GPT-5.6 used a prompt to close a 30-year gap in convex optimization • Hacker News Board

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#221

Post by semiquaver » Sat, Jul 18, 2026, 6:57 PM UTC

thmoonbus wrote: post #133

semiquaver wrote: post #101

Earlier quoted context omitted.

> you can't have one LLM to read your mind to prompt another LLM I’m excited to inform you that we as a species have developed a particularly useful facility known as Language which these LLM tools are evidently rather handy at wielding. This facility is particularly useful in this context when it takes the form of “dialog” or “questioning”, which can be used to propagate abstract ideas by means of mutually-feedback-…

so, promoting?

I would not characterize it thus.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#222

Post by StilesCrisis » Sat, Jul 18, 2026, 6:57 PM UTC

fidotron wrote: post #96

simianwords wrote: post #82

Earlier quoted context omitted.

Is there any proof that they are not good at special reasoning? Arc agi 1 and 2 are saturated.

I will be posting something to that effect later this week. (Hopefully). Basically current gen LLMs apparently do spatial reasoning the way they seemingly do everything else: by reference to previous example. I didn't see them work out which known example to use for a given problem until specifically prompted, in my case by accident.

If you ask an LLM, "what known example did you use to solve this?" it is very likely to cite something plausible-sounding. That absolutely doesn't mean it is what it actually did. It is trying to give the "right answer" and please.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#223

Post by kevincox » Sat, Jul 18, 2026, 7:01 PM UTC

tripleee wrote: post #151

slashdave wrote: post #144

Earlier quoted context omitted.

There is more to human life than programming and math proofs.

unfortunately many won't get to experience it much because we'll be stressed and struggling to make a living

The problem isn't that we are gaining more knowledge and better technology. The problem is that we are allowing the rich to use the technology to subjugate the majority.

If AI improves human productivity so much that millions of people no longer need to work that should be an incredible thing. But the flawed structure of our society punishes those people rather than freeing them to persue endeavors that interest then.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#224

Post by qnleigh » Sat, Jul 18, 2026, 7:05 PM UTC

pessimizer wrote: post #126

threethirtytwo wrote: post #108

Genuine question: If you still or did think LLMs are just stochastic parrots that just summarize everything and have no form of creativity, what do you think after seeing results like this? I'm very curious how people reconcile their fear/hatred of AI with actual objective reality. This is actually what interests me most about the whole AI thing. How we tell ourselves what we tell ourselves.

I'm very curious why people conflate thinking LLMs are stochastic parrots with "fear/hatred" of AI. It seems like you're arguing with people who agree that it works and it helps, but you're trying to insist that this implies that they should kneel down and pray to it. Is "stochastic parrot" too disrespectful for you? Do you think it is a slur? edit: and this is a genuine question, also. How do you do stochastic parro…

I have absolutely no problem with people disliking or fearing AI. It's energy consumption, effects on education and potential for displacing good jobs are all quite disturbing. But "stochastic parrot" means that "all it does is randomly repeat things that it has seen before without understanding them." It's infuriating to see this written about an instance of an AI solving an open math probably. Do you think the models are just randomly repeating facts until they accidentally emit a proof? If so, then how do they synthesize that knowledge into something logically coherent?

Alternatively, if you think that even Maxwell was a stochastic parrot, then presumably almost every human who has ever lived was also a stochastic parrot except a few rare examples like Einstein. Not sure what definition you are using but it seems too broad to be useful.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#225

Post by barnacs » Sat, Jul 18, 2026, 7:16 PM UTC

qnleigh wrote: post #216

barnacs wrote: post #118

Earlier quoted context omitted.

I hold my stance that LLMs are stochastic parrots. Making the parrots ever more complex and training on ever more data produced by intelligent, creative beings may make them more useful or convincing but does at no point give rise to intelligence or creativity.

I won't touch creativity, but if this and other results like it do not demonstrate intelligence, what does? How was it able to solve problems that specialist mathematicians have tried and failed to solve for years?

Mathematics is a language. If anything, it's much more well defined and formal than most others. Train on enough examples and statistical autocomplete gets you places. I'm surprised how anyone would even consider this intelligence?

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#226

Post by skekke » Sat, Jul 18, 2026, 7:18 PM UTC

pfdietz wrote: post #160

pydry wrote: post #153

Earlier quoted context omitted.

>Unless you’re claiming that AIs will suddenly (and very soon) stop improving Most technologies level off sharply after bouts of boundless improvements. In 1968 they thought we'd be flying to the moon by now but instead we're flying across the ocean in planes not that different from the 747 that existed back then.

They sometimes start improving again. In the context of your comment, look how the cost/kg to LEO has suddenly dropped radically. This was mostly due to institutional change that allowed previous non-technological barriers to improvement to be bypassed.

