One great problem, three kinds of immersion
From a story to your own conjecture
Problem stories open curiosity. The problem workshop is the next place, where curiosity becomes a testable idea.
- 1 · DiscoverYou are hereMeet the questionLearn when it appeared and why it still holds people’s attention.
- 2 · ChallengeTest one caseMake your first observation in five minutes with a drawing, calculation, or colors.
- 3 · DevelopBuild on ideasPublish an observation and grow it through comparisons, conjectures, and counterexamples.
Moving Sofa Problem — A Claimed Optimality Proof Under Review
What is the largest planar shape that can turn a right-angle corner in a unit-width corridor? In 2024 Jineon Baek posted a 119-page preprint claiming Gerver’s shape is optimal. It is a compelling proposed resolution still undergoing scrutiny.
Test small cases immediately with a drawing, divisors, or colored pencils.
The starting level measures how easily you can understand and test small cases. It is not the difficulty of a complete proof.
Jump to your first five minutesJineon Baek — author of the 119-page 2024 optimality preprint
Highlighted by Scientific American among notable 2025 mathematics results · peer review ongoing
See the puzzle visually
What is the largest shape that can turn through an L-shaped corridor of width 1? In 2024 Jineon Baek posted a 119-page preprint claiming Gerver’s 2.2195 is optimal. It is a compelling proposed proof still under public review in 2026.
Problem statement
What is the maximum area of a connected planar rigid shape that can move around a right-angle corner in a unit-width corridor? A 2024 preprint claims that Gerver’s shape, of area about 2.2195, is optimal.
The story of this puzzle
Moser popularized the problem in 1966. Hammersley proposed an area π/2+2/π≈2.2074 construction, and in 1992 Joseph Gerver produced an 18-piece boundary of area about 2.2195. In November 2024 Jineon Baek posted a 119-page arXiv preprint claiming a proof of Gerver optimality using variational and geometric arguments. Scientific American highlighted it among notable 2025 mathematics results. As of the public 2026 record, expert and journal review is still in progress, so the service distinguishes a compelling claimed proof from a fully settled published theorem.
Try it yourself
Try with paper. Draw an L-corridor of width 1, fit shapes (rectangles, semicircles, rounded rectangles) and rotate around the corner. Which has the largest area? Gerver's shape stitches 18 curves that each fit precisely at different rotation angles.
Beyond MathVoyage
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