A mathematician from South Korea has successfully solved a longstanding problem in geometry, known as the moving sofa problem. Dr Baek Jin Eon, a 31-year-old research fellow at the Korea Institute for Advanced Study, demonstrated that no shape larger than a previously proposed design can navigate through a right-angled corridor of fixed width. This breakthrough concludes a challenge that has persisted for nearly 60 years.
The moving sofa problem asks a straightforward yet complex question: what is the two-dimensional shape with the largest possible area that can be transported through an L-shaped corridor of width one? Although the problem appears simple, it has perplexed mathematicians for decades. In 1992, mathematician Joseph Gerver introduced a complex curved shape known as Gerver’s sofa, which was believed to be an optimal solution. However, proving that no larger shape could exist remained elusive until Dr Baek’s recent work.
After dedicating seven years to the problem, Dr Baek published a comprehensive 119-page proof on the preprint server arXiv in late 2024. His findings conclude that “no sofa wider than Gerver’s sofa can exist.” This proof stands out as it relies solely on logical reasoning, distinguishing it from many previous attempts that utilized large-scale computer simulations.
A Journey Through Mathematical Challenges
Describing the arduous research process, Dr Baek likened it to an iterative journey of building and abandoning ideas. “You keep holding on to hope, then breaking it, and moving forward by picking up ideas from the ashes,” he shared in an interview. His reflective nature led him to view mathematical research as a cycle of dreaming and awakening.
The significance of Dr Baek’s accomplishment has not gone unnoticed. Scientific American has recognized his work as one of the “Top 10 Math Discoveries of 2025.” The magazine highlighted that Dr Baek’s solution is remarkable for its complete independence from computer assistance, contrasting sharply with the more common reliance on technology in contemporary mathematical research.
Dr Baek’s proof is currently under peer review at the Annals of Mathematics, a highly esteemed journal in the field. Although the review process is still ongoing, confidence in the validity of his findings is strong within the mathematical community.
Impact Beyond Academia
The moving sofa problem has transcended academic circles, finding a place in popular culture through its mention in the American sitcom Friends. One memorable scene features characters struggling to maneuver a sofa up a staircase, with the term “Pivot!” becoming a cultural catchphrase. Scientific American humorously noted that explaining Ross Geller’s iconic shout required a substantial mathematical paper.
Dr Baek began exploring the moving sofa problem during his compulsory military service and continued through his doctoral studies in the United States. His dedication to the field led him to be selected for the June E Huh Fellow programme in 2023, which supports young mathematicians under 39 for up to a decade. He is now focused on further challenges in optimization problems and combinatorial geometry.
This development marks a significant milestone not only for Dr Baek but also for the field of mathematics, as it highlights the enduring intrigue of geometric puzzles and the innovative spirit of researchers dedicated to solving them.
