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Posted by tedsanders 10 hours ago

An OpenAI model has disproved a central conjecture in discrete geometry(openai.com)
882 points | 658 commentspage 8
throwaway613746 6 hours ago|
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buddhahastha 9 hours ago||
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dist-epoch 10 hours ago||
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embedding-shape 10 hours ago||
> It's not a new result, LLMs can't produce new results

Who else disproved this longstanding conjecture before the model did so, since obviously it must have been in the training data since before?

ekjhgkejhgk 10 hours ago|||
Your understanding of this technology is out of date, and getting out of date faster as time goes by.
throwaw12 10 hours ago||
Thanks for giving me a hope that there is a still place for human knowledge workers.
bradleykingz 9 hours ago||
ok. so what are the implications of for math
brcmthrowaway 9 hours ago||
End times are approaching
fromMars 4 hours ago||
Seems rather depressing to me but maybe I am a Luddite.
JacobAsmuth 4 hours ago|
Exactly. I would rather we let these discoveries stay hidden for a while longer such that human ingenuity may untangle them from the coils of reality. A machine? A mechanical man? Deins to produce something as pure as mathematics without the divine fervor of the ineffable spirit of Man?! It's just not what God wants.
pickleRick243 3 hours ago|||
Human ingenuity is untangling perhaps the deepest question of all- what is the essence of Reason and the intellect that so privileges man? I don't know if it's what God wants, but it's certainly getting close to some existentially fundamental questions.

While many seem to be anxious or pessimistic about the future of intellectual/artistic pursuits (understandable although I disagree), I do find the utter lack of curiosity or interest in the incredible machinery that is causing all the fuss to be striking.

unmole 3 hours ago||||
I can't tell if this is satire.
csallen 3 hours ago||
I had the exact same thought. It depends entirely on what voice you read it in, I suppose.
pickleRick243 3 hours ago||
Haha, now I do think it is more likely satire. I don't think HN has many people who would post like this sincerely.
h4h4itsfunny 3 hours ago|||
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voooduuuuu 9 hours ago|||
Ask an LLM to invent a new word and post it here. You will see that it simply combines words already in the training data.
satvikpendem 9 hours ago||
Funny that the replies are dead. It's true that generally we shouldn't have AI output on HN but this case is an exception as we are explicitly asking for it, so it's interesting that people still flag the replies.
CamperBob2 7 hours ago||
And this is really not OK. I've been a victim of the same filter.

Dang/Tomhow, are you reading this? Would it make sense to modify your slop filter to avoid auto-flagging/killing replies that credit the LLM explicitly? Otherwise valid discussions will continue to get hosed.

Nevermark 7 hours ago|||
You must be joking? Unless by combining words you mean digging deep into Latin and Greek etymology, finding something pithy and linguistically associative.

I can assure you, the percentage of people who can do what they do when it comes to crafting terms, and related sets of terms, for nuanced and novel ideas is very very small.

It happens this is something I do nearly every day.

Models respond to the level of dialogue you have with them. Engage with an informed perspective on terminological issues and they respond with deep perspectives.

I am routinely baffled at the things people say models can't do, that they do effortlessly. Interaction and having some skill to contribute helps here.

robmccoll 8 hours ago|||
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baq 9 hours ago|||
Mathematics can be mostly boiled down to a few sentences with very lengthy possible combinations, so yeah that is not a problem
konart 9 hours ago|||
So LLM is german?
Garlef 8 hours ago|||
What does "new word" even mean?
dpoloncsak 9 hours ago|||
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dmos62 9 hours ago|||
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SparkyMcUnicorn 9 hours ago||
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atleastoptimal 8 hours ago||
To all AI skeptics:

What is preventing AI from continuing to improve until it is absolutely better than humans at any mental task?

If we compare AI now vs 2022 the difference is outstandingly stark. Do you believe this improvement will just stop before it eclipses all humans in everything we care about?

davebren 7 hours ago||
> What is preventing AI from continuing to improve until it is absolutely better than humans at any mental task?

No matter how much compute time it's given to combine training samples with each other and run through a validation engine it will still be missing some chunk of the "long tail". To make progress in the long tail it would need to have understanding, and not just a mimicry of understanding. Unless that happens they will always be dependent on the humans that they are mimicking in order to improve.

atleastoptimal 7 hours ago|||
What is the difference between what LLM's do and "true" understanding?

