ChatGPT 5.5 Pro helped push four-person EFX fair division proof to nine objects
kimmonismus · x · 2026-09-03
Kimmonismus recounts a call with computer scientist Eyad Alkassar about how ChatGPT 5.5 Pro helped move the frontier on an open CS problem.
The problem is intuitive: four people dividing nine objects, each valuing them differently, seeking an allocation where nobody would envy another's pile even after any single item is removed from it — known as EFX (envy-freeness up to any good).
- Whether complete EFX allocations always exist for four or more people remains open
- The previous general guarantee for four people covered only seven objects
- A new preprint by Alkassar, Mahmoud Fouz and renowned computer scientist Kurt Mehlhorn extends the proof to nine objects
- It started as a dinner challenge from Alkassar to Mehlhorn to use AI
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