Korean Mathematician Crack Moves Sofa Problem After Six Decades
Korean researcher Baek Jin‑eon has proved that the complex curved shape proposed by Joseph Gerver is the largest rigid object that can navigate a right‑angled corridor, finally solving the long‑standing moving‑sofa problem. The result, presented in a 119‑page preprint, eliminates the need for computer‑assisted estimates and was highlighted by Scientific American as one of the top ten mathematical breakthroughs of 2025. Baek’s work rests on rigorous logical reasoning and introduces new optimization techniques for a problem that previously lacked a formal theoretical framework.
Baek Jin‑eon, a 31‑year‑old research fellow at the June E Huh Center for Mathematical Challenges at the Korea Institute for Advanced Study, has resolved a geometry puzzle that has resisted a definitive proof for almost sixty years. The *moving sofa* problem, first articulated in 1966 by Leo Moser, asks for the shape of maximum area that can be carried around a right‑angled corner in a corridor of unit width. Although the puzzle is simple to state and has appeared in secondary‑school textbooks, no mathematician has yet proven that the currently best‑known shape is indeed optimal.
In 1992, Rutgers mathematician Joseph Gerver proposed a sophisticated, curved figure with an area of approximately 2.2195 m², superseding the earlier 2.2074 m² shape introduced by John Hammersley in 1968. For decades, researchers have refined conjectured shapes and narrowed the numerical bounds, but the exact upper limit remained unestablished.
Baek’s 119‑page preprint, released on the arXiv in late 2024, argues rigorously that Gerver’s figure is a hard upper bound. Unlike prior work that leaned heavily on extensive computational searches and numerical verifications, Baek employs purely analytical reasoning, developing new optimization tools tailored to the problem’s unique geometry.
"I keep holding on to hope, then breaking it, and moving forward by picking up ideas from the ashes," Baek explained in an interview with a Korean Institute for Advanced Study web magazine. “I’m closer to a daydreamer by nature, and for me mathematical research is a repetition of dreaming and waking up.” The paper is currently under review at *Annals of Mathematics*, one of the discipline’s most selective journals.
Baek’s motivation stemmed from the puzzle’s lack of a clear theoretical foundation. "This sofa problem doesn’t have much historical context, and it wasn’t even clear whether there was theory behind it," he said. "I tried to connect it to existing ideas and turn it into an optimization problem, creating tools suited to the question.” He emphasized that breakthroughs of this magnitude often require years of accumulation: "It takes a long time for a problem to gain context. I feel like I planted a small seed."
Baek earned his Ph.D. from the University of Michigan and has held positions at the National Institute for Mathematical Sciences and Yonsei University, where he solved the problem at age 29 during his postdoctoral tenure.
Scientific American recognized Baek’s work as one of the top ten mathematical breakthroughs of 2025, underscoring the significance of his contribution to the field of geometric optimization and the broader mathematical community.