Korean mathematician solves 60-year-old moving sofa problem with pure logic

A 31-year-old mathematician in South Korea has done what the scientific world could not: he has solved the moving sofa problem, a deceptively simple geometry puzzle that has resisted solution for nearly six decades. His name is Baek Jin-eon, and he did it without a single computer simulation, armed only with rigorous logical reasoning and 119 pages of mathematical proof.

The problem itself sounds like something you could sketch on a napkin. Imagine a rigid sofa—an object that cannot bend or fold—trying to navigate a right-angle turn in an L-shaped hallway that is exactly one meter wide. What is the largest possible shape that object could have and still make it through without getting wedged? The question seems almost trivial until you actually try to answer it. In 1966, an Austro-Canadian mathematician named Leo Moser posed this puzzle to the world, and it spread through American universities like a mathematical virus, capturing the imagination of professors and students who kept returning to it, year after year, unable to let it go.

For sixty years, researchers made incremental progress. In 1968, a British mathematician named John Hammersley proposed a shape measuring approximately 2.2074 square meters. Nearly thirty years later, Joseph Gerver from Rutgers University refined the answer to 2.2195 square meters—a curved figure that seemed to represent the upper limit. But here was the problem: nobody could prove it. The answer floated in a kind of theoretical limbo. Researchers could not demonstrate that you could not do better, which meant the question remained fundamentally unresolved, no matter how close the estimates seemed to be.

Baek first encountered this puzzle while working as a researcher at the National Institute for Mathematical Sciences during his mandatory military service in South Korea. What captivated him was not just the question itself, but the absence of a solid theoretical foundation beneath it. Here was a problem that seemed elementary yet remained unsolved, suspended without the conceptual scaffolding that might support a real answer. That missing framework became his obsession. For seven years, he pursued it through his doctorate at the University of Michigan and then as a postdoctoral researcher at Yonsei University. At 29 years old, he solved it.

His approach was radically different from everything that had come before. While his predecessors had relied on computer simulations to refine their estimates and narrow the possibilities, Baek used only logical reasoning. He established, through pure mathematical thought, that Gerver's shape truly represented the insurmountable limit—the absolute maximum. No numerical brute force. No computational assistance. Just conceptual density, page after page, each one packed with rigorous argument.

In late 2024, Baek published his results on arXiv, the preprint server where researchers share discoveries before formal peer review. The paper is now under evaluation at Annals of Mathematics, one of the most prestigious journals in the field. Scientific American recognized the breakthrough as one of the ten greatest mathematical advances of 2025. To understand his dedication, you need to know that Baek has dreamed of mathematics since childhood. When he learned in third or fourth grade that he could study mathematics as a profession, it became his life's ambition. Even when his family faced financial hardship, he never wavered. His passion is not performative; it is fundamental. "Even if I did something else," he has said, "I don't think I could abandon the beauty of mathematics."

He describes the research process itself like an artist confessing to their craft. "You hold onto hope, then you crush it, and you move forward by gathering ideas from the ashes," he explained in an interview shared by the Korean Institute of Advanced Study. "By nature, I'm rather a dreamer. For me, mathematical research is a repetition of dreams and awakenings." Now an Associate Researcher at the June E Huh Center for Mathematical Challenges at the Korean Institute of Advanced Study, Baek views his success not as a finish line but as a seed planted. "It takes time for a problem to gain its context," he reflects. With one sofa mystery solved, thousands more remain waiting in the mathematical universe.