Mathematician solves decades-old banking problem with new findings
A long-standing mathematical puzzle known as the “sofa problem,” posed in 1966 by Austrian-Canadian mathematician Leo Moser, may have finally been solved. The problem concerns determining the maximum area of a single, planar shape that can navigate a right-angled corner in a corridor of unit width. This question, despite its apparently simple premise, has puzzled mathematicians for more than half a century.
Jineon Baek, a postdoctoral researcher in mathematics at Yonsei University in South Korea, has reportedly proposed a solution. According to one study Shared on the preprint website ArXiv on December 2, Baek showed that the maximum area of the hypothetical bank is 2.2195 units. This value refines the previously established range from 2.2195 to 2.37 units. While the evidence awaits peer review, experts are expected to verify its accuracy.
Origin and previous developments
The problem was initially conceptualized by Leo Moser and progress was made in 1992 when Joseph Gerver, professor emeritus at Rutgers University, proposed a U-shaped solution consisting of 18 curves. Gerver’s calculations suggested the lower limit of 2.2195 units for the area of the bank. Disagreements persisted over whether a larger bank could exist, with a 2018 computer-aided analysis suggesting an upper limit of 2.37 units.
Key insights from Baek’s proof
Baek’s findings reportedly confirm that Gerver’s solution represents the optimal configuration. By meticulously analyzing the shape’s geometry and movement, Baek demonstrated that the U-shaped design could achieve the maximum possible area for navigating the corner.
Although the study has yet to be published in a peer-reviewed journal, the mathematical community has shown significant interest. Images of the ‘Gerver sofa’ circulated on social media following Baek’s announcement, sparking discussions about the implications of this long-awaited resolution.
This breakthrough is expected to close the chapter on one of mathematics’ enduring conundrums, pending independent verification of Baek’s work.