[flagged]

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#227

Post by rocqua » Sat, Jul 18, 2026, 7:19 PM UTC

nicf wrote: post #155

vatsachak wrote: post #91

Earlier quoted context omitted.

Math is way more automatable than programming. In math, a proof is a proof. We don't know if we can get there and so getting there is the hard part. In software, we always know that we can solve the problem. So HOW to solve the problem is the hard part. Because the type of solution involves maintainability, which involves planning, LLMs suck at it. This leads to "LLM slop code" whereby the LLM creates ad-hoc convolut…

I've spent some time working both as a math researcher and as a software engineer, and I think this comment actually underrates the similarity between the two fields as they're actually practiced. Some math research does involve grabbing a single, fully specified conjecture off the shelf and hunting for a proof of it, and it's true that if you manage to solve a long-standing open problem, other mathematicians will be…

It seems to me you hooked onto the wrong part of proofs vs software compared to what OP meant. The difference OP cares about isn’t how much one cares about style. Instead the important difference lies in validation. A proof can be validated as either correct or wrong. That type of hard feedback really helps combat the optimism and desire for shortcuts of modern models.

Now, that still doesn’t help an LLM distinguish between good and bad correct proofs. But it still really helps a lot. On top of that, taste in proofs is a lot more uniform than taste in coding. That helps LLMs be better at judging the quality of a proof, because there’s less disagreement in the wider world.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#228

Post by ben_w » Sat, Jul 18, 2026, 7:23 PM UTC

georgemcbay wrote: post #94

timcobb wrote: post #30

Earlier quoted context omitted.

I can't stop wondering myself.... I'm writing some software with AI and wondering, why am I doing this? Will anyone need this? Will anyone have money to buy this? Best I've come up with is we'll need to be adopted by technofeudlaist overlords to be our patrons like in the roman days

> Best I've come up with is we'll need to be adopted by technofeudlaist overlords to be our patrons like in the roman days Continually progressing AI (combined with our current socioeconomic systems) throws a lot of uncertainty into our mid to long term future, but I don't think this is going to be what happens. There are billions more of "us" than of "them", people don't respond well en masse to a drastic worsening…

> There are billions more of "us" than of "them", people don't respond well en masse to a drastic worsening of their societal status and "they" are lagging very far behind on building their robot armies.

Fortunately, yes, those robot armies do seem to be rather behind schedule*.

However, even if Musk dies of old age before anything like the Optimus can be connected to useful artificial intelligence, it can still be driven by the common joke a few years back that "AI" really stood for "Actually Indians".

When all the people currently upset about "immigrants coming here taking our jobs" discover those same people are now staying home and remote-working those same jobs over a VR headset and a Starlink connection... my guess is that by this point, Musk will have no political allies left.

> If we poorly navigate this transition the outcome should be worrying them more than it worries us.

It can screw everyone over. Literal communism was invented in response to Laissez-faire capitalism, and while Laissez-faire died with the Great Depression, the form of capitalism which succeeded it in the USA came into conflict with the USSR and gave us the Cold War, the Cuban Missile Crisis, etc.

* 2022 "next year": https://www.cnbc.com/2022/04/08/elon-musk-says-tesla-is-aimi...

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#229

Post by peddling-brink » Sat, Jul 18, 2026, 7:26 PM UTC

qarl2 wrote: post #45

peddling-brink wrote: post #13

Earlier quoted context omitted.

Today maybe. I disagree in the long term. While they’ll never have the same subjective experience as humans, what stops an LLM from applying similar lines of thought* in a manner that results in a novel conjecture? They are prediction machines, and so are we in a way. We can give them nearly limitless resources to scale their predictive capabilities. We have billions of years of training baked in. They distill direct…

> While they’ll never have the same subjective experience as humans You state this as a fact - are you aware the question is unresolved? EDIT: I'd love to know why you're downvoting me for stating a known fact.

Ok, I guess never is a real long time and eventually when we merge our consciousness with the machines we may have the same subjective experience.

I can confidently state that GPT-5.6 Sol is not experiencing the same reality as me. They _might_ be "experiencing" and I personally think they are, but their reality and experience is not the same as ours.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#230

Post by tripleee » Sat, Jul 18, 2026, 7:29 PM UTC

kevincox wrote: post #223

tripleee wrote: post #151

Earlier quoted context omitted.

unfortunately many won't get to experience it much because we'll be stressed and struggling to make a living

The problem isn't that we are gaining more knowledge and better technology. The problem is that we are allowing the rich to use the technology to subjugate the majority. If AI improves human productivity so much that millions of people no longer need to work that should be an incredible thing. But the flawed structure of our society punishes those people rather than freeing them to persue endeavors that interest then…

Only solution I can think of is higher taxes for the rich used to provide universal income. I'm not sure how the realities of that would play out, though.

Anything based on a free market just ends up in.. this.