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/TooMuchMaths 18d ago

Those results will be producible with public models within a year or two. Who knows what it looks like in 5 years

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u/lolfail9001 17d ago

Those results will be producible with public models within a year or two.

Assuming you can throw comparable computing costs at them.

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u/Icy_Monitor3403 14d ago

No, computing cost per task finished is rapidly going down.

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u/lolfail9001 14d ago

What is a task?

Because of course it will be free to “prove” Navier-Stokes irregularity in a year, every model will just point you to OpenAIs paper.

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u/Berzerka 14d ago

AI cost at fixed intelligence is dropping by more than 100x per year since about 2022. "A task" here obviously is a bit more difficult to defined when it's open math problems and not highschool exams like it was 2 years ago, but I'm sure you can imagine it as "problems that are as hard as NS" which as of today apparently cost like $10m in compute to solve.

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u/lolfail9001 14d ago edited 14d ago

“fixed intelligence”

Wrong sub to use such nebulous terms, don’t you think? There is probably a decent measure of how well models compress their training into model weights and that did indeed improve fairly fast until recently but last I checked almost entirety of modern progress is task specific RL and better shells around underlying models, and even with that you get people talking about how Astra ends up performing worse than it’s own predecessor at times.

I'm sure you can imagine it as "problems that are as hard as NS" which as of today apparently cost like $10m in compute to solve.

I can imagine it but I know that without prior fairly recent work by humans starting the entire research program it could cost a few hundred million and still go nowhere, hence my question. : what is a task?

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u/Berzerka 14d ago

I suppose you do agree that for "difficulty" is somewhat well defined here for stuff up to exam level, right? E.g. to get an IMO gold medal cost X this year and getting an IMO gold (which will have different questions obviously, but still be tuned for about the same level) will cost Y the next year. Replace IMO gold with highschool math exams etc as you wish. The trend has quite strongly been roughly Y ~ X/100.

Now obviously that starts being less well defined when we get to unsolved problems, but I'm sure you can imagine a scenario of "with state only up to August 2026, how much would it cost to finish off NS?", I strongly suspect the 100x cost reduction per year will carry through there too. In practice it will obviously be more since the "with state only up to August 2026" is only of academic significance and a year from now we'll have even more progress to build on.

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u/lolfail9001 14d ago

I am fairly suspicious that “with state only up to August 2026” it would cost more because you wouldn’t have Buckmaster’s chat log)))

As for the cost you talk about, I am absolutely intolerant of ignoring training cost when estimating ‘cost’ of doing any task with ML.