 1999 breakthrough dealt with partition numbers, or how many different ways an integer can be represented as the sum of positive integers.

For example, the partition number of 4, commonly denoted as ** p(4)**, is 5, since there are five ways of writing 4 as the sum of positive integers:

4

3+1

2+2

2+1+1

1+1+1+1

Ramanujan discovered patterns in these partition numbers. For instance, he found that for any value of *n*, the partition number ** p(5n+4)** is always divisible by 5. So when

*n*=5, the value of

**, or**

*p*(5x5+4)**, is 4,565, which is divisible by 5. The same holds true for any value of**

*p*(29)*n*.

Ramanujan also found that the value of ** p(7n+5)** is always divisible by 7, and

**is always divisible by 11, no matter what number is plugged in for**

*p*(11*n*+6)*n*. No other such expressions using another prime number as

*n*’s coefficient appear in the work he left behind. In an unpublished notebook, Ramanujan wrote that he wasn’t aware of any other expressions with “equally simple properties” for partition functions.

Ono discovered that Ramanujan’s enigmatic claim was correct—“simple” expressions like the ones Ramanujan found don’t exist, but more complicated ones do. Drawing on other recent advances in partition numbers and aided by a number-crunching computer program, Ono proved that, for all the prime numbers from 5 to infinity, there exist expressions of the form ** p(an +b)** where the resulting partition numbers are divisible by the prime number represented by

*a*.

Ono notes these are often “monstrosities,” like ** p(48037937n+1122838)**, which is always divisible by 17. Only for the primes 5, 7, and 11 do the values of a equal the prime divisor. This is likely what Ramanujan meant by an expression with “simple properties,” says Ono.

Ono has since made other significant advances in partition numbers, including devising the first exact formula for calculating the partition number for any value of *n*. In 2011 he presented this formula and related patterns to a standing-room-only crowd at a special three-day conference at Emory.