Korean Mathematician Solves Long-Standing Moving Sofa Problem

A breakthrough in geometry has emerged as Dr Baek Jin Eon, a 31-year-old mathematician from South Korea, has resolved the notorious moving sofa problem. This challenge, which has perplexed researchers for nearly six decades, revolves around finding the two-dimensional shape with the largest area that can be moved through a right-angled corridor of fixed width. Dr Baek’s proof, published on the preprint server arXiv in late 2024, demonstrates unequivocally that no shape larger than the previously proposed design, known as Gerver’s sofa, can navigate the corridor.

The moving sofa problem was first introduced in 1966 and asks a deceptively simple question: What is the maximal area of a shape that can be transported through an L-shaped corridor of width one? Despite its straightforward premise, the problem has challenged mathematicians for decades. In 1992, mathematician Joseph Gerver proposed a complex curved shape, which many believed could be the solution. However, proving that no larger shape existed remained elusive until now.

After dedicating seven years to this intricate problem, Dr Baek successfully confirmed that Gerver’s design is indeed optimal. His comprehensive 119-page proof is notable not only for its clarity but also for its reliance on logical reasoning rather than computer simulations, a departure from many previous attempts in the field.

Recognition and Impact on Mathematics

Describing his research journey, Dr Baek likened it to a process of trial and error, where ideas are built, dismantled, and reimagined. “You keep holding on to hope, then breaking it, and moving forward by picking up ideas from the ashes,” he shared. His approach reflects a deep commitment to mathematical inquiry and creativity, revealing a personal connection to the subject.

The significance of Dr Baek’s work has not gone unnoticed. Scientific American recognized his achievement by naming it one of its “Top 10 Math Discoveries of 2025,” highlighting the fact that his solution did not rely on advanced computational tools. The magazine humorously noted that explaining the iconic “Pivot!” scene from the popular television show Friends, where characters struggle to move a sofa up a staircase, would require a 119-page paper, underscoring the cultural resonance of the moving sofa problem.

Currently, Dr Baek’s proof is undergoing peer review at the Annals of Mathematics, one of the most esteemed journals in the mathematics community. While the review process is ongoing, the confidence in his results is palpable among mathematicians worldwide.

A Journey Through Mathematics

Dr Baek’s fascination with the moving sofa problem began during his mandatory military service, where he served as a research specialist. He continued his exploration through his doctoral studies in the United States and later as a postdoctoral researcher in South Korea. His contributions to the field have been recognized through his selection for the June E Huh Fellow programme, which supports promising young mathematicians under 39 for up to a decade.

Now, Dr Baek is focusing on optimisation problems and challenges in combinatorial geometry, further contributing to the rich tapestry of mathematical research. His solution to the moving sofa problem not only closes a long-standing chapter in mathematical history but also inspires future inquiries into geometric puzzles that continue to captivate the imagination.