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

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

#291

Post by smaudet »

YZF wrote: post #166
zarzavat wrote: post #147

Earlier quoted context omitted.

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 cont…

> It's not a zero sum game.

Resources are, though. The planet cannot support a race of digital super-people, and us, and an continually growing economy.

It's the height of folly to think that, as things are going, we are going anywhere "good".

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

#292

Post by vanuatu »

WarmWash wrote: post #170
piloto_ciego wrote: post #159

Earlier quoted context omitted.

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.

I play the game for a manufactured challenge

People in the real world all having god mode cheats is good, actually

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

#293

Post by piloto_ciego »

dudul wrote: post #283
piloto_ciego wrote: post #279

Earlier quoted context omitted.

We're going to have to (collectively at some point) decide that we shouldn't tie survival to working. Whether that's UBI, or Fully Automated Luxury Gay Space Communism, or UBS, or some AI managed economy, or some other such thing, we need to decide that "hey, we don't want to tied survival to output under our current system." That's really the Rubicon we have to cross, and there are a LOT of people who can't really c…

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…

I mean, a at least something like million people died just in the US with the most conservative estimates that I've seen (and by 2022). It was pretty dark, yeah.

But we also decided during that time to literally pay people to stay home for awhile. That was a really revolutionary thing and it was awesome. We could decide to do that again.

You can ad hominem until the cows come home, but yeah, we literally just kind of have to collectively decide that there are better ways to do things.

There's a fantastic book called "The Last Emperor of Mexico" I read a few years ago that really talks about how the idea of a Republic or Democracy in general was a pretty novel concept in the mid 1800s. People were a lot more skeptical about it than we're lead to believe now. But eventually, the ideas of aristocracy and some "well bred" group of various types of monarchs became silly on it's face. Now the default is that we should have some sort of democratic representation. That would seem utopian AF in 1820.

Well, we're going to have to bridge that sort of gap for getting rid of the need to justify our existence through work too. The transition is going to be weird, but we'll have to come up with something else and run with it.

Dream big buddy, I know it's hard, lord knows I do, but dream big, and work little by little towards those things you want to see in the world.

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

#294

Post by moomoo11 »

adamtaylor_13 wrote: post #281
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…

Why is this depressing and bleak? No one is stopping you from doing math if that's what you want to do. Should I ban table saws because they make people too good at woodworking? Should we ban right-angles? This line of thought doesn't lead anywhere fruitful.

just ignore these people

gig economy is a blessing to keep the LCD busy and doing something productive instead of being nihilistic losers

it’s better to focus on how to keep these “knowledge” workers busy for the AI age

they don’t like to work and complain even on a w2 job (where someone else had to figure out how to capitalize them) so in many ways they’re far more dangerous and hopeless.

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

#295

Post by theteapot »

LPisGood wrote: post #86
_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…

It should be noted that optimization of a convex bounded lipschitz function is exactly what most modern statistical learning (AI) models are based on.

What do you mean by this? A neural network hypothesis space is not typically strictly convex or a lipschitz function.

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

#296

Post by qarl2 »

dudul wrote: post #283
piloto_ciego wrote: post #279

Earlier quoted context omitted.

We're going to have to (collectively at some point) decide that we shouldn't tie survival to working. Whether that's UBI, or Fully Automated Luxury Gay Space Communism, or UBS, or some AI managed economy, or some other such thing, we need to decide that "hey, we don't want to tied survival to output under our current system." That's really the Rubicon we have to cross, and there are a LOT of people who can't really c…

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.

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

#297

Post by spicyusername »

xeromal wrote: post #165
_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!

Not to diminish the comment, but most things are not as complex as they sound when phrased in everyday language or sound much more complex than they are when phrased in technical language.

Technical language is a tool that allows insiders to say less and refer to more, and to be specific, but it's just a tool. Most things can be described in accessible ways.

I think you'd be surprised at what you could understand and at just how few domains are truly complex enough that a layman couldn't understand with a little bit of patience and an accessible summary.

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

#298

Post by vanuatu »

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…

kind of a hilarious conspiracy theory

You are correct that LLMs are trained on existing proofs but hiring researchers to solve unsolved problems is just unrealistic, both in terms of how none of the mathematicians simply came out and took credit for their own discovery or exposed this, and how training sets are not easily memorized (rather, the meta techniques are learned).

OpenAI just has better training methods and techniques for pure math over Anthropic, it’s one of their biggest strengths

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

#300

Post by charlieyu1 »

7373737373 wrote: post #258
a_imho wrote: post #58

If I recall correctly there was a proposed proof to the abc conjecture by Mochizuki https://en.wikipedia.org/wiki/Abc_conjecture#Claimed_proofs which was rejected due to being rather inpenetrable to humans. Shouldn't this be an ideal target for LLMs?

Similarly, I'd love to see LLMs create a formal proof of the https://en.wikipedia.org/wiki/Classification_of_finite_simpl...

I’d like to see four color conjecture and an elementary proof of FLT.
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