A significant breakthrough in geometry has been achieved by Dr. Baek Jin Eon, a 31-year-old research fellow at the Korea Institute for Advanced Study. He has successfully resolved the “moving sofa problem,” a challenge that has perplexed mathematicians for nearly 60 years.
The moving sofa problem asks for the two-dimensional shape with the largest possible area that can navigate through an L-shaped corridor of width one. This seemingly simple question has eluded proof for decades. In 1992, mathematician Joseph Gerver proposed a complex curved shape, known as Gerver’s sofa, as a potential solution, but no one could confirm whether a larger shape could exist.
After seven years of dedicated research, Dr. Baek demonstrated that Gerver’s design is indeed optimal, proving that no shape larger than Gerver’s sofa can fit through the corridor. His comprehensive 119-page proof was published on the preprint server arXiv in late 2024, concluding with the assertion that “no sofa wider than Gerver’s sofa can exist.”
Dr. Baek's proof stands out as it was achieved solely through logical reasoning, without reliance on computer simulations, marking a significant advancement in mathematical research
Baek likened his extensive research process to the act of repeatedly building and abandoning ideas. He expressed, “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,” viewing mathematical research as a cycle of dreaming and waking up.
His groundbreaking work has been recognized by Scientific American as one of its “Top 10 Math Discoveries of 2025,” a selection that highlights significant breakthroughs in the field. The magazine noted that, unlike many researchers who rely on large-scale computer simulations to determine the maximum sofa size, Baek Jin Eon’s final solution does not depend on computers at all.
Currently, Dr. Baek’s proof is under peer review at the Annals of Mathematics, one of the most prestigious journals in the discipline. Despite the ongoing review process, confidence in the result remains high within the mathematical community.
The moving sofa problem has captured the imagination of both popular culture and academia, most famously referenced in the US sitcom Friends, where characters face challenges maneuvering 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 work on this problem while serving as a research specialist during his mandatory military service, continuing through his doctoral studies in the US and later as a postdoctoral researcher in South Korea.