I feel like people grasping straws on the shrinking limitations of AI systems are just copying the "god of the gaps" fallacy

davebren 6 hours ago||
> What is the difference between what LLM's do and "true" understanding?

The thing where you can understand the meaning of this sentence without first compiling a statistical representation of a 10 trillion line corpus of training data.

Unless you're an NPC of course.

smashers1114 6 hours ago||
I mean brains get a lot of training data too in order to understand language. I don't think you provided a relevant difference.

Or rather, maybe I don't understand what you mean :)

davebren 6 hours ago||
When you think about the word apple and what it signifies, what do you experience? Is there a feeling of "appleness"? Do you think that sense of meaning is equivalent to the numerical weights of an LLM?
enoint 8 hours ago|||
That’s one possibility. If it fails to convince a critical mass that it’s a net improvement in their lives, then the impediment to continual improvement will be sabotage.
KalMann 7 hours ago|||
I think there's been natural but steady progress with since 2024 with the release of the o1 model, which showed impressive reasoning capabilities. But I think it's wrong to look at the magnitude of the accomplishments and assume that will be field independent. We don't know the range of problems reasoning techniques are useful for. What we see here is refinement of capabilities that have been noticeable for years.
layer8 6 hours ago|||
> everything we care about

One qualitative distinction that remains for the time being is that humans care about things while AIs do not. Human drive and motivation is needed to have AI perform tasks.

Of course, this distinction isn’t set in stone.

rzmmm 8 hours ago|||
Maybe after decades. 2022 models were microscopic compared to latest models.
gowld 5 hours ago|||
It depends on if AI can invent cold fusion before running our of all the energy on Earth.
xandrius 8 hours ago||
You should really look up a video about what GPTs fundamentally are.
Rover222 8 hours ago||
You should also really look up a video about what neural synapses really are.
ninjagoo 2 hours ago||
Many folks are upset about the supplanting of human effort by ai. Umanwizard voiced this valid concern below [1], but his comment got downvoted, unfairly, IMHO, instead of just being addressed. So putting out at least my response as its own top-level comment for visibility.

> the closer the expertise you spent your whole life building is to being worthless.

Perhaps it is time for life to be considered intrinsically valuable, instead of being "worthy" only based on output or capability. Disability, animal and environmental advocates have been fighting for this for a long time. Not too long ago women and minorities were in the same boat. Even now, there are many advocating and fighting for a return to the dark old days.

> Along with all the rest of what humans find meaningful and fulfilling.

Some humans. Many are content to enjoy simply existing, and the beauty of life and the universe around us. Just like many non-scientists today enjoy and benefit from the work of scientists, tomorrow too many will enjoy learning from, and applying the coming advancements and leaps in many fields.

And those of a scientist or other research-type mindset? No doubt they will contribute meaningfully by studying the frontier, noting what remains unanswered, and then advancing the frontier, just like researchers do today; just because scientists in the past solved many questions doesn't mean that there aren't any questions to answer today.

IMHO, AI means that the frontier expands faster, not that it is obliterated. Even AI cannot overcome the laws and limitations of physics/universe: even Dyson spheres only capture the energy of one star, thus setting a limit on the amount of compute, and thereby a limit on intelligence. And we are a loooong way from a Dyson sphere.

[1] https://news.ycombinator.com/item?id=48215122

reactordev 10 hours ago|
I dunno, I'm skeptical without proof. I've had the MAX+ plan for a while and I'm sorry, the quality between GPT vs Claude is night and day difference. Claude understands. GPT stumbles over every request I give it.
nathan_compton 9 hours ago|
Weird thing to say about a report which literally has the attached mathematical proof.
reactordev 9 hours ago|||
Except its not a proof. It's an existential proof of what? Projecting points and loosing density? Nah, it's wrong. At least with Edros you could solve f(x) or not solve it (inf). You can not with this. All they did was balance a really fancy quadratic equation. The projection from C^f to R² doesn't demonstrate geometric injectivity, so nⱼ = |X| isn't established, and the bound collapses.