At the start of a YouTube video titled “The art of problem solving: the least common multipleRichard Rusczyk invites viewers to play a game. Every twenty-four seconds we’re supposed to clap; every forty-five seconds we’re supposed to jump. The challenge is to keep going until we clap and jump at the same time. Rusczyk, who is dark-haired, clean-shaven, and childish, waves to a digital timer that appears in a corner of the screen. He starts the clock, looks at it and fidgets. “Um, how long is that going to take?” He asks, rolling his eyes like a teenager. “I hate waiting.”
When the stopwatch reaches twenty-four seconds, Rusczyk applauds. When he reaches forty-five, he jumps. Meanwhile, on a digital board, he starts trying to figure out when the hit and the jump will coincide. During a continuous seven-minute take, Rusczyk jumps and claps at the right time while jotting down equations. First, he tries to write multiples of twenty-four, but is bored. Then he tries to express twenty-four and forty-five as products of their components of prime numbers: twenty-four is equal to 23 x 31, and forty-five is 32 x 51. “It will work,” he said, clapping. When he concludes that it will take three hundred and sixty seconds for the clap and the jump to converge, he clap and leap simultaneously; it turns out that the timer has reached three hundred and sixty. It is an exuberant and precise performance intended for college students or the youngest, able to do advanced mathematics.
Rusczyk, who lives near San Diego, founded Art of Problem Solving (or AoPS) eighteen years ago as a resource for budding math wonders. Exceptionally gifted young mathematics students often find classroom mathematics unbearably easy and tedious; their parents may have difficulty obtaining sufficiently stimulating lessons. By providing online math education that is more complex than what is found in standard gifted and talented programs, AoPS has become a lifeline for math whiz. Its free online forums also serve as a vital social network, allowing math prodigies to connect with soul mates every day.
Rusczyk started posting free videos over ten years ago; it ad-libs with no script written. He made âLeast Common Multipleâ, with its quirky dramatization of a banal digital concept, in 2011, at the age of forty. Some of his videos have garnered hundreds of thousands of views; sometimes they feature his alter ego, a gritty-voiced character in dark tones and a black hoodie. On screen, Rusczyk conveys a playful and experimental fearlessness that engages young learners. “It’s a slightly intangible quality that some people have, and he has it in spades,” mathematician Sam Vandervelde, who runs the Proof School, a private liberal arts academy focused on mathematics at San Francisco.
Kristen Chandler, former math teacher and CEO of MathAccount, a nonprofit organization that runs a popular series of college math contests, told me that Rusczyk was “a rock star at our competitions.” (With Raytheon Technologies and the Ministry of Defense STEM, AoPS is a sponsor of the MathCounts program.) Prior to the pandemic, Rusczyk attended the MathCounts National Finals each May as a guest speaker; Chandler recalled how contestants and parents flocked to get his autograph and take selfies with him. A contestant asked Rusczyk to sign his forehead with a marker.
Over the years, AoPS has grown steadily. It has published printed textbooks, math Olympiad preparation materials, and an accredited online program, including a adaptive learning system containing thousands of difficult math problems. In 2012, he began rolling out Beast Academy, a primary education program in which advanced math concepts are imparted to young prodigies by comic book monsters. He also opened ten brick and mortar learning centers across the country. In 2019, around thirty-six thousand math students around the world were using its paid online program or in-person classes, and tens of thousands more were consulting its textbooks for independent study.
In the spring of 2020, when schools closed, the company’s website traffic increased five to six times and enrollments doubled. About 100 AoPS employees have started telecommuting, with the exception of Rusczyk and four warehouse workers. At night or on weekends, Rusczyk and his wife, Vanessa, would drive to the empty company headquarters – a two-story office building on the outskirts of Rancho Bernardo – to help fill book orders. One Sunday while he was in the office, we connected via Zoom. He was dressed in a short-sleeved blue plaid shirt. Five foot seven, with cropped hair, Rusczyk has a quick, self-deprecating mind and sometimes laughs like a child, almost doubled up. On a brief visit, he showed me stacks of book boxes in the warehouse and framed illustrations of Beast Academy monsters. In a dark hallway, the fluorescent lighting on the ceiling had stopped working, except for a strangely flickering panel. âThis is where the zombies are going to bring me into the zombie apocalypse,â he said with a smile. (He read a lot of science fiction and fantasy as a kid.)
