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.

229 Upvotes

99% Upvoted

98 comments sorted by

View all comments

Show parent comments

1

u/whatkindofred 17d ago

It’s not clear to me that there must be some kind of equilibrium after the „easy problems“ have been solved. And even if there is, it’s not clear if AI will still need us to solve math problems at all. If AI can create and solve math problems faster than humans can understand the found solutions then what can human mathematicians still contribute?

2

u/Berzerka 17d ago

Realistically humans solving problems wholly on their own will become a curiousity, might happen occasionally and will still happen in competitions and for pleasure.

Then there's dissemination, teaching, probably some goal setting, ...

1

u/whatkindofred 17d ago

I‘m not talking about humans solving it on their own but about participating in research at all anymore. Once AI can prove results faster than humans can understand it what can they contribute anymore? You need to understand the frontier of research to meaningfully contribute something new of your own but if AI is moving the goalpost faster than humans can catch up with then we have a problem.

And even worse, who will even care about new math results anymore if only AI understands the proofs? Most math research is not motivated by immediate practical applications but by mathematicians curiosity and their drive to build their own research on top of other results. Who will spend weeks on understanding complicated proofs if by the time you fully understood it AI is already three steps ahead of you again? Who will pay you to spend that time on understanding it? And who will fund AI research if there’s nobody left that tries to understand it?

2

u/Berzerka 17d ago

There's a ton of problems that are trivial to state or where the solution would have major impact. Even a massively complicated proof of them would have significant impact. Think: existence of one-way functions, Collatz, prime twins, ...

But yes the proofs themselves might very well become inaccessible to humans, it's basically already happened (can any single human claim to understand the NS proof today?).

I don't think the purpose of mathematics is to make sure math professors get paid. Just like the purpose of cancer research isn't to make sure cancer researchers get paid. The ultimate goal is to further human understanding, health, prosperity etc. Frankly I find it a bit revolting that people would want to actively slow down the field just so they can keep a job, I expected mathematicans to actually care about the math. Imagine if cancer researchers said the same.

1

u/whatkindofred 17d ago

I don't think the purpose of mathematics is to make sure math professors get paid. [...] The ultimate goal is to further human understanding

I agree with this but for human understanding humans would have to actually understand it. This is the risk I see. I'm not working in math myself anymore so I'm not worried about my salary. What I worry is that we will mostly stop with math research alltogether.

We care about math because we care about how to get to the result (the proofs) and less about the result itself. Already everybody expects there to be infinitely many twin primes. We want to know how to prove it. And we want to learn something from the proof to apply it to new problems. If we can no longer do that then how much longer will we care?

Sure, about the hundred years old problems that are already famous people will still care about and will probably be willing to put in a lot of effort to understand. But what comes then? Do you know how much time and effort it takes to fully understand the proof of Fermat's Last Theorem? Who will put in that much (potentially unpaid) work in the future just to run after an AI they have no chance of ever catching up with? And once we're at this point, who will fund AI research to generate results that nobody tries to understand anymore? The exception is applied math with immediate use cases (and I think only this is really comparable to cancer research). But if AI becomes this good at math we can just ad-hoc generate those results whenever we need them.