What does it take to solve a puzzle that’s stumped mathematicians for nearly sixty years? For Baek Jin-eon, it meant years of stubborn dedication, a fearless approach to right angles, and 119 pages of pure reasoning—no computer assistance required.
The Moving Sofa Problem: Child’s Play, Mathematicians’ Obsession
The so-called “moving sofa problem” seems simple at first: Imagine trying to maneuver a rigid sofa around a right-angled corner in an L-shaped hallway that’s exactly 39.4 inches wide (1 meter). What’s the largest-sized sofa you could possibly move around that bend, squeezing through without forcing it? The question is easy enough to state, but devilishly hard to answer.
The puzzle was first posed in 1966 by Austro-Canadian mathematician Leo Moser. It settled into American math textbooks, captivating professors and students. Over decades, mathematicians carefully chipped away at possible solutions, each one nudging a bit closer to perfection.
Back in 1968, British mathematician John Hammersley suggested a sofa shape covering about 23.77 square feet (2.2074 square meters). In 1992, Joseph Gerver at Rutgers University improved this with a curved design of roughly 23.89 square feet (2.2195 square meters). For more than thirty years, no one managed to do better—or prove that Gerver’s shape was the absolute limit.
Baek Jin-eon: The Mathematician Who Refused to Give Up
Baek Jin-eon, a South Korean mathematician, first encountered this infamous challenge during his mandatory military service at the National Institute for Mathematical Sciences. He was drawn in by its very lack of structure—a problem floating without a clear framework, almost in conceptual “weightlessness.” That absence became the engine for years of work. For seven years, from his doctoral studies at the University of Michigan to his postdoctoral research at Yonsei University in South Korea, Baek pursued the sofa’s secret. By age 29, he had found a solution.
Unlike those before him, Baek avoided computer simulations entirely. He relied only on logic and rigorous mathematical analysis, ultimately showing in a 119-page proof that Gerver’s sofa is as large as possible—you cannot design a bigger rigid sofa to round the bend. Every step was written with pen and paper, not code.
A Dream Fulfilled—And New Ones Begin
Baek’s detailed proof was published on arXiv in late 2024. As of early 2026, it has been recognized by Scientific American as one of the ten most significant mathematical breakthroughs of 2025, and is under review at the prestigious Annals of Mathematics.
For Baek, mathematics has always been a dream. “When I learned in third or fourth grade that you could study mathematics professionally, it became my dream,” he said. Even when his family faced financial hardship, he never gave up. “Even if I did something else, I don’t think I could give up the beauty of mathematics.” Describing his research process, Baek likens it to an artist’s struggle: “You keep hope, then crush it, and advance by picking up ideas from the ashes.” For him, each discovery is a cycle of dreams and awakenings.
Baek is now an associate researcher at the June E Huh Center for Mathematical Challenges at the Korean Institute for Advanced Study. He sees this achievement not as an end, but a new beginning: “It takes time for a problem to gain its context,” he says.
A Sofa, a Pivot, and a Touch of Humor
With a nod to pop culture, Scientific American joked that solving the moving sofa problem requires more effort than Ross screaming “Pivot!” in the classic Friends episode—here, it took 119 pages of proof.
Now, with one legendary sofa puzzle finally resolved in the mathematical world, Baek has turned his attention to new optimization and combinatorial geometry challenges. One stubborn sofa has found its place. Hundreds of puzzles remain. If only moving your couch at home were this satisfying.