Now fifty years old, Rusczyk easily bonded with children obsessed with math because he was one of them. Growing up, he was quick with calculations and showed a brilliant and intuitive understanding of geometric relationships. He had a competitive streak and won many math contests. But, at the same time, he experienced deflating setbacks that helped deter him from the academic pursuit of mathematics. He loved math – it had taught him resilience, creativity, and the joys of finding his tribe. Still, he faced a conundrum: If you’re a math prodigy who doesn’t want to become a mathematician, what do you do with your life? The art of problem solving was his solution.
Rusczyk was born in Idaho Falls. He and his younger sister attended elementary schools in half a dozen states as their father, a US naval officer and nuclear engineer, moved from base to base. Small but naturally athletic, Rusczyk played basketball and published professional baseball stats. In 1983, Claire read a newspaper article about the launch of the MathCounts program. Rusczyk, who was in seventh grade, signed up and did well; he loved being surrounded by dozens of teenagers who were having fun wrestling with numbers. Two years later, after the family moved to Decatur, Alabama, he placed twenty-fourth in the MathCounts National Finals.
Rusczyk became the star of his high school math team, which competed in the Southeast. He also participated individually in the American Mathematics Competitions, a rigorous series organized by the Mathematical Association of America (MAA). The competitions developed into the United States Mathematical Olympiad, which at the time consisted of five questions and three and a half hours of examinations. Rusczyk played tennis and ran cross-country, but he loved math even more and the company of his math buddies. Its shelves were filled with ribbons and math competition trophies. âI was definitely a trophy hunter,â he said. He spent hours practicing old math competition problems in his bedroom.
In June 1987, after his second year, he was invited to the MAA Mathematical Olympiad Summer Program, reserved for those who had placed in the top category of the United States Mathematical Olympiad. The program was a one-month intensive math boot camp, held annually at West Point or the Naval Academy in Annapolis. (A redesigned program is now hosted by Carnegie Mellon University.) At West Point, Rusczyk was one of two dozen training campers, almost all boys. They stayed in Spartan dormitories and were woken up early by the wake-up bugle. Largely based on three exams in the first week, each lasting about four hours, six students would be chosen to represent the United States at the International Mathematical Olympiad, or IMO, in July.
Rusczyk arrived excited, expecting him to be able to hold on. On the first day, a teacher stood in front of a blackboard and wrote âCountâ in chalk; the subject – “factors in free fall” – was unfamiliar. Within minutes, Rusczyk was bewildered. It quickly became clear that he wasn’t even close to being the brightest child in the room. It was a disturbing feeling. Other students have absorbed mathematics like sponges; some were clearly geniuses. Rusczyk couldn’t solve a single problem during the grueling practice exams. Being overwhelmed by his cerebral classmates was inspiring but also terrifying. âI closed at the end of the first week,â he recalls.
Still, the group was friendly, joking about board games and the Ultimate Frisbee. Rusczyk, who had brought his basketball, nimbly dribbled around the other campers. He made strong friendships, especially with Vandervelde, a compatriot from the South. He noticed that Vandervelde and other top students, including the future mathematician and writer Jordan Ellenberg, seemed fascinated by thinking about abstract numerical concepts and questions for their own good. Rusczyk realized that for him the attraction of mathematics lay more in competition and camaraderie.
Rusczyk was not part of the IMO team; he later learned that a few other students were also struggling. The following summer he attended training camp again, this time in Annapolis, and was still frequently puzzled. Nevertheless, he continued to study; During his final year of high school, he began working on mathematical proofs, achieving a more authentic understanding of concepts. He graduated as a valedictorian, won the United States Mathematical Olympiad – at that time eight medals were awarded each year – and returned to training camp for a third summer. Although he did not qualify for the IMO team that year, Vandervelde and Ellenberg did, he was chosen as a replacement. He left the camp soon after falling ill, ranked among the top eight high school math students in the country.