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Have you not heard of things like AlphaFold?
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
#82Crazy 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
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.
Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#83Earlier quoted context omitted.
This apparently required a 10-page prompt. It seems like someone needs to know enough to write it?
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”
Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#84[dead]
Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#85Crazy 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
Ever heard of the infinite monkey theorem?
This is basically what LLMs do on really hard tasks. Prompt it a million times on a really hard problem and it might output the correct answer once.
Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#86I 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.
Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#87> 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…
This apparently required a 10-page prompt. It seems like someone needs to know enough to write it?
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.
Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#88> 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 them. Even in the energy industry where I work, where you'd think it would be obvious from the context that you should prioritize runtime safety over debug safety, the current AI models struggle to do so. As far as seniority goes, though. If we can find a young developer with little experience who actually knows computer science, we're much more likely to hire them... Since they are cheaper.
This isn't something which is unique to software development though. We're currently building enterprise AI apps that we can deploy into the AI agents working for anyone of our employees. The key thing we're currently seeing is that the people in a team who are the ones that everyone turn to for advice, are the only people who aren't in "danger". Even people who are great at their jobs are being outperformed by AI in many cases.
I think it'll be a massive challenge for our society in the coming years. Maybe we're even going to get to the point where the AI will also be capable of replacing a lot of the "domain experts". Right now that seems far out, but then, if you had asked me about AI four months ago I would've told you it was all hype.
Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#89Earlier quoted context omitted.
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…
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.
Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#90Earlier 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”
We're also at the point where you can roll out context to your entire organisation. I created an app for our m365 Cowork and deployed it to everyone who develops software. It does a couple of things, but it main knows our compliance policies and can guide developers through writing the documentation needed for NIS2 compliance. It also guardrails against non-approved packages, and helps developers find alternatives, or if none can be reasonably found, how to get a new package/dependency approved (or rejected).
A few months back this would be something every developer kind of did on their own. Maybe they shared skills, we certainly encouraged it and tried to do all the change management things, but nobody really had the same versions of the skills. Which was horrible in the deployment pipelines, something like the compliance documentation often had to go back and forth several times before it could be approved. Now it's just there, for everyone.
In a year or two, I expect a lot of these things to have become even more standardized. So that we don't even really have to build our own apps, but can simply use the ones in the catalog with minimal configuration (and that config will likely only be necessary because I'm from a tiny country that nobody will maintain standards for).