Korean Mathematician Solves 60-Year-Old Moving Sofa Problem

A mathematician from South Korea has successfully solved the enduring “moving sofa problem,” a geometrical puzzle that has perplexed researchers for nearly six decades. Dr Baek Jin Eon, a 31-year-old research fellow at the Korea Institute for Advanced Study, proved that no two-dimensional shape larger than a previously proposed design can navigate a right-angled corridor of fixed width. This groundbreaking work concludes a mathematical inquiry that began in 1966.

The moving sofa problem poses a seemingly simple question: what is the largest area of a shape that can be transported through an L-shaped corridor that is one unit wide? While the concept is easy to visualize, finding a definitive answer has eluded mathematicians for decades. In 1992, mathematician Joseph Gerver introduced a complex curved shape, now known as Gerver’s sofa, as a possible solution. Despite its prominence, no one had been able to substantiate that a larger shape could not exist—until now.

After seven years of dedicated research, Dr Baek demonstrated that Gerver’s design is indeed optimal. He published his extensive proof, comprising 119 pages, on the preprint server arXiv in late 2024. His findings assert that “no sofa wider than Gerver’s sofa can exist.” Notably, Dr Baek’s proof is distinguished by its reliance solely on logical reasoning, eschewing the extensive computer simulations that many researchers have utilized in their attempts to solve this problem.

Reflecting on his research journey, Dr Baek described the process as one of constant iteration and renewal. “You keep holding on to hope, then breaking it, and moving forward by picking up ideas from the ashes,” he explained in an interview. “I’m closer to a daydreamer by nature, and for me, mathematical research is a repetition of dreaming and waking up.”

Dr Baek’s work has gained significant recognition, earning a place on Scientific American’s list of the “Top 10 Math Discoveries of 2025.” The magazine highlighted the surprising aspect of Baek’s solution: “while many researchers have relied on large-scale computer simulations to solve for the maximum sofa size, it is surprising that Baek Jin Eon’s final solution does not depend on computers at all.”

Presently, Dr Baek’s proof is undergoing peer review at the Annals of Mathematics, one of the field’s most esteemed journals. Despite the ongoing review process, confidence in the validity of his results remains high within the mathematical community.

The moving sofa problem has not only intrigued mathematicians but has also captured the public’s imagination, notably through its humorous reference in the popular US sitcom Friends, where the character Ross Geller famously shouts “Pivot!” while attempting to maneuver a sofa up a staircase. Scientific American humorously noted that explaining this iconic moment would require a 119-page paper.

Dr Baek’s journey into this mathematical conundrum began during his mandatory military service, where he worked as a research specialist. He continued his exploration of the problem through his doctoral studies in the United States and later as a postdoctoral researcher in South Korea. His talent was recognized last year when he was selected for the June E Huh Fellow programme, which supports young mathematicians under 39 for up to a decade.

Looking ahead, Dr Baek is focused on furthering his research in optimization problems and challenges within combinatorial geometry, as he continues to make significant contributions to the field.