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

#161

Post by jltsiren » Sat, Jul 18, 2026, 5:00 PM UTC

semiquaver wrote: post #15

jdw64 wrote: post #7

What I'm feeling is that there's a need to study how to use AI well. I've seen professors using AI, and it was amazing. In that sense, I think AI prompt input will become stratified. In the past, implementation skills were very important, but these days, concepts feel more important this is one of those things. It's not that AI brings equality, but rather that the output varies depending on how much background knowle…

You’re at least 18 months out of date claiming that prompting will be the new hot skill. Turns out LLMs are also good at prompting other LLMs.

One of the key skills of a professor is asking the right questions. Figuring out something worth working on, and then framing it in an appropriate way and asking questions that allow someone with specific tools and skills to make progress in the topic. Usually the tools and skills are those available to a new student, but working with an LLM is similar.

That skill comes with experience. Most people don't have it immediately after PhD.

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

#162

Post by qsera » Sat, Jul 18, 2026, 5:01 PM UTC

seiferteric wrote: post #22

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…

They also have ability to go deep and wide in a way that humans just can't. We have limits, get tired, distracted and biased where AI does not. I think there a lot of problem where all the information needed to solve them is there, but we just can't put the pieces together. Like no matter how many people you throw at some problems, you hit human limits and more people won't help, but AI will because it is just relent…

>biased where AI does not.

AI can be totally biased...

The fact that it can spout bullshit all day long to a human who can be tired and would actually act on the said bullshit, is not very comforting...

For example, an LLM could confidently declare something a tired human would take as a fact, but would backfire in a real world.

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

#163

Post by qarl2 » Sat, Jul 18, 2026, 5:05 PM UTC

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.

Heh. I see you're being met with screeching and downvotes.

Not much to do about it, I guess, but continue to call it out.

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

#164

Post by piloto_ciego » Sat, Jul 18, 2026, 5:06 PM UTC

qarl2 wrote: post #39

baal80spam wrote: post #2

Waiting for comments saying that LLMs can't produce anything new and general goalpost moving.

HEH. Don't know why you're getting downvoted. It's painfully obvious that there is a vicious AI backlash now, where every amazing advancement is met with denial and loathing. Oh wait, sorry, I do know why you're getting downvoted. Fear.

A lot of people who thought they were special and “better” than mere blue-collar workers are realizing that in fact;l they are the same just working with a different medium.

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

#165

Post by xeromal » Sat, Jul 18, 2026, 5:08 PM UTC

_alternator_ wrote: post #76

I know a bit about this field. This conjecture reads as somewhat more niche than the cyclic double cover conjecture recently proved by OpenAI, but nevertheless represents a real contribution. You want to know how long it takes to solve an optimization problem, in this case over convex, lipschitz functions. (The restriction to a spherical domain is not really a restriction, you can just change variables for any bounde…

Sometimes I read a comment on HN that is so advanced that it's just as readable to me as Greek. Love reading it just to see someone work though!

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

#166

Post by YZF » Sat, Jul 18, 2026, 5:10 PM UTC

zarzavat wrote: post #147

Quothling wrote: post #88

Earlier quoted context omitted.

Around here AI isn't really more of a threat to juniors than it is to seniors. It's a threat to the people who have been taught "recipies" rather than applied computer science. You can have excellent seniors who can do TDD, DRY, SOLID and so on, who also happen to have no idea what a L1 cache miss is. The current AI models know all of those things, but they struggle applying them correctly without someone piloting th…

AI is a threat to everyone. People who claim that AI will never be able to do X have consistently been proven wrong. The only people who are safe are those whose jobs depend in some way on their humanity. e.g. yoga teachers, bouncers, etc

Nobody knows.

It's not a zero sum game. You can have AI "senior engineers" working under humans building bigger things than we've been able to.

We also don't know where the capabilities of current AIs will plateau. The benchmarks aren't really telling the entire story. From my perspective of using the models there are certain axis where they're not making a lot of progress, like being able to have large accurate context on the scale that humans can. There are other dimensions where there is still a large gap between human capabilities and LLMs. It's true that relative to other areas (lessay chess) LLMs are more generalized but they are still not fully generalized (back to the chess example, LLMs are not good at chess).

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

#167

Post by vatsachak » Sat, Jul 18, 2026, 5:12 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…

I think that your take is quite optimistic. Having published in top tier journals my only experience is that mathematicians care about what other mathematicians worked on and failed to solve. Theory building papers are dime a dozen and don't get published in high tier journals unless they solve a problem.

Math is such that most theories are built after solving a problem and actually don't solve a larger class of problems. Etale Cohomology is an example of a rare exception. Grothendieck was mad that Deligne used adhoc complex analysis techniques to prove Weil. But everyone else was thrilled.

Whereas in CS, a good theory (library) solves a large class of problems. The reason being is that CS tackles general problems while math specific ones. Math on average solves problems that don't lead to solutions to other problems.

To me at least, math is more of a game like chess and coding is more of an art. There are aspects which are a game, like performance engineering but I'm pretty sure that LLMs will become superhuman at that soon

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

#168

Post by WarmWash » Sat, Jul 18, 2026, 5:12 PM UTC

simianwords wrote: post #82

fidotron wrote: post #32

Earlier quoted context omitted.

It's still clear that LLMs lack spatial reasoning, either in the concrete or abstract, and while that sort of reasoning has been downplayed by academia for at least a century it is fundamental to technology and industry. (And many would say for science and mathematics too). They will, however, get there as well either directly or as interfaces to models that do, and your core point stands.

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

On a token level, text tokens are orders of magnitude more information dense than visual tokens.

You don't have to do much statistical analysis to figure out what is meant by the token string "cat under a tree". However you need to do an enormous amount to encode any permutation of pixels that show a cat under a tree from the set of all possible pixels arrangements that illustrate that (along with the massive fringes of ambiguity).

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

#169

Post by qarl2 » Sat, Jul 18, 2026, 5:12 PM UTC

piloto_ciego wrote: post #164

qarl2 wrote: post #39

Earlier quoted context omitted.

HEH. Don't know why you're getting downvoted. It's painfully obvious that there is a vicious AI backlash now, where every amazing advancement is met with denial and loathing. Oh wait, sorry, I do know why you're getting downvoted. Fear.

A lot of people who thought they were special and “better” than mere blue-collar workers are realizing that in fact;l they are the same just working with a different medium.

I see a trend line from anti-AI back to anti-evolution to vitalism all the way to Galileo.

Humans have a deep need to be special magic flowers - and they can't stand it when science eventually shows them they're not.

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

#170

Post by WarmWash » Sat, Jul 18, 2026, 5:16 PM UTC

piloto_ciego wrote: post #159

sashank_1509 wrote: post #116

This is all a depressing and bleak future that I don’t look forward to. One solution is to ban LLM’s, to artificially create a demand for human thought, that just feels like living in an artificially constructed zoo. Another solution is humans don’t do anything that AI can do better , / doesn’t need the human touch. So I suppose we will all become artists, sportsmen or politicians, the only jobs that will remain exce…

This is utopian friend! Literally anything you wanted to make is no plausible to make if not now then in the next couple years. The thing you’re worried about is capitalism and the connection with working to having the right to keep living. If you can throw off that mental shackle you can start to see how this can be amazing, but you have to drop the idea that everyone has to work at a job for someone else to provide…

You ever play a video game with god mode cheats enabled, so you can unlock all the unlocks, get all the best gear, and be an unstoppable force with unlimited money?

Yeah, it's fun for 30 minutes.