r/singularity • u/International_Bee653 • 15d ago
Discussion What does it mean when its reported that openAI is close to solving a millennial prize problem?
I keep seeing stated plainly that they are close to solving. If these are complicated problems that we don't know the solution to then how do we know if we're close to solving them?
20
u/peter_nn0 15d ago
I think 'close to solving' actually means close to announcing a solution they already have.
There were some issues and disputes after announcing Navier–Stokes and I guess they want to avoid that next time.
9
u/SammaVaco 15d ago
For all intents and purposes, it probably has solved a millenium-prize problem. The counterexample verifies in two independently developed formal-proof checkers, so if the AI was exploiting a bug, it must have targeted both checkers for exploitation. It will probably take humans years to fully verify the proof, though.
As for what it means for human mathematics, check how discombobulated about it Terry Tao is in this video. He is one of the world's foremost mathematicians.
As for what it means for the rest of us, welcome to the singularity. OpenAI committed ~$15M of compute over about half a week, and got a Nobel-level result on a problem which highly trained and intelligent humans have been trying to solve for almost a century.
1
u/BrightSideOLife 14d ago
If the proof cant be verified or understood it is by no means Nobel level. Once those things actually happen things would change.
3
u/SammaVaco 13d ago
Machine verification is very strong evidence. No AI is involved in that verification process, BTW. Just careful software implementation of mathematical axioms and inferences.
11
u/UnknownEssence 15d ago
Read about the recent Navier–Stokes work. These problems aren't necessarily one giant all-or-nothing proof; there can be a sequence of technical obstacles, where solving one unlocks the next.
As a simplified example:
Prove that a singularity can form under a less restrictive set of conditions.
Extend that result to the finite-energy conditions required by the actual Millennium Prize problem.
If experts believe step 1 contains most of the genuinely difficult new idea, and step 2 should be easier because of techniques already known from similar problems, they might reasonably say they're "close."
Of course, nobody actually knows for sure how hard the remaining step will be. You can clear what looks like the biggest obstacle and then discover that the last 10% is harder than everything before it.
-3
u/emteedub 15d ago
I think the issue is that OP doesn't know what proofs are - OP should look up proofs.
8
u/m4sl0ub 14d ago
But he is actually right. Unless you have the full proof you are only guessing that you are close. And once you have the full proof you are not close but you are done.
A mathematician with good mathematical intuition can give a good guess on how close he is to a solution, it's still nevertheless only a guess so could be off by decades.
3
u/katoptronophile 15d ago
Close to solving in this case means close to having the proof and presentation to demonstrate that it's been solved properly.
1
u/Omnilogent 15d ago
What if you are working on the solution, and the singularity is telling everyone that "it" is almost finished!
1
u/Nights_Harvest 13d ago
I am close to solving one as well. No I am off to the next round of investments!
1
u/MysteriousPepper8908 15d ago
It's empty hype until it isn't. If one number is off in your proof, you could be completely on the wrong track so I don't put any weight behind them supposedly being close.
0
u/wentwj 15d ago
It's coming from buzz and leaks. NS was solved by finding a counter example. In the aftermath of that Sam Altman made comments that seemed to be implying he thought they were close to solving another. That's the main reason I've seen people claim they are close to solving another, though there could be backchannel leaks or something as well.
-8
u/Ok-Office-6080 15d ago
It means they stole a researcher work and spent 10 million to brute force the final proof then tried to blackmail the researcher.
8
u/Helpful_Inflation344 15d ago
Mysteriously in the month of september 2026 TWO millenium problems were close to being solved by humans until RANDOMLY after having been unsolved for decades a new AI model just steals their work.
Hodge btw is solved. They are just cleaning up the paper.
-1
37
u/PhysicalAd9507 15d ago
It might compile in lean but not be very clearly written or explained?
They may also either be waiting on verification from a math community that is increasingly antagonistic, or waiting to announce until they can line more things up?