A mathematician from South Korea has successfully solved one of geometry’s most enduring conundrums, known as the “moving sofa problem.” This challenge, which has puzzled researchers for nearly 60 years, concerns identifying the two-dimensional shape with the largest area that can navigate through an L-shaped corridor of width one. Dr Baek Jin Eon, a 31-year-old research fellow at the Korea Institute for Advanced Study, has proven that no shape larger than a design proposed in 1992 can fit through such a corridor.
The moving sofa problem was first introduced in 1966 and poses a deceptively simple question that has stumped mathematicians for decades. In 1992, mathematician Joseph Gerver suggested a complex curved shape known as Gerver’s sofa as a potential solution. Despite its plausibility, no one had managed to demonstrate that a larger shape could not exist—until now. After seven years of rigorous work, Dr Baek has confirmed that Gerver’s design is indeed optimal. He outlined his findings in a comprehensive 119-page proof published on the preprint server arXiv in late 2024.
Dr Baek’s approach was distinct in that it relied exclusively on logical reasoning rather than advanced computer simulations, which have been the norm for many earlier attempts at this problem. He expressed the challenges of his research process, stating, “You keep holding on to hope, then breaking it, and moving forward by picking up ideas from the ashes.” His reflections illustrate the persistence required in tackling such complex mathematical concepts, describing his research as a blend of dreaming and awakening.
The significance of Dr Baek’s achievement has been recognized widely; Scientific American named his work one of the “Top 10 Math Discoveries of 2025.” The publication highlighted the surprising fact that Baek’s solution does not depend on computational tools, showcasing a more traditional approach to problem-solving in mathematics.
Currently, Dr Baek’s proof is under peer review at the Annals of Mathematics, a leading journal in the field. While the review process is ongoing, the mathematical community holds a high level of confidence in his findings. The moving sofa problem has also permeated popular culture, most notably referenced in the US sitcom Friends, where characters famously struggled to maneuver a sofa up a staircase. Scientific American humorously remarked that explaining Ross Geller’s memorable “Pivot!” required a substantial 119-page paper.
Dr Baek’s journey in mathematics began during his mandatory military service when he worked as a research specialist. He continued to develop his expertise through his doctoral studies in the United States and further as a postdoctoral researcher in South Korea. Recently, he was selected for the June E Huh Fellow programme, which supports young mathematicians under 39 for a period of up to a decade. He remains focused on optimization problems and challenges in combinatorial geometry, inspired by the success of his groundbreaking work on the moving sofa problem.
