SEOUL: A South Korean mathematician has won international recognition for solving a geometry puzzle that had resisted proof for nearly six decades.
US magazine Scientific American named the research by Dr Baek Jin-eon among its top 10 mathematical breakthroughs of 2025, the mathematics community said on Sunday (Jan 4).
Dr Baek, 31, is a research fellow at the June E Huh Center for Mathematical Challenges at the Korea Institute for Advanced Study (KIAS).
The so-called moving sofa problem asks how large a rigid shape can be while still being able to pass around a right-angled corner in an L-shaped corridor of a constant width of 1m.
First posed in 1966 by Austrian-Canadian mathematician Leo Moser, the puzzle became widely known because it can be understood without advanced mathematics and has appeared in US textbooks.
Over decades, researchers proposed increasingly efficient shapes while narrowing the possible range of solutions, but were unable to prove where the upper limit lay.
In 1968, British mathematician John Hammersley introduced a shape with an area of about 2.2074sq m.
In 1992, Rutgers University professor Joseph Gerver proposed a more complex curved figure with an area of roughly 2.2195 sq m, which became the leading candidate.
Although Dr Gerver’s design emerged as the leading candidate, no proof had shown that a larger shape was impossible.
Dr Baek’s work aimed to settle that question.
After seven years of research, he released a 119-page paper in late 2024 on the preprint server arXiv, arguing that Dr Gerver’s figure represents a hard upper limit.
Unlike earlier studies that relied heavily on computer-assisted estimates, Dr Baek used logical reasoning to establish optimality.
Describing the research process, he compared it to repeatedly building and discarding ideas.
“You keep holding on to hope, then breaking it, and moving forward by picking up ideas from the ashes,” he said in an interview with a web magazine published by KIAS.
“I’m closer to a daydreamer by nature, and for me, mathematical research is a repetition of dreaming and waking up.”
The paper is now under review at Annals Of Mathematics, one of the field’s most selective journals.
Dr Baek said the problem appealed to him because it lacked a clear theoretical framework.
“This sofa problem doesn’t have much historical context, and it wasn’t even clear whether there was theory behind it,” he said.
“I tried to connect it to existing ideas and turn it into an optimisation problem, creating tools suited to the question.”
He added that progress in such problems takes time. “It takes a long time for a problem to gain context,” Dr Baek said. “I feel like I planted a small seed.”
Dr Baek completed his doctorate at the University of Michigan and previously served as a research specialist at the National Institute for Mathematical Sciences.
He solved the problem at the age of 29 while working as a postdoctoral researcher at Yonsei University. - The Korea Herald/ANN
