A South Korean mathematician has successfully solved the moving sofa problem, a challenge in geometry that has perplexed researchers for nearly 60 years. Dr. Baek Jin Eon, a 31-year-old research fellow at the Korea Institute for Advanced Study, demonstrated that no shape larger than a previously proposed design can navigate through a right-angled corridor of fixed width, definitively addressing the puzzle first posed in 1966.
The moving sofa problem asks a seemingly simple question: what is the two-dimensional shape with the largest possible area that can be transported through an L-shaped corridor with a width of one unit? While it appears straightforward, it has eluded resolution for decades. In 1992, mathematician Joseph Gerver introduced a complex shape, known as Gerver’s sofa, as a strong candidate for the solution. However, proving that a larger shape could not exist remained an open question until now.
A Breakthrough in Mathematical Research
After a rigorous seven-year investigation, Dr. Baek confirmed that Gerver’s design is indeed optimal. He published his comprehensive 119-page proof on the preprint server arXiv in late 2024, concluding definitively that “no sofa wider than Gerver’s sofa can exist.” Uniquely, Dr. Baek’s work relied solely on logical reasoning rather than extensive computer simulations, marking a significant departure from many previous approaches.
Reflecting on the lengthy research journey, Dr. Baek described the process as one of resilience and creativity. “You keep holding on to hope, then breaking it, and moving forward by picking up ideas from the ashes,” he shared in an interview. “I’m closer to a daydreamer by nature, and for me, mathematical research is a repetition of dreaming and waking up.”
Recognition and Future Endeavors
Dr. Baek’s remarkable achievement has garnered global attention, being named one of the “Top 10 Math Discoveries of 2025” by Scientific American. The magazine noted the surprising aspect of his proof: “while many researchers have relied on large-scale computer simulations to solve for the maximum sofa size, it is surprising that Baek Jin Eon’s final solution does not depend on computers at all.” Currently, his proof is under peer review at the prestigious journal Annals of Mathematics, with strong confidence in its validity from the mathematical community.
The moving sofa problem has transcended academic circles, becoming a pop culture reference, most notably in the US sitcom Friends, where characters famously struggled to maneuver a sofa up a staircase. Scientific American humorously remarked that “explaining the ‘Pivot!’ shouted by Ross Geller required a 119-page paper.”
Dr. Baek began his exploration of the moving sofa problem while serving as a research specialist during mandatory military service and continued his studies in the United States before returning to South Korea as a postdoctoral researcher. Recently, he was selected for the June E Huh Fellow program, which supports young mathematicians under 39 for up to a decade. He is now focused on further challenges in optimization and combinatorial geometry.
