alt Hacker NewsGPT-5.6 used a prompt to close a 30-year gap in convex optimization
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> 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?
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.com/r/math/comments/1uxj3cy/after_openais...
In the prompt I basically just throw all reasonable approaches at it, without making a big distinction for what to explore most, and these approaches would all be reasonable for someone who knows the area. Sol helped me with the prompt as well, for which I gave it the CDC prompt, some ideas and specifications, a crystal clear problem description, and then modified things slightly myself after. One thing I do wonder is how much it accessed memory of previous chats, since as mentioned I had worked with 5.5 and 5.4 on this previously, and the main construction is not so different from something I discussed there. But, the function class max of affine functions that worked in the end was also in my prompt, so I'm not totally sure.
So it's not clear to me the degree to which "GPT-5.6 used a prompt" to close the gap etc, or the author basically did all the work himself and assigned it to GPT-5.6 out of enthusiasm.
In the Reddit post there was clarification that this was done with Sol Pro not Ultra - curious what is everyone’s mental model of the difference.
My understanding is that ChatGPT Pro is effectively a multi agent system, or somehow uses multiple LLMs in parallel and selects a best answer. And Ultra is more similar to Claude-Code UltraCode where the main agent can choose to create a dynamic JS workflow that deterministically orchestrates multiple agents to handle different parts of a task and have adversarial checkers etc.
Is that more or less the difference? Any substantiating sources would be great to see.
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?
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
We have a non peer reviewed proof in a niche area of mathematics claiming to have been "co-written" by an LLM. What are the comments about? Lamenting or celebrating humanity's intellectual death... Very insightful.
I tried using AI to solve some advanced math problems. One thing I see is that they can throw an enormous amount of brute force into a problem. When mathematical logic can be brute forced we will see some interesting advances.
Not yet peer reviewed
The amount of people several months ago stating that no one cares about the "unsolved" mathematical problems that AI is able to solve is funny.
Can't wait for GPT to prove that P=NP (or not)!
I can't see this article as Reddit doesn't allow me to view it. Do we have to use Reddit though? It's a horrible website.
It says I've been "blocked by network security". MSIE on Windows. Reddit must really be circling the drain.
Genuinely asking... How do you get chatgpt to work for 148 mins when I can't get gemini to think for even a minute at a time?
Basically, he proved that *information is power.* If you don't know which way to go (the subgradient), you're gonna be calculating forever!
The problem is that we're going to have another deepseek moment when someone uses GLM or Kimi K3 to do this.
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 except for select few. Maybe this is ok, I don’t know.
Another solution is we find a way to mind-meld with AI so that human + Ai >> AI alone. This is dystopian, who gets to decide who mind melds with AI, how much will it cost etc etc.
For the stupid copes that the prompt required human ingenuity, let me first add that the author used GPT5.6 to write most of the prompt. He just gave some mild direction. That amount of direction does not require deep expertise and the expertise required will keep falling with time, eventually an undergrad can create this loop and then maybe a high school student.
And prompt engineering / loop engineering nonsense is not real. Calling it engineering is a psy-op because it is something simple, imprecise and future models will be much better at it than you.
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 that this wasn't a matter of "ChatGPT, solve this unsolved problem. Make no mistakes." and required substantial domain expertise and human research beforehand.
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 knowledge you have. You could call it a stratification of input
I'm starting to feel like there's no place left for programmers like me who focus on quickly churning out MVPs.
nah, scientist with the name Shakey Onail found this and all creds are given to LLMs is crazy
Waiting for comments saying that LLMs can't produce anything new and general goalpost moving.
could machine-learning even handle a TEN PAGE PROMPT just a year ago?
this is changing my mind, at least about experts using advanced tools like any profession where it's like the magic of watching a lifetime of hard-earned skill at work
> After seeing OpenAI’s CDC result, I wrote a much more elaborate prompt following the same general methodology. My prompt is about ten pages long and attached at the end of the preprint (see collection of links below). There is a lot baked into this prompt, on approaches to try and also on how exactly the model should proceed, but it's built exactly in the style of OpenAI's CDC prompt. One note is that I gave it a relatively small error requirement, to prove the quadratic lower bound under order d⁻⁴ accuracy.
> After 148 minutes, GPT-5.6 Sol Pro returned a proposed proof resolving the quadratic dimension dependence at accuracy of order d⁻³. After checking things myself, I formally verified the proof in Lean, and it passed the formal verification check.
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.
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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)
Is this interesting? AI does what we made it to do, news at 8?
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 bounded domain.) Anyway, showing upper bounds on time complexity is "easy" because it's just the runtime of your algorithm. Showing (nontrivial) lower bounds is usually much harder because it requires constraining all algorithms.
This proof apparently shows that the lower bound time complexity is equal to the time complexity of an existing 30-year old algorithm: it requires Omega(d^2) function evaluations to solve over this class of functions.
My gut says likely implies that d is the minimal number of evaluations if you have a gradient oracle because you can approximate a gradient with d function evaluations, but I'm not sure how hard it is to make that rigorous.