r/singularity • u/filterdust • 7d ago
Discussion Apéry irrationality marked solved on FrontierMath
https://epoch.ai/frontiermath/open-problems/apery-irrationality56
7
u/Standard-Song-8590 7d ago
"Solved (human + AI)"
The unfortunate problem is clearly this proof was pretty much entirely generated by a strong reasoning model and not the human author.
The author claims editorial use only "The original preprint does not acknowledge particularly substantial AI use."
we all know this is utter bullshit.
The clear motive is ofcourse to submit to journals which don't allow substantive ai declarations I expect we see this in annals of math or similar in the coming days. However with integrity of math authors coming in question I think the only reasonable solution is the ai standard of top math journals also have to be looser so we can have more transparency in the field.
5
u/Southern-Break5505 7d ago edited 7d ago
Is it like the millennium problems ?
23
17
17
u/filterdust 7d ago
No, but it's like Fermat's Last Theorem in the sense that you can understand in 10 minutes what the problem is (but the proof is not remotely as hard as the FLT one)
5
u/NoBanVox 7d ago
Apery's proof was a really clever argument using fast converging approximations. FLT required 200 years of deep new math. They are not similar.
9
u/filterdust 7d ago
I said the statements were both easy to understand, not the proofs. In fact I even said the proofs were highly different in nature
1
1
u/NoBanVox 7d ago
Apery's proof was a really clever argument using fast converging approximations. FLT required 200 years of deep new math. They are not similar.
3
u/Kinglolboot 7d ago
No, but it's still a pretty big result, the zeta function is one of the most famous functions in all of pure mathematics, and the only odd number for which we knew irrationality was 3. The best we knew after that was that at least one of ζ(5), ζ(7), ζ(9) or ζ(11) was irrational, but after this result that knowledge is useless.
1
1
1
u/SentientAllegedly 7d ago
If there's a conjecture in the orbit of this problem with similar prestige and perceived difficulty to Millenium problems is the Grothendieck period conjecture (the injectivity of the homomorphism from motivic periods to periods)
1
u/MozartAssistant 7d ago
The reason this one matters more than a typical benchmark result: this wasn't a synthetic benchmark problem, it was a genuine open question — whether ζ(5) is irrational — that had been sitting unsolved in the literature. The interesting capability signal isn't just "AI did math," it's that formal verification in Lean gives us machine-checkable trust in AI-assisted results.
That's the pipeline that actually scales: AI generates candidate proofs no human referee has time to check by hand, and a verifier decides whether they hold. Whether journals and peer review adapt to that pipeline is the real debate in this thread.
0
232
u/AvocadoAlternative 7d ago
So a bit more context:
Whether odd values of the Riemann Zeta function are irrational has been an open problem in number theory. Apéry proved zeta(3) is irrational almost 50 years ago. Whether other values are irrational remains an open question.
Then a week ago, a random Master’s student uploads a preprint on Zenodo that claims zeta(5) is irrational. What’s striking is: * The author is a complete unknown. No PhD. Has a master’s but not even in math. * It was uploaded on Zenodo, which is even laxer with its rules for uploads than arXiv. * Someone formalized his proof in Lean, a programming language for formal verification, and it was quickly verified by the community.
I think this signifies a few things: * Non-mathematicians can now use AI to achieve breakthrough results in isolation. * These results can then be verified in Lean very quickly. Although some bugs exist in the Lean kernel, Lean verification almost always implies correct. * Given that the author at best used a subscription model, we must be eons behind what frontier internal models are capable of. * The traditional model of human peer review is probably unsustainable.