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

#211

Post by ratg13 » Sat, Jul 18, 2026, 6:25 PM UTC

Levitz wrote: post #134

mw67 wrote: post #14

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

Intelligence on its own is not very useful though. We put it on a pedestal because it creates huge potential when paired with other things, wisdom, discipline, empathy, but on its own?

AI / LLMs are not intelligence .. they are just a prediction engine that has been branded as 'intelligence' by marketing employees

At the end of the day it is still making a best guess at what the user wants based on data it has seen before.

It still requires someone smarter than the output to be able to evaluate if the result is any good, or just hand waving.

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

#212

Post by shinryuu » Sat, Jul 18, 2026, 6:35 PM UTC

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.

For whom is the question you should ask.

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

#213

Post by raincole » Sat, Jul 18, 2026, 6:39 PM UTC

throwaway1707 wrote: post #132

threethirtytwo wrote: post #108

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.

I had to create an account to respond to this because I am quite convinced these math problems they are "solving" are pure marketing. Why is it only GPT doing this, why not Claude? Why does Terrance Tao do marketing for OpenAI? I suspect OpenAI has hired math researchers to solve obscure problems and put them in their training set, purely for marketing reasons. There was a good comment on the Pelican bicycle svg yest…

It's such a weird train of thoughts lol. You're using the fact that

- Claude isn't doing that

as evidence to support the assumption that

- it's a marketing trick

Which is obviously non sequitur, as if it were a marketing trick, Anthropic could do it too. Anthropic isn't known for not spending on marketing.

Honestly, nowadays I question human's reasoning ability more than I question AI's.

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

#214

Post by School-Cotton » Sat, Jul 18, 2026, 6:40 PM UTC

z3t4 wrote: post #31

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.

When machines are doing all the work - we no longer have to.

What makes you think the people who own the machines will share their resources with you?

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

#215

Post by shinryuu » Sat, Jul 18, 2026, 6:42 PM UTC

derac wrote: post #209

raincole wrote: post #199

Earlier quoted context omitted.

It genuinely scares me that some people's first reaction to this news is banning LLM.

Maybe we should also burn books and lobotomize ourselves to make science more fun and challenging. The ego here sickens me. I don't care about your ego. I want accelerated material science, medical science, energy, better outcomes for people across the world.

I also want better outcomes for people around the world.

Memes like the permanent underclass and the massive incentive of replacing workers across the world does not bode well for a better outcome for people across the world.

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

#216

Post by qnleigh » Sat, Jul 18, 2026, 6:45 PM UTC

barnacs wrote: post #118

threethirtytwo wrote: post #108

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.

I hold my stance that LLMs are stochastic parrots. Making the parrots ever more complex and training on ever more data produced by intelligent, creative beings may make them more useful or convincing but does at no point give rise to intelligence or creativity.

I won't touch creativity, but if this and other results like it do not demonstrate intelligence, what does? How was it able to solve problems that specialist mathematicians have tried and failed to solve for years?

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

#217

Post by lg5689 » Sat, Jul 18, 2026, 6:48 PM UTC

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?

There was recently an announcement that a group trying to formalize it found a gap exactly where other mathematicians were pointing. So to the extent there was any doubt, it should be gone now--the proof was incorrect.

But I agree LLMs have a lot of potential for checking proofs--both informally (they can read quickly and find gaps) and formally (by attempting to formalize).

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

#218

Post by thesz » Sat, Jul 18, 2026, 6:50 PM UTC

_alternator_ wrote: post #115

hodgehog11 wrote: post #92

Earlier quoted context omitted.

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.

I'd push back on this. Most of the core optimization techniques (eg, ADAM, stochastic gradient descent) are straight out of the convex optimization literature. Generally you need to use optimizers that work well on convex objectives because near minimizers, functions tend to be convex. (Proof by contradiction: a non-convex point has a strict descent direction.) The fact that neural networks are highly nonconvex has e…

ADAM does not work on simple convex problems [1].

  [1] https://parameterfree.com/2020/12/06/neural-network-maybe-evolved-to-make-adam-the-best-optimizer/
  [2] https://arxiv.org/pdf/1905.09997

[1] refers to [2], which shows that ADAM is not as efficient as gradient descent with line search on some problems, including neural networks.

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

#219

Post by sota_pop » Sat, Jul 18, 2026, 6:53 PM UTC

xeromal wrote: post #180

alexpotato wrote: post #174

Earlier quoted context omitted.

> so advanced that it's just as readable to me as Greek I used to feel this way about statistics. The language and terms are hard to understand and many of the formulas are taught as "just memorize this" instead of building up from first principles. But then I started using statistics to analyze something I cared a lot about (paintball) and I quickly realized it's like learning anything new: - there is jargon - and c…

I gotta know what you use stats for regarding paintball. I haven't played in years but I loved playing back in the tipman 98 custom era (not sure if that's still a popular marker).

Wow, a blast from the past to be sure. Was not but any means avid, but did own a tipman. And was always dazzled when someone showed up with an angel.

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

#220

Post by slashdave » Sat, Jul 18, 2026, 6:56 PM UTC

threethirtytwo wrote: post #188

slashdave wrote: post #146

Earlier quoted context omitted.

Must be nice knowing you have a clear understanding of "objective reality" that others don't.

Is it not objective reality that the feat performed by the LLM here is much more then parroting or summarizing something? It's doing math proofs. At this point, it's fully clear that objective reality is that the LLM is not parroting anything here.

It's parroting proofs. This is no different than parroting a story.

https://lean-lang.org