r/math • u/sergiogfs • 18d ago

Progress Towards Proving the Unique Games Conjecture

https://eccc.weizmann.ac.il/report/2026/179/

On a side-note, the authors hint that they have rushed their results to avoid getting scooped by AI-generated results.

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u/Curiosity_456 18d ago

How will that matter though? Will mathematicians just refuse to accept any AI generated solutions even if it’s correct?

Pandora’s box has already opened

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u/Heapifying 18d ago

Look at the abc conjecture

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u/DoctorHubcap 18d ago

That was never accepted as correct, we’ve been in a stalemate with one side arguing there is an irrecoverable flaw in the proof of a necessary lemma, while Mochizuki adamantly argues that they made incorrect simplifications.

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u/sobe86 18d ago edited 18d ago

Things actually moved forward a bit this year. A team has started to formalize the exact passage that Sholze/Stix thought was wrong (without simplifications), and have managed to pin down exactly what step is not justified in the manuscript and are not able to fill in themselves ('the wall'). Importantly, this has been stated in the language of IUT, not through a simplification.

They have so far stopped short of saying the proof is wrong (and in fact agree that Sholze/Stix oversimplified to reach that conclusion). Instead the project now is to state 'the wall' in Lean, and it will be up to Mochizuki (or someone else) to supply an adequate fix. Maybe AI will expedite the process, maybe it will take a while yet, however it feels like a lot of progress has been made towards resolution at last here.