At the beginning of a YouTube video entitled “The art of problem solving: Smallest common multiple“Richard Rusczyk invites the audience to a game. We should clap every 24 seconds; every forty-five seconds we’re supposed to jump. The challenge is to keep going until we clap and jump at the same time. Ruczyk, who is dark-haired, clean-shaven, and boyish, points to a digital timer that appears in one corner of the screen. He starts the clock, stares at it, and fidgets. “Um, how long will that take?” he asks, rolling his eyes like a teenager. “I hate waiting.”
When the timer reaches 24 seconds, Rusczyk claps. At forty-five he jumps. Meanwhile, he tries to find out on a digital board when the clap and the jump coincide. During one continuous seven-minute recording, Rusczyk jumps and claps at the right time while scribbling equations. At first he tries to write a multiple of twenty-four, but he gets bored. Then he tries to express twenty-four and forty-five as the products of their prime components: twenty-four is 23 x 31, and forty-five is 32 x 51. “That will work,” he says and claps. Just as he concludes that it will take three hundred and sixty seconds for the clap and jump to come together, he claps and jumps at the same time; The timer happened to have reached three hundred and sixty. It’s an exuberant, precise feat for middle school or younger kids who are able to do advanced math.
Rusczyk, who lives near San Diego, founded Art of Problem Solving – or AoPS – 18 years ago as a resource for budding math prodigies. Particularly gifted young math students often find math in the classroom unbearably easy and tedious; their parents may have difficulty getting enough stimulating instruction. By offering online math lessons that are more complex than standard programs for gifted and talented people, AoPS has become a lifeline for math professionals. The free online forums also serve as a major social network allowing math prodigies to connect with like-minded people every day.
Ruczyk started posting free videos more than a decade ago; he ad-libs with no written script. In 2011, at the age of forty, he shot “Least Common Multiple” with its bizarre dramatization of a monotonous numerical concept. Some of his videos have received hundreds of thousands of views; occasionally they show his alter ego, a character with a rough voice in dark tones and a black hoodie. On the screen, Rusczyk conveys a playful, experimental fearlessness that sweeps young learners away. “It’s a somewhat intangible quality that some people have, and he has it in abundance,” said mathematician Sam Vandervelde, director of Proof School, a private, mathematically-oriented academy of fine arts in San Francisco.
Kristen Chandler, a former math teacher and executive director of MathCounts, a nonprofit that runs a popular high school math competition series, told me that Rusczyk is “a rock star in our competitions.” (Together with Raytheon Technologies and the Department of Defense STEM(AoPS is a sponsor of the MathCounts program.) Before the pandemic, Rusczyk attended the national MathCounts finals as an invited speaker in May each year; Chandler recalled attendees and parents flocking to get his autograph and take selfies with him. A competitor asked Rusczyk to mark himself on his forehead with a marker.
For years, AoPS grew gradually. It published printed textbooks, math Olympiad prep materials, and an accredited online curriculum, including a free one adaptive learning system with thousands of difficult math problems. In 2012 it began with the launch of the Beast Academy, an elementary school curriculum that teaches advanced math concepts from hilarious cartoon monsters to young child prodigies. It also opened ten stationary learning centers across the country. As of 2019, approximately 36,000 math students from around the world were using the paid online curriculum or face-to-face courses, and tens of thousands more were consulting his textbooks for independent study.
In the spring of 2020, when schools closed, the company’s website traffic increased five- to six-fold and enrollments doubled. AoPS’s hundred employees began teleworking, with the exception of Rusczyk and four warehouse workers. At night or on the weekend, Rusczyk and his wife Vanessa went to the vacant company headquarters – a two-story office building in the suburb of Rancho Bernardo – to order books. One Sunday when he was in the office, we connected through Zoom. He was wearing a short-sleeved blue plaid shirt. Rusczyk, six feet tall with cropped hair, has a quick, self-deprecating joke and sometimes laughs like a child, almost hunched over. On a quick tour, he showed me stacks of book boxes in the warehouse and framed illustrations of monsters from the Beast Academy. In a dark hallway, the fluorescent ceiling lighting no longer worked except for an eerily flickering panel. “This is where the zombies take me into the zombie apocalypse,” he said with a grin. (He read a lot of science fiction and fantasy as a kid.)
