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- Hacker News
- Is this a proof a human could have come up with? Is it elegant? How significant was the human contribution?by esafak
- Obviously a Fields Medal–level achievement... Even the most optimistic person would not have expected it to happen so quickly six months agoby linzhangrun
- I skimmed through it. Looks fine. Had a bit of trouble following step 5 of theroem 10.5 (page 89), but after a second look it became all too obvious.by dinga
- basically trivial.by _zoltan_
- I was more confused by the application of Nakayama’s lemma in the following paragraph, but then it suddenly became clear to me.by cmenge
- And in other news (elliptic curve of rank 31): https://news.ycombinator.com/item?id=49412774
Announced by the same people, basically at the same time.
by frozenseven - I’ve been turning the handle on GPT for weeks, feeding in toy models of physics and seeing what pops out the other end.
It’s mostly this type of mathematics: classifying what high dimensional spaces can and can’t do.
Maths like this is where the AIs will be most useful in the next few years: tirelessly grinding through every possibility on the edge of human knowledge, filling in gaps and completing maps of no-go regions in the theory space.
by jiggawatts - LGTM
- It seems the trend for AI math is:
>Proofs which fewer and fewer people are able to understand
>Those who do understand, the rate at which models make discoveries exceed the amount of time those humans have in a day
>As a result, we will increasingly use other AI models to validate the proofs AI make for us
I don't see a future where this doesn't apply to everything. Let's say you're an evil CEO, you could ask an AI model to run for days cooking up every possible nefarious scheme to get out of a class-action lawsuit scott-free, to avoid taxes via complex financial engineering, etc. The plans will be far more complex than any human can understand. There simply aren't enough humans with the mental bandwidth to oppose you, so it's just machine vs machine, and if you have more money to pay for more compute, you win.
- Tax law is not arbitrarily complicated, and unexpected edge cases are settled by human judges, not by mathematical proofs.
- > It seems the trend for AI math is:
> > Proofs which fewer and fewer people are able to understand
This is the trend for proofs of famous old theorems in general, even pre-AI. Some particularly extreme examples are the proofs of Fermat's Last Theorem [0], the abc conjecture [1], the classification of finite simple groups [2], and the four colour theorem [3].
[0]: https://en.wikipedia.org/wiki/Wiles's_proof_of_Fermat's_Last...
[1]: https://mathoverflow.net/questions/232087/have-there-been-an...
[2]: https://en.wikipedia.org/wiki/Classification_of_finite_simpl...
[3]: https://en.wikipedia.org/wiki/Four_color_theorem#Proof_by_co...
- This kind of papers go way over my head, but recently I was surprised that ChatGTP (free) found the proof for an expression had a square value for some variables. It dug up a relationship from a paper from 2009 and correctly applied it to the case.
The chat: https://chatgpt.com/share/6a7f1b08-b9dc-83ea-b911-aaf8b65f1c...
by fjfaase - Reducing the problem to a quadratic form is pretty natural, and the paper from 2009 (though i see 2015) is quite an overkill. The result is a fairly standard consequence of the theory of representation by quadratic forms, and follows from Legendre's three square's theorem after some massaging. There's a good couple of centuries of foundations behind it.by nk_kolja
- by scuppernong
- 100 pages of dense mathematics created by Claude. It doesn't even have an abstract or a summary. What are we looking at here? Has anyone read this? Please explain like I'm not a math PhD.by mr_mitm
- There's an abstract on page 3. But it's quite ... abstract.
By the end of the first sentence I'm pretty sure it would take me quite some time to understand what it's about (the first sentence of the abstract, not the whole paper)
by cmenge - I’m pretty sure no one (except perhaps Anthropic insiders who had prior access, and probably not even them) has properly digested this paper yet, and some caution is warranted given the notoriety of this problem and the history of claimed solutions that did not stand up to scrutiny. But if it stands up, it’s a really big deal.
Background: https://mathoverflow.net/questions/1973/is-there-a-complex-s...
by robinhouston