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Korean mathematician solves decades-old 'moving sofa problem'

Published: 05 Jan. 2026, 12:56

Baek Jin-eon, a researcher at the June E Huh Center for Mathematical Challenges at the Korea Institute for Advanced Study, explains the moving sofa problem. [KOREA INSTITUTE FOR ADVANCED STUDY]

A 31-year-old Korean mathematician solved one of the oldest math puzzles and was recognized as one of Scientific American’s top math breakthroughs of 2025.

The “Optimality of Gerver's Sofa” study by Baek Jin-eon, a research fellow at the June E Huh Center for Mathematical Challenges at the Korea Institute for Advanced Study, was listed as one of “The 10 Biggest Math Breakthroughs of 2025" by the magazine Scientific American.

The “moving sofa problem” asks a deceptively simple question: What is the largest "sofa," or shape, that can slide through an L-shaped hallway measuring 1 unit across — with the exact unit not mattering — without being lifted?

Canadian mathematician Leo Moser posed the problem in 1966. While the challenge seems simple, mathematicians have long treated it as a conundrum, especially after Joseph Gerver introduced a candidate shape known as “Gerver's sofa” in 1992.

Combining multiple curves, the form of “Gerver’s sofa” had the largest known area at the time, and researchers treated it as the most promising solution for decades.

No one, however, could prove that no shape larger than Gerver’s sofa could pass through the hallway. The problem therefore remained unsolved, and some researchers focused on narrowing the range of possibilities through computer simulations.

Baek Jin-eon, a researcher at the June E Huh Center for Mathematical Challenges at the Korea Institute for Advanced Study, explains the moving sofa problem. [KOREA INSTITUTE FOR ADVANCED STUDY]

After seven years of work, Baek posted a 100-plus page paper in late 2024 that proves no shape with an area larger than Gerver’s sofa can pass through the hallway, regardless of how it moves.

Earlier studies relied on computers to test possible sofa shapes one by one, but Baek pursued a proof-based approach. He translated the sofa’s shape and motion into a mathematical framework, then applied optimization theory to determine the largest possible area under the problem’s constraints and showed that Gerver’s sofa reaches that limit.

Baek has submitted his study to the Annals of Mathematics, one of the field's most prestigious journals. It now awaits peer review.

Baek graduated from the Korea Science Academy of KAIST and the mathematics department at Pohang University of Science and Technology and earned his doctorate at the University of Michigan. He was selected last year as a research fellow at the June E Huh Center for Mathematical Challenges, a program that provides long-term support for mathematicians under age 39, and he continues his research in combinatorial geometry and optimization.

Baek's achievement wasn't by chance. He fell in love with math as a child and never once let go of his dream of becoming a mathematician, despite his family's financial hardships.

Baek Jin-eon, a researcher at the June E Huh Center for Mathematical Challenges at the Korea Institute for Advanced Study [KOREA INSTITUTE FOR ADVANCED STUDY]

“After I learned in third or fourth grade that I could study math as a profession, my dream has always been the same: to be a mathematician,” Baek said in an interview that the Korea Institute for Advanced Study released in May 2025. “Even if I did something else, I don’t think I could let go of the beauty of mathematics.”

Baek also said he wants to return the support he received as a student.

“My family did not have much, but my mother kept looking for educational [opportunities], and that is how I learned about the KAIST Global Institute of Talented Education.”

He said middle school teachers pooled their own money to buy him a laptop and help him attend an English cram school as he prepared to take the entrance exam for a selective science-focused high school.

“That kind of support [...] made me who I am today,” Baek said. “I grew through people’s [...] and institutions’ support, so I want to return that [favor] to society someday.”

This article was originally written in Korean and translated by a bilingual reporter with the help of generative AI tools. It was then edited by a native English-speaking editor. All AI-assisted translations are reviewed and refined by our newsroom.
BY KWEN YU-JIN [[email protected]]