A decades-old mathematical puzzle, famously visualised by a struggling Ross Geller in the sitcom Friends, has finally been solved. A Korean mathematician has provided definitive proof for the solution to the 'moving sofa problem', a challenge that has perplexed geometricians for nearly 60 years.
The Pivot Problem: A 60-Year Geometric Quest
The problem, first posed in 1966, asks a seemingly simple question: what is the largest possible area of a two-dimensional shape that can be manoeuvred around a right-angled corner in a corridor of width one? While easy to imagine, a rigorous proof remained elusive.
In 1992, mathematician Joseph Gerver proposed a complex, curved shape as the likely answer, which became known as 'Gerver's sofa'. For over three decades, however, no one could prove that a larger shape was impossible.
Now, Dr Baek Jin Eon, a 31-year-old research fellow at the Korea Institute for Advanced Study, has ended the debate. After seven years of dedicated work, he has demonstrated that Gerver's design is indeed optimal. His monumental 119-page proof, published on the arXiv preprint server in late 2024, conclusively states that 'no sofa wider than Gerver's sofa can exist'.
A Triumph of Pure Logic Over Computation
What makes Dr Baek's achievement particularly notable is his methodology. Unlike many modern mathematical efforts that lean on powerful computer simulations, his proof relied entirely on logical reasoning and analytical geometry. This feat was highlighted when his work was named one of Scientific American's 'Top 10 Math Discoveries of 2025'.
Describing his arduous journey, Dr Baek compared the process to a cycle of dreaming and disillusionment. 'You keep holding on to hope, then breaking it, and moving forward by picking up ideas from the ashes,' he explained. He began working on the problem during his mandatory military service in South Korea and continued through his doctoral studies in the United States.
From Academic Puzzle to Pop Culture Icon
The moving sofa problem's journey from academic journal to public consciousness was cemented by its appearance in Friends. The scene where Ross, Rachel, and Chandler desperately shout 'Pivot!' while trying to haul a sofa up a staircase became a perfect, if frustrating, real-world analogy. Scientific American wryly noted that 'explaining the 'Pivot!' shouted by Ross Geller required a 119-page paper'.
Dr Baek's proof is currently undergoing peer review at the prestigious Annals of Mathematics. While the formal process continues, the mathematical community has expressed high confidence in his groundbreaking result. A recipient of the June E Huh Fellow programme, which supports exceptional young mathematicians, Dr Baek now continues his research into optimisation and combinatorial geometry.
