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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

#21

Post by throw310822 »

qsera wrote: post #4
baal80spam wrote: post #2

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

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…

The author explains he's an expert in the domain and that he had worked sporadically on the problem for about a year, also with the help of previous LLMs. So whatever he means by "I wouldn't really say that this result is using or creating some fundamentally new techniques" it doesn't mean that the result was trivial. Also, says it might not make sense to work on low or even medium hanging fruits in the future- and I bet that's by far the largest share of work for most mathematicians.

Sure, it's not a breakthrough that opens new roads in mathematics- is this where the goalpost has moved now?

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

#22

Post by seiferteric »

peddling-brink wrote: post #13
WA wrote: post #6

Earlier quoted context omitted.

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

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 relentless.

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

#24

Post by jdw64 »

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.

Rather than prompt engineering, I think it should be called overall harness engineering. Anyway, that's how I feel these days

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

#25

Post by applfanboysbgon »

throwthrowuknow wrote: post #20
applfanboysbgon wrote: post #10

Two points: - Hasn't been peer reviewed yet, so take with a grain of salt. This applies to all claimed proofs, not just AI-generated ones. Even humans hallucinate proofs too! - The prompt is on page 27 here[1]. It is ten pages of advanced mathematics priming the model in the right direction, apparently informed by a year of prior research. That doesn't invalidate the result if it is genuine, but it is worth noting th…

Saying “solve this problem” doesn’t get good results most of the time with humans either, it’s entirely underspecified so the person assigned that problem may solve it in a variety of unacceptable ways or not at all or perhaps worse solve the wrong problem because you weren’t clear about its definition. This actually happens all the time. What matters is the ability to communicate clearly and with precision as well a…

> Saying “solve this problem” doesn’t get good results most of the time with humans either

Sure. That is not even remotely the point I was getting at. Already we see the thread filling up with comments about how human skills are irrelevant, using a mathematics PhD applying his expert skills in a way that the people who are saying that could never have done to justify their inane conclusion.

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

#26

Post by jdw64 »

aprilthird2021 wrote: post #16
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…

> I'm starting to feel like there's no place left for programmers like me who focus on quickly churning out MVPs. Of course there is. The same way this was only possible as a result from the professor who prompted it with his specialized 10 page prompt and most importantly his deep knowledge of the problem space, the muscle memory and intuition you've built over the years is what will allow you to get more out of any…

So these days I've been writing down my thoughts on my personal homepage. Things I've learned, my background knowledge, and so on.

I've been realizing that there are more books tied to my background knowledge than I expected, but I'm not sure what will happen as AI advances further.

These days, I'm living for the fun of building my own personal wiki on my homepage

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

#27

Post by esafak »

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

Once we figure out the pesky problem of how we're going to pay for housing, food, and healthcare.

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

#28

Post by weregiraffe »

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

Mathematics is a human-designed game that involves rearranging symbols.

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

#29

Post by rakel_rakel »

> 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 profession from working on the low hanging fruits for a while, to then move to the medium-hanging, and later go on to work on previously unsolved stuff?

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

#30

Post by timcobb »

esafak wrote: post #27
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

Once we figure out the pesky problem of how we're going to pay for housing, food, and healthcare.

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

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