The open problem -- the "moving sofa problem" -- has possibly just been solved! | Hacker News Reader

The open problem -- the "moving sofa problem" -- has possibly just been solved!

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12 pointsNavinF4 comments

Would appreciate if someone could summarize the thread here, since tweets after the first are not visible if you don't have an account.

I 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

I think it would probably take me 50 years just to fully comprehend this proof alone. Amazing work.