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

#301

Post by piloto_ciego » Sat, Jul 18, 2026, 9:22 PM UTC

vanuatu wrote: post #292

WarmWash wrote: post #170

Earlier quoted context omitted.

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.

I play the game for a manufactured challenge People in the real world all having god mode cheats is good, actually

yeah! Like can you imagine a world where you could just effectively "conjure" new furniture for your house and robots would assemble it in a few hours? Or molecular assemblers would grow it while you slept?

Or imagine a world where we could basically cure every disease? Or a world where people could assume any form factor that they wanted? I don't know, the list goes on and on in a post-scarcity world... and we're seeing how we basically live in a sort of digital post-scarcity now and it is really cool.

If I need a software tool these days I don't buy it, I tend to see if I can make it. Now imagine that for physical things? What a time to be alive.

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

#302

Post by piloto_ciego » Sat, Jul 18, 2026, 9:26 PM UTC

qarl2 wrote: post #296

dudul wrote: post #283

Earlier quoted context omitted.

Oh! Damn! Stupid me! "We have to collectively decide this", when is the meeting to vote on that again? When is the last time we all decided something collectively? WTF does the pandemic have to do with this? "dark time", oh yeah, people stuck at home watching Netflix, what an incommensurable suffering! Buddy, I can admire the naive childish optimism to a degree, but come on. "We just have to all decide". Do you live…

> WTF does the pandemic have to do with this? I'm not sure, but if I may guess, I suspect he's talking about the fact that the entire US shut down for a year and people survived because the US Government printed money and gave it away free to businesses so they wouldn't collapse. (PPP loans.) If we can do something like that for the pandemic, we can do something similar when push really comes to shove.

Thank you! We can decide to just... you know... do things.

Like, am I crazy here? The rules that we live by are largely made up and the points don't matter - we can decide to live in a better world if we want to. It's hard, and there are obstacles, for sure, but this appeal to doom for the sake of doom just... why? We have made unfathomable progress over the last century and if we keep trying we can make progress like that over the next century too!

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

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Post by sashank_1509 » Sat, Jul 18, 2026, 9:29 PM UTC

piloto_ciego wrote: post #268

sashank_1509 wrote: post #259

Earlier quoted context omitted.

Exactly, a lot of people keep attacking me as anxiety for losing my livelihood. It’s not that. It’s just depression that another avenue for human craftsmanship has been taken over by the machines. Humans are not just infinite consumers. If AI solves all of humanity problems, it’s like living in a zoo, not a life worth living imo.

This has always been the case though that "another avenue of human craftsmanship has been taken over by the machines." It's good if we can have robots building things instead of having humans slumped over a workbench in a sweatshop piecing things together. It's good if we can have LLMs spitting out code rather than CS grads working 15 hour days at fintech startups or whatever. The conditions were never (ever) good be…

Surgeons too now? Another avenue for human skill destroyed.

I actually want to exit. I want to live in a society where humans flourish not AI.

Actually one just needs to walk the streets of Japan and compare that to US. Tokyo has hundreds of small shops with humans doing specific niche stuff, perfecting their arts. That’s all so beautiful.

America has massive warehouses and supermarkets, with completely uninterested and bored out of their mind humans working and I suppose now we will replace them with robots. Great I guess. Maybe all Americans should just sit at home and consume Netflix and Doritos ig.

I want technology to increase human flourishing, not turn us into WallE humans. I am only interested in technological progress when it is done by humans who trained their whole lives for it, as it is a display of human excellence and that can be a beautiful thing. I’m not interested in it if some AI builds it.

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

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Post by alexpotato » Sat, Jul 18, 2026, 9:37 PM UTC

sigmarule wrote: post #197

xeromal wrote: post #180

Earlier quoted context omitted.

I gotta know what you use stats for regarding paintball. I haven't played in years but I loved playing back in the tipman 98 custom era (not sure if that's still a popular marker).

That era is now! (Still)

Paintball had a peak in the mid-2000s (I would say 2006) due to a combination of:

- Millenials who were kids of the baby boomers being in their late teens early 20s

- Disposable income due to the real estate bubble / positive consumer sentiment

It dropped off a lot after the 2008 GFC though.

BUT

A lot of those kids playing in the mid 2000s are now parents of ~10 year olds so apparently there is a bit of a resurgence going on.

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

#305

Post by piloto_ciego » Sat, Jul 18, 2026, 9:42 PM UTC

sashank_1509 wrote: post #303

piloto_ciego wrote: post #268

Earlier quoted context omitted.

This has always been the case though that "another avenue of human craftsmanship has been taken over by the machines." It's good if we can have robots building things instead of having humans slumped over a workbench in a sweatshop piecing things together. It's good if we can have LLMs spitting out code rather than CS grads working 15 hour days at fintech startups or whatever. The conditions were never (ever) good be…

Surgeons too now? Another avenue for human skill destroyed. I actually want to exit. I want to live in a society where humans flourish not AI. Actually one just needs to walk the streets of Japan and compare that to US. Tokyo has hundreds of small shops with humans doing specific niche stuff, perfecting their arts. That’s all so beautiful. America has massive warehouses and supermarkets, with completely uninterested…

Then, you know, build that world locally, at least for yourself.