Rusczyk, who is now fifty, easily connects with math-obsessed children because he used to be one of them. He grew up fast in arithmetic and showed a brilliant, intuitive understanding of geometric relationships. He had a competitive streak and won many math competitions. At the same time, however, he experienced deflationary setbacks that kept him from studying mathematics. He loved math – it had taught him resilience, creativity, and the joy of finding one’s tribe. Still, he was faced with a mystery: if you are a math prodigy and don’t want to be a mathematician, what do you do with your life? Art of Problem Solving was his solution.
Ruczyk was born in Idaho Falls. He and his younger sister attended elementary schools in half a dozen states while their father, a U.S. Navy officer and nuclear engineer, moved from one base to the next. Small but athletic by nature, Ruczyk played basketball and impaled professional baseball stats – those “got him numbers,” told me his mother, Claire, a former elementary school teacher. In 1983 Claire read a newspaper article about the introduction of the MathCounts program. Ruczyk, who was in seventh grade, signed up and did well; he loved being around dozens of teenagers having fun wrestling with numbers. Two years later, after the family settled in Decatur, Alabama, he finished 24th in the national MathCounts finals.
Rusczyk became the star of his high school math team that traveled to competitions in the southeast. He also competed individually in the American Mathematics Competitions, a rigorous series organized by the Mathematical Association of America (MAA). The competitions built on the Mathematics Olympiad in the United States, which was then a five-question, three-and-a-half-hour exam. Rusczyk played tennis and cross-country, but he was even more fond of math and the company of his math friends. His bookshelves were filled with ribbons and trophies for math competitions. “I was definitely a trophy hunter,” he said. He spent hours practicing on old math competition problems in his bedroom.
In June 1987, after completing his sophomore year, he was invited to the MAA’s Summer Mathematics Olympiad program, reserved for those placed in the top tier of the United States Mathematical Olympiad. The program was an intense month long math boot camp held each year at either West Point or the Naval Academy in Annapolis. (A redesigned program is now being run by Carnegie Mellon University.) At West Point, Rusczyk was one of two dozen boot campers, almost all boys. They lived in spartan dormitories and were woken early by the horn of the wake-up calls. Based essentially on three exams in the first week – approximately four hours each – six students were selected to represent the United States at the International Mathematical Olympiad (IMO) in July.
Ruczyk arrived excitedly, expecting to assert himself. On the first day a professor stood at a blackboard and wrote “counting” in chalk; the subject – “falling faculties” – was alien. Within minutes, Rusczyk was confused. It quickly became apparent that he wasn’t even close to the brightest kid in the room. It was an unsettling feeling. Other students absorbed the math like sponges; some were clearly geniuses. Rusczyk was unable to solve a single problem during the strenuous practice exams. Getting outdone by your cerebral classmates was inspiring but also terrifying. “I closed at the end of the first week,” he recalls.
Even so, the group was friendly and joked about board games and Ultimate Frisbee. Rusczyk, who had brought his basketball with him, dribbled nimbly around the other campers. He made strong friendships, including with Vandervelde, a compatriot from the south. He noted that Vandervelde and other top students – including budding mathematician and writer Jordan Ellenberg – were excited about thinking about abstract numerical concepts and questions for their own sake. Rusczyk realized that the allure of mathematics for him was more in competition and camaraderie.
Ruczyk didn’t make it to the IMO team; He later learned that several other students were also having difficulties. The next summer he visited the boot camp again, this time in Annapolis, and was still often at a loss. Nevertheless, he continued to study; in his senior year of high school, he began working through some math evidence to gain a more real understanding of the concepts. He graduated from the top of his class, was the winner of the Mathematical Olympiad in the USA – at that time eight medals were awarded every year – and returned to the boot camp for a third summer. Although he failed to qualify for the IMO team that year either – Vandervelde and Ellenberg – he was selected as a replacement. He left the camp early after falling ill and was one of the top eight math students in the nation.