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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

#91

Post by vatsachak »

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 convoluted logic with redundancies and no reuse of existing standard library batteries.

Unless you're a Grothendieck who gets mad at Deligne for not solving the Weil's conjecture "THE RIGHT WAY", software is fundamentally different than math in this respect.

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

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

#92

Post by hodgehog11 »

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.

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.

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

#93

Post by danielbln »

bredren wrote: post #83
jvanderbot wrote: post #54

Earlier quoted context omitted.

Yeah, back to the gold-in-gold out use of LLMs.

I was thinking this past week I have gotten so lazy w my prompting via CLIs. Back in the before I had put such discipline into my prompting and supporting context. Now I’m like, “look here and here and here are some tools, and /skill /skill okay go.” Or “restate this request in your own words and enrich it as appropriate handling any gaps. Okay go”

This made me chuckle because it's so true. So much detailed steering and finagling in the past, now I point the agent to a bunch of information sources, skills, similar repositories that might hold useful input and tell it very roughly what I need and off it goes, I'll grab coffee.

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

#94

Post by georgemcbay »

timcobb wrote: post #30
esafak wrote: post #27

Earlier quoted context omitted.

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

> 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 of their societal status and "they" are lagging very far behind on building their robot armies.

If we poorly navigate this transition the outcome should be worrying them more than it worries us.

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

#95

Post by marcosdumay »

Quothling wrote: post #88
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…

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…

So... The AIs with no model of the world are replacing software developers that have no model of the world?

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

#96

Post by fidotron »

simianwords wrote: post #82
fidotron wrote: post #32

Earlier quoted context omitted.

It's still clear that LLMs lack spatial reasoning, either in the concrete or abstract, and while that sort of reasoning has been downplayed by academia for at least a century it is fundamental to technology and industry. (And many would say for science and mathematics too). They will, however, get there as well either directly or as interfaces to models that do, and your core point stands.

Is there any proof that they are not good at special reasoning? Arc agi 1 and 2 are saturated.

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.

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

#97

Post by abixb »

throw310822 wrote: post #89
Izmaki wrote: post #77

Earlier quoted context omitted.

Seconded on the "not cheap" argument here. I've spent $25 worth of tokens completing a one-week task in an afternoon, or rather my company spent the money. I would never have personally felt OK with throwing this much money after some prompting back and forth for a few hours, one lazy Saturday afternoon. I ran the risk of not finding the solution before the token usage would be too high for me to want to carry on, if…

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.

/r/whooosh

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

#98

Post by anorwell »

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?

It was rejected for being wrong (or most charitably, incomplete).

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

#99

Post by rakel_rakel »

Quothling wrote: post #88
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…

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…

Interesting, thanks. I don't know where "around here" is, but the signals I've seen in a lot of articles is that the demand for junior software people has taken a dive since a year or two back, with student programs etc getting cancelled. One googler said they were getting a junior to their team and that was kind of a big deal because it hadn't happened in that whole department for a long time.

In relation to that, I guess my question becomes: if the same thing will happen in math research, who will write the ten page math proof prompts in the future?

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