A significant breakthrough in mathematics has occurred with the resolution of the “moving sofa problem,” a challenge 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, has proven that no shape larger than a previously suggested design can navigate a right-angled corridor of fixed width.
The moving sofa problem poses a seemingly simple question: what is the two-dimensional shape with the largest area that can fit through an L-shaped corridor of width one? Although the question is easy to visualize, it has eluded proof for decades. In 1992, mathematician Joseph Gerver introduced a complex curved shape, known as Gerver’s sofa, as a likely solution. Despite extensive efforts, no one had successfully demonstrated that a larger shape could not exist.
After seven years of meticulous research, Dr Baek conclusively showed that Gerver’s design is indeed optimal. He published his comprehensive 119-page proof on the preprint server arXiv in late 2024, asserting that “no sofa wider than Gerver’s sofa can exist.” Remarkably, Dr Baek’s work relies solely on logical reasoning instead of extensive computer simulations, setting it apart from many prior attempts.
Reflecting on his research journey, Dr Baek compared it to a cycle of hope and disappointment. He remarked, “You keep holding on to hope, then breaking it, and moving forward by picking up ideas from the ashes.” He describes himself as “closer to a daydreamer by nature,” indicating that his mathematical inquiries often resemble a process of dreaming and waking.
This groundbreaking research has garnered widespread acclaim, with Scientific American naming it one of its “Top 10 Math Discoveries of 2025.” The publication highlighted that while many researchers have utilized computer simulations to explore maximum sofa sizes, Dr Baek’s solution is notable for its independence from such technology.
Currently, Dr Baek’s proof is undergoing peer review at the Annals of Mathematics, one of the field’s most prestigious journals. Despite the ongoing review, confidence in his findings remains high among the mathematical community.
The moving sofa problem has gained traction beyond academic circles, becoming a cultural reference through its mention in the US sitcom Friends. In one memorable scene, characters struggle to maneuver a sofa up a staircase, with the phrase “Pivot!” becoming emblematic of the show’s comedic moments. In a light-hearted nod, Scientific American quipped that “explaining the ‘Pivot!’ shouted by Ross Geller required a 119-page paper.”
Dr Baek began tackling this complex problem during his mandatory military service. He continued his work throughout his doctoral studies in the United States and later 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 up to a decade. Dr Baek is now focused on further challenges in the realms of optimization and combinatorial geometry, promising to contribute more to the field in the years ahead.
