Live data from Hacker News

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

old.reddit.com

341–350 of 414 posts

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

#341

Earlier quoted context omitted.

Terrence Tao getting paid by openAI is, to you, the most probable conclusion... much more so then the LLM actually being able to come up with math proofs?

Terrance Tao has for a fact appeared in promotional material for OpenAI. Based on my Googling the consensus seems to be he is paid for it, but I cannot confirm that. I do think it's very likely that OpenAI pays for solutions like these to put in the training set, and then we get material like this Reddit thread. They market themselves as selling "intelligence", and solving these math problems is something people view…

You can go through my commenter history and know I'm no fan of LLMs. I don't overstate LLM capabilities and am highly skeptical of them in general. 5.6 Pro is genuinely pretty good at certain kinds of math problems that just require trying out lots and lots of solutions, mostly because it's stubborn and can run a bunch of instance in parallel. It is NOT good at coming up with unique ideas or recognizing when its proof approach is doomed, and if the correct approach isn't in its "bag of tricks" for tackling a specific kind of problem, it is not going to get it without a lot of guidance. That said: I 100% believe that it's solved the problems people are claiming that it solved.

The way you should read this is (IMO) not that LLMs have somehow achieved AGI, but that a lot of mathematical research is more about knowing a huge amount of mathematical background, being stubborn, and getting lucky with an approach than it is about brilliant insight. Many people who don't think of themselves as particularly mathematically gifted could have made progress on