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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

#101

Post by semiquaver »

cromka wrote: post #19
semiquaver wrote: post #15

Earlier quoted context omitted.

You’re at least 18 months out of date claiming that prompting will be the new hot skill.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.

That doesn't make any sense; you can't have one LLM to read your mind to prompt another LLM.

  > 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-guided-iterative-Language-use-turns, or more concisely, “conversation.”

One might even say that this remarkable facility can be used to “read” the ideas from one entity’s mind, such that after sufficient dialog the second entity obtains a (possibly lossy, but there are mitigations for this) copy of the ideas of the first. You might further be surprised to learn that this sort of idea-transfer business using language has already been happening in our society and species for quite some time indeed.

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

#102

Post by ben_w »

WA wrote: post #6
qsera wrote: post #4

Earlier quoted context omitted.

From the post lol >So I wouldn't really say that this result is using or creating some fundamentally new techniques in convex geometry or optimization theory. What this means from my perspective is that if a result is attainable with existing techniques, modern AI methods will be able to solve those problems. I don't think researchers in math/TCS will be made obsolete, but I think it will instead no longer make sense…

If knowledge is a Swiss cheese, LLMs can help fill the holes, but not make the cheese bigger.

Famously, all of maths is axioms and tautologies, so I'm not sure this will assuage any professional mathematicians currently having an existential crisis.

Maths was already infinite, it's still infinite, but who wants to spend all their lives changing rooms inside Hilbert's Hotel?

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

#103

Post by sashank_1509 »

vatsachak wrote: post #91
rakel_rakel wrote: post #29

> I don't think researchers in math/TCS will be made obsolete, but I think it will instead no longer make sense to work on any low-hanging, or even medium-hanging (you know what I mean) fruit. We'll be needed for problems where actual novel approaches are needed. I wonder how this compares to what we see happening with "juniors" in software development? In math research, do you also get the training for the professio…

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…

> So I'll say it again, AI will win a fields medal for before managing a McDonald's simply because there are enough big problems within arms reach than their current capacity to plan over time

AI can manage a McDonald’s already. If manage means directing humans to do something to ensure the store is running. If manage means running robots, then yes maybe that is 5 years away but just directing humans to run a store, that is possible right now.

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

#104

Post by esafak »

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…

I don't know how you would translate the strength of a robot army to a human one; they haven't fought yet.

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

#105

Post by vatsachak »

sashank_1509 wrote: post #103
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…

> So I'll say it again, AI will win a fields medal for before managing a McDonald's simply because there are enough big problems within arms reach than their current capacity to plan over time AI can manage a McDonald’s already. If manage means directing humans to do something to ensure the store is running. If manage means running robots, then yes maybe that is 5 years away but just directing humans to run a store,…

No it can't. Show me a business which uses in context learning to manage a McDonald's

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

#107

Post by nicf »

rakel_rakel wrote: post #29

> I don't think researchers in math/TCS will be made obsolete, but I think it will instead no longer make sense to work on any low-hanging, or even medium-hanging (you know what I mean) fruit. We'll be needed for problems where actual novel approaches are needed. I wonder how this compares to what we see happening with "juniors" in software development? In math research, do you also get the training for the professio…

I was trained as a mathematician and worked as a math researcher for a little while (now working as a private tutor), and based on my experience I'd say this description is basically right, with one extra wrinkle.

In order to get a Ph.D., you have to do some sort of original research, so in that sense you're working on "previously unsolved stuff" basically right from the start. But that doesn't entail doing anything all that ground-breaking; most Ph.D. dissertations (very much including mine!) contain work that a more senior researcher in the same subfield could probably have produced without too much difficulty. The software development analogy is a pretty good one: a lot of the point of getting junior researchers to do research is to help train them to one day become senior researchers, and often the work itself is nothing all that special.

Given the trajectory of these LLM proofs, this seems like it's going to have to change pretty soon, and to be honest I'm pretty grateful that I'm not in charge of deciding what that's going to look like, because I don't have any good ideas! I'm actually pretty worried about the future of the field.

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

#108

Post by threethirtytwo »

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.

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

#109

Post by dash2 »

oulipo wrote: post #57

Except solving problem is probably the least (even though it's important) interesting thing in research... The most interesting thing in research is finding new questions, that we understand and that we know why they are important. And that's something that humans need to do (by definition)

I keep hearing this but lots of maths problems are practically important! We want to know the answer because it will be useful for applied science, or statistics, or engineering. It’s not all just about knowledge for its own sake.

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

#110

Post by cromka »

semiquaver wrote: post #101
cromka wrote: post #19

Earlier quoted context omitted.

That doesn't make any sense; you can't have one LLM to read your mind to prompt another LLM.

> 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-…

You mean promoting, right? Did you read the thread?
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