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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

#331

Post by piloto_ciego »

dudul wrote: post #321
piloto_ciego wrote: post #302

Earlier quoted context omitted.

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 lik…

> We can decide to just... you know... do things. OK, this is Twitter-level conversation here, not interested. But hey, stay positive, more power to you.

You’re the one saying that we can’t. Not me.

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

#332

Post by [deleted] »

vatsachak wrote: post #257
nicf wrote: post #239

Earlier quoted context omitted.

No, what I'm saying is that I don't agree that taste in mathematics is more uniform than taste in coding! Mathematicians argue about taste all the time. Just as you might look at a piece of code and agree that it compiles and doesn't have any fatal bugs but still think it's badly written, hard to follow, hard to modify, or whatever else, mathematicians judge mathematical work using very similar criteria.

Maybe a subset of mathematicians, but if someone proved that RH was undecidable we would still give them the millennium prize.

[deleted]

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

#333

Post by thfuran »

natsucks wrote: post #201
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…

call me naive, but i really think the pursuit for the new, the better, the interesting, is boundless and humans will never stop. and so for those of us that dream and push and are plain curious will never run out of ways to be useful. and hopefully the fruits of all this tech will be ample enough to support the ones that don't want to or can't participate in that way.

If AI is better at being (or simulating; I think the distinction is irrelevant in this context) curious, better at examining that curiosity, better at pursuing it to discovery, better at applying the discoveries, better at sharing the discoveries, and able to push the frontier of knowledge (if that’s even the right word) literally beyond human comprehension in every domain, what usefulness exactly is left? Or are you just implicitly saying you don’t believe AI will ever get all that superhuman?

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

#334

Post by godwinson__4-8 »

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

Your first two sentences were correct. The last one is already being proven false.

It's a threat to everyone. UBI is the only way.

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

#335

Post by fidotron »

StilesCrisis wrote: post #222
fidotron wrote: post #96

Earlier quoted context omitted.

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.

> 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.

That's not what I said happened though. It didn't solve the problem (for weeks) until I (accidentally) told it which example it happened to know was relevant, and then it solved it in hours.

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

#336

Post by dwohnitmok »

YeGoblynQueenne wrote: post #326

So if you dig down a bit it turns out the author had been trying to solve that problem for a year with GPT 5.4 and 5.5 and he fed all that information to the prompt he gave to Sol Pro which may or may not had direct access to the author's chat history. So the claimed "148 minutes" was really "a year plus 148 minutes". Moreover, it seems the prompt included the technique used to solve the problem: https://old.reddit.c…

> Moreover, it seems the prompt included the technique used to solve the problem:

I don't believe this is true. The author sent techniques he used, but I don't believe any of those were ultimately what GPT-5.6 used.

GPT-5.6 also provided the Lean formalization, which was not provided at all by the author.

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

#337

Post by rgoulter »

codingdave wrote: post #38
mw67 wrote: post #14

Crazy how intelligence is cheap, efficient and commonplace now. We humans better refocusing our energy on our core values/principles, given most of our skills are becoming irrelevant

If it were commonplace, there wouldn't be a post and discussion about it. Cheap? Arguable - while it didn't cost thousands, it wasn't free. Cheap is in the eye of the beholder. Efficient...How do we even measure that? The massive infrastructure and training to take a product to the point where someone could do this is massive. Ignoring everything behind the scenes and acting like one session and result is the whole p…

'Maybe cheap but not free' is a good observation.

If I'm getting paid for the work, I'm happy to leverage the LLMs so I can do more. If I'm paying for the work, I expect more from it.

For hobbyist stuff, where I'm not expecting to receive money? LLMs let me do things I otherwise wouldn't have done.

I've agreed with thoughts like "the LLM wrote the code, surely it's not worth sharing" or "I could just have the LLM write my own version of that". I'd also wondered about my own personal projects, surely "an LLM could have written all of this". -- But how I feel about that changes a bit based on how much it'd take the LLMs to get the same output.

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

#338

Post by dwohnitmok »

lucianbr wrote: post #173
dwohnitmok wrote: post #87

Earlier quoted context omitted.

The author also used GPT-5.6 to write the prompt. This did involve giving GPT-5.6 access to his previous work and a back and forth process (so definitely still used the author's expertise to some degree), but the prompt itself is also largely AI generated.

What's the difference between using GPT to write the prompt to GPT, and "thinking"? The LLM uses the first tokens to predict more tokens, and then uses those tokens to predict even more tokens.

Roughly speaking it is the difference between having a contractor go out and do some work and having that same contractor first come up with a plan to do some work, run that by you, and then go out to do that work.

Part of it is as a another comment in this chain mentions the chance to review the prompt. Part of it is that it forces the AI system to plan things in a certain order, in much the same way that forcing the contractor to write the plan out first forces the contractor to proceed in a certain predefined order that may (or may not!) be better at getting to a final answer.

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

#339

Post by goldylochness »

YeGoblynQueenne wrote: post #326

So if you dig down a bit it turns out the author had been trying to solve that problem for a year with GPT 5.4 and 5.5 and he fed all that information to the prompt he gave to Sol Pro which may or may not had direct access to the author's chat history. So the claimed "148 minutes" was really "a year plus 148 minutes". Moreover, it seems the prompt included the technique used to solve the problem: https://old.reddit.c…

sounds like a feature, not a bug

it might imply using weaker models to attempt the problem first is a good supplementary prompt to a more advanced model trying to do the same

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

#340

Post by georgeburdell »

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!

I don’t think OP made much effort to make the comment accessible to non-experts, and so it should be taken as a gauge of the fundamental difficulty of the topic.
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