Korean Mathematician Conquers Long-Standing Moving Sofa Problem

A mathematician from South Korea has successfully resolved one of geometry’s most perplexing challenges, known as the “moving sofa problem.” Dr Baek Jin Eon, aged 31 and a research fellow at the Korea Institute for Advanced Study, achieved this significant milestone through a proof that does not rely on computer simulations. His work concludes nearly 60 years of inquiry into the shape that can navigate a right-angled corridor of fixed width with the largest possible area.

The moving sofa problem, which originated in 1966, poses a seemingly simple question: what is the two-dimensional shape with the maximum area that can fit through an L-shaped corridor of width one? Despite its straightforward nature, this problem has eluded definitive proof for decades. In 1992, mathematician Joseph Gerver proposed a complex, curved shape, known as Gerver’s sofa, as a potential solution. However, it remained unproven whether a larger shape could exist until Dr Baek’s breakthrough.

After dedicating seven years to this research, Dr Baek’s proof, which spans 119 pages, was published on the preprint server arXiv in late 2024. He demonstrated that Gerver’s design is indeed optimal, stating unequivocally, “no sofa wider than Gerver’s sofa can exist.” His methodology stood out as it relied entirely on logical reasoning rather than extensive computational resources, a departure from many prior attempts.

Describing the arduous research journey, Dr Baek emphasized the challenges he faced. “You keep holding on to hope, then breaking it, and moving forward by picking up ideas from the ashes,” he explained in an interview. He characterized his approach to mathematical research as a cycle of dreaming and awakening, illustrating the creative process inherent in problem-solving.

The mathematical community has responded positively to Dr Baek’s work, which was recently recognized by Scientific American as one of its “Top 10 Math Discoveries of 2025.” The publication highlighted the uniqueness of Baek’s solution, noting that it does not depend on computer simulations, a common tool in contemporary mathematical research.

Currently, Dr Baek’s proof is undergoing peer review at the Annals of Mathematics, a leading journal in the field. While the review process is still ongoing, there is considerable confidence in the validity of his findings. The moving sofa problem has also made its mark in popular culture, most notably featured in the US sitcom Friends, where a comedic scene involves characters struggling to maneuver a sofa up a staircase. In a light-hearted remark, Scientific American quipped that explaining the infamous “Pivot!” shouted by Ross Geller could require a lengthy academic paper.

Dr Baek’s journey to this achievement began during his mandatory military service, where he first engaged with the moving sofa problem. He continued his exploration through his doctoral studies in the United States and later as a postdoctoral researcher in South Korea. In recognition of his potential, he was selected for the June E Huh Fellow programme, which supports young mathematicians under the age of 39 for up to a decade.

As Dr Baek continues his research, he is now focusing on optimization problems and challenges in combinatorial geometry. His recent success not only resolves a long-standing mathematical enigma but also showcases the enduring nature of inquiry and creativity in the field of mathematics.