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

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Article URL: https://old.reddit.com/r/math/comments/1uxj3cy/after_openais_cdc_proof_announcement_gpt56_used_a/

Comments URL: https://news.ycombinator.com/item?id=48957779

Points: 578

# Comments: 377

Hacker News 讨论

578 points · 377 comments · 查看原帖

  1. _alternator_

    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 t

  2. 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?

  3. YeGoblynQueenne

    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 ac

  4. d4rkp4ttern

    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.

  5. a_imho

    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?

  6. mw67

    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

  7. pona-a

    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.

  8. charlieyu1

    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.