The problem
Determine the supremum of areas of plane regions ("sofas") that can be moved continuously through a right-angled hallway of width 1 (an L-shaped corner), and exhibit a maximiser.
The Moving Sofa Problem
historicReferences
History & significance
Moser asked in 1966. Dan Romik's research programme systematised candidate shapes; Dan Gerver's 1992 design reached ≈ 2.2195 — long believed optimal, never proven. Lower and upper bounds crept from 2.0929 upward over decades of incremental geometry.
Connected problems
The resolution (human proof)
Settled November 2024 by Jineon Baek (Yonsei University): a 119-page arXiv paper proves Gerver's sofa attains the maximum area ≈ 2.219531… The proof pins down the shape of maximisers via careful analysis of rotation paths and eliminates all rival families — purely human mathematics, no computation heavier than calculus. A rare modern instance of a beloved folkloric problem dying of elegance rather than exhaustion.