In 2026, the mathematical community awarded its highest honor, the Fields Medal, to Yu Deng for solving a problem that had long seemed intractable: the random data problem in partial differential equations (PDEs). But Deng's journey to this pinnacle was anything but linear—it was marked by doubt, depression, and a surprising source of solace in Japanese manga.
Deng's work tackles a fundamental question: can PDEs, which describe everything from fluid flow to quantum fields, always produce a solution when their starting conditions are chaotic? Specifically, he focused on what mathematicians call "rough" initial data—waves that oscillate wildly or contain abrupt jumps. If a PDE could be shown to have a solution even under these extreme conditions, it would reveal deep truths about the equation's structure and, by extension, about the physical systems it models, such as the Gibbs measure used in statistical mechanics.
After earning his undergraduate degree at MIT in 2011, Deng moved to Princeton for graduate school, where his advisor Alexandru Ionescu quickly recognized his talent. "He was brilliant from the beginning," Ionescu recalls. "Even as a graduate student, without experience... he was very good at getting at the essence of the thing." Yet despite this early promise, Deng soon hit a wall. The existing mathematical tools couldn't handle the random data problem. "We could get some results, but they were not satisfactory," Deng says. He pivoted to other questions, but none captured his imagination in the same way. A period of aimlessness followed, and Deng admits he felt "a bit depressed."
During his postdoc at the Courant Institute at New York University, Deng found comfort in an unexpected place: manga, particularly the yuri genre, which focuses on deep friendships and romance between women. "I remember him at Courant. He was always holding a manga," says Jalal Shatah, a former math department chair there. Deng explains that these stories, which "feel nice and warm and beautiful," helped him be kinder to himself and "more comfortable with life." This emotional support became crucial as his postdoc ended without tenure-track offers from his top choices. For several months, Deng considered returning to China or taking a finance job. "I told them I still want to do math, but if I realize I cannot reach what I'm aiming for, then maybe I could consider this," he says.
In a moment of deep introspection, Deng took a train to Long Beach, New York. There, walking the shoreline and writing poetry in the style of the Tang dynasty poet Li Shangyin, he confronted his fears. He wrote about the tension between his desire to escape and his dream of doing mathematics, about tides that seemed as unsettled as his own mind. This poetic reckoning, combined with the emotional resilience he had cultivated through manga, allowed Deng to recommit to his research.
Returning to the random data problem with renewed focus, Deng developed novel techniques that bridged probability theory and analysis. His breakthrough showed that even for PDEs with extremely rough initial data, solutions exist and are well-behaved in a probabilistic sense—a result that has implications for fields as diverse as fluid dynamics and quantum field theory. The work also shed new light on the Gibbs measure, a concept central to understanding how physical systems reach equilibrium. For more on how mathematicians are tackling fundamental questions, see our coverage of Jacob Tsimerman's proof of the André-Oort conjecture.
Deng's story resonates beyond mathematics. It highlights how personal struggles and unconventional sources of inspiration can fuel scientific creativity. His path—from depression to manga to a Fields Medal—offers a powerful reminder that the most profound discoveries often emerge from a place of vulnerability. As Deng himself puts it, the equilibrium he sought in his equations mirrored the balance he had to find in his own life. For a deeper dive into how mathematicians uncover hidden patterns, check out our article on the mathematics of shuffling.
The Fields Medal, awarded every four years to mathematicians under 40, is a testament to Deng's perseverance and ingenuity. His work not only solves a long-standing problem but also opens new avenues for exploring the interplay between randomness and order in mathematical physics. As the field celebrates his achievement, it also acknowledges the human side of genius—the doubts, the detours, and the quiet moments of recovery that make breakthrough possible.
