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The open problem -- the "moving sofa problem" -- has possibly just been solved!
- big-green-man 2y agoLinked paper from the x thread: https://arxiv.org/pdf/2411.19826 https://arxiv.org/pdf/2411.19826
- aeonik 2y agoI had ChatGPT summarize this paper for me. It's pretty impressive to me that a single post doc has this much breadth in a single paper. Convex Geometry - Brunn-Minkowski theory - Surface Area Measure Measure Theory - Lebesgue–Stieltjes Measure - Green’s Theorem Differential Geometry - Weak derivatives for boundaries - Trajectories and rotation paths Optimization and Functional Analysis - Quadratic functionals - Concavity and global optimization Combinatorial Geometry - Balanced polygons - Iterative approximation and discretization Computational Geometry - Numerical simulations - Verification of bounds and injectivity Advanced Theorems - Mamikon’s Theorem - Jordan Curve Theorem
- jonathrg 2y agoWould appreciate if someone could summarize the thread here, since tweets after the first are not visible if you don't have an account.
- Weetile 2y agoI think it would probably take me 50 years just to fully comprehend this proof alone. Amazing work.