GPT-5.6 used a prompt to close a 30-year gap in convex optimization • Hacker News Board

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

#51

Post by xg15 » Sat, Jul 18, 2026, 2:10 PM UTC

cromka wrote: post #19

semiquaver wrote: post #15

Earlier quoted context omitted.

You’re at least 18 months out of date claiming that prompting will be the new hot skill.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.

That doesn't make any sense; you can't have one LLM to read your mind to prompt another LLM.

Waiting for the next Neuralink announcement...

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

#52

Post by nicce » Sat, Jul 18, 2026, 2:11 PM UTC

fidotron wrote: post #36

skeke wrote: post #34

Earlier quoted context omitted.

Oh brother AI hasn’t even taken the class of jobs associated with customer service lmao

Do we employ mathematicians in customer service roles?

Luckily the job situation for pure mathematicians was already bad.

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

#53

Post by fidotron » Sat, Jul 18, 2026, 2:12 PM UTC

sscaryterry wrote: post #46

fidotron wrote: post #36

Earlier quoted context omitted.

Do we employ mathematicians in customer service roles?

Thats a silly and obtuse comment.

You mean the answer betrays the point: customer service is surprisingly hard, we just have a large number of people that are capable of doing it.

This is what the whole https://people.csail.mit.edu/brooks/papers/elephants.pdf is about.

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

#54

Post by jvanderbot » Sat, Jul 18, 2026, 2:12 PM UTC

skybrian wrote: post #48

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…

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.

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

#55

Post by lozenge » Sat, Jul 18, 2026, 2:13 PM UTC

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…

It is lean-verified, so it can be trusted unless the Lean statement of the hypothesis is not an accurate description of the hypothesis.

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

#56

Post by JustFinishedBSG » Sat, Jul 18, 2026, 2:14 PM UTC

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…

My experience may not be entirely representative because to be entirely honest I’m not exactly a great researcher and there are brilliant PhD students. That said it indeed was my experience that in the pre-PhD / early PhD period ( or even longer … ) your advisor proposes (gives) you pretty low hanging stuff that he mostly already knows how to solve, at least at a high level, with the expectation that it will teach you to use the mathematical tools you need.

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

#57

Post by oulipo » Sat, Jul 18, 2026, 2:17 PM UTC

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)

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

#58

Post by a_imho » Sat, Jul 18, 2026, 2:18 PM UTC

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?

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

#59

Post by elhart05 » Sat, Jul 18, 2026, 2:19 PM UTC

[dead]

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

#60

Post by ch4s3 » Sat, Jul 18, 2026, 2:20 PM UTC

skybrian wrote: post #48

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…

This apparently required a 10-page prompt. It seems like someone needs to know enough to write it?

Certainly. This feels similar, to me, to how building complex software with LLMs works today in practice. You need to know a lot to set up goals and guardrails and verify outputs. For me, making the bits change was always the fun part, not tangling with text in my editor, though that had its moments.