Like, I'm building a cabin in the woods (original, I know), but you can build things and do things. You can be that kind of human if you want. But, if Americans could sit at home and consume netflix and doritos I suppose some would, but many would decide to start doing other things too.

I don't think the worlds we want to live in are that far apart to be honest. If I could make a living doing it, I'd try to build wooden sailboats for a living. That would be awesome. I would love it! In a world where I don't have to work to win capitalism tokens, I would probably spend a few years just building wooden sailboats to sail around the bay by my cabin.

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

#306

Post by eichin » Sat, Jul 18, 2026, 9:45 PM UTC

piloto_ciego wrote: post #285

dudul wrote: post #277

Earlier quoted context omitted.

I admire the naivety. I'm sure CS grads are delighted...

Why the ad hominem? I mean, seriously, you think I haven't been "in the trenches?" Dude, I'm nearly 40. I've seen the shit. When I was flying for a living, literal close friends died because of the results of avarice. Dream big dude! This constant "doom and gloom" narrative is toxic to your ability to flourish. I have been there, I understand the urge to doom and gloom, but we make the world we want to live in. We do…

what's getting built is more like Asimov's Spacers/Solarians, though. (Vastly reduced population wielding thousands of robots each)

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

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Post by frozenseven » Sat, Jul 18, 2026, 9:48 PM UTC

throwaway1707 wrote: post #132

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 had to create an account to respond to this because I am quite convinced these math problems they are "solving" are pure marketing. Why is it only GPT doing this, why not Claude? Why does Terrance Tao do marketing for OpenAI? I suspect OpenAI has hired math researchers to solve obscure problems and put them in their training set, purely for marketing reasons. There was a good comment on the Pelican bicycle svg yest…

Terence Tao also uses Anthropic's models in his work. Oh, you didn't know that? Well, now you can pivot to saying that he's getting paid off by both companies. This is actually one of the hallmarks of both conspiratorial nonsense and military-grade cope. Any fact, regardless of how mundane or extraordinary, gets re-imagined as evidence of the same mad-hatter conclusion.

I hope people are screenshotting this stuff. This really needs to be documented. It's remarkable how wild it's getting.

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

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Post by ashley95 » Sat, Jul 18, 2026, 9:51 PM UTC

_alternator_ wrote: post #115

hodgehog11 wrote: post #92

Earlier quoted context omitted.

Very confused by this comment. The older (poorer) parts of the ML literature focus on models with convex and (gradient-)Lipschitz objectives, but that's not representative of reality, not even close. Modern objectives for AI models are famously nonconvex (catastrophically, from the point of view of classical optimisation theory), and that's where the interesting research is.

I'd push back on this. Most of the core optimization techniques (eg, ADAM, stochastic gradient descent) are straight out of the convex optimization literature. Generally you need to use optimizers that work well on convex objectives because near minimizers, functions tend to be convex. (Proof by contradiction: a non-convex point has a strict descent direction.) The fact that neural networks are highly nonconvex has e…

The optimizers are lifted from convex optimization, but the point above was that they are applied to highly non-convex problems. They work for finding local minima, but a lot of the deeper literature does not translate (e.g. the conjecture being discussed in this post).

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

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Post by efdee » Sat, Jul 18, 2026, 10:05 PM UTC

ratg13 wrote: post #211

Levitz wrote: post #134

Earlier quoted context omitted.

Intelligence on its own is not very useful though. We put it on a pedestal because it creates huge potential when paired with other things, wisdom, discipline, empathy, but on its own?

AI / LLMs are not intelligence .. they are just a prediction engine that has been branded as 'intelligence' by marketing employees At the end of the day it is still making a best guess at what the user wants based on data it has seen before. It still requires someone smarter than the output to be able to evaluate if the result is any good, or just hand waving.

Can you tell me the difference between that and doing code review for a task performed by a non-senior?

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

#310

Post by throw310822 » Sat, Jul 18, 2026, 10:09 PM UTC

Izmaki wrote: post #274

throw310822 wrote: post #89

Earlier quoted context omitted.

Is is sarcasm? $25 to perform in half a day a week of work, that is not cheap, it's a massive saving of money- probably in the thousands.

It's not sarcasm. If I had to pay $25 to perform my work from an ever-growing pile of projects, I would be losing money. That's not "cheap intelligence" for me. It certainly is for my employer, though, because for the mere price of $25 extra per day they can get 4*X the product per period of time. In Scrum terms my personal velocity grows by a factor of four or more with access to agentic AI workload, but if it means…

I'll simplify it for you: AI is cheap for those who pay for it.