29-year-old South Korean mathematician cracks geometry puzzle unsolved since 1966

U.S. magazine Scientific American recently named the work of Dr. Baek Jin-eon among the world’s top 10 mathematical breakthroughs of 2025, highlighting a result that mathematicians have chased since the 1960s.

Dr. Baek, now 31, is a research fellow at the June E Huh Center for Mathematical Challenges at the Korea Institute for Advanced Study (KIAS). He completed the breakthrough when he was 29, The Straits Times reported.

The puzzle, known as the "moving sofa problem," asks a deceptively simple question: What is the largest possible shape that can move around a right-angled corner in an L-shaped corridor that is 1 meter wide?

Illustration of the "moving sofa problem". Photo courtesy of KIAS

First posed in 1966 by Austrian-Canadian mathematician Leo Moser, the problem became famous because it can be understood without advanced mathematics. It has appeared in textbooks and fascinated generations of researchers.

Over the years, mathematicians proposed increasingly efficient shapes, gradually narrowing the range of possible solutions. In 1968, British mathematician John Hammersley introduced a shape with an area of about 2.2074 sq.m. In 1992, Rutgers University professor Joseph Gerver proposed a more intricate curved figure with an area of roughly 2.2195 sq.m.

Gerver’s design became the leading candidate, but no one could prove that a larger shape was impossible.

That was the gap Dr. Baek set out to close.

After seven years of work, he released a 119-page paper in late 2024 on the preprint server arXiv, arguing that Gerver's figure represents a strict upper limit. Unlike earlier attempts that relied heavily on computer-assisted estimates, Dr. Baek used logical reasoning to establish the result.

Describing the process, he said mathematical research often involves building ideas, discarding them, and starting again.

"You keep holding on to hope, then breaking it, and moving forward by picking up ideas from the ashes," he said in an interview published by KIAS.

"For me, mathematical research is a repetition of dreaming and waking up," he added.

The paper is now under review at Annals of Mathematics, one of the most selective journals in the field.

Dr. Baek said the problem appealed to him because it lacked a clear theoretical framework.

"It wasn’t even clear whether there was theory behind it," he said, adding that he worked to connect the puzzle to existing ideas and reframe it as an optimization problem.

Dr. Baek earned his doctorate from the University of Michigan and previously worked at the National Institute for Mathematical Sciences. He solved the problem while working as a postdoctoral researcher at Yonsei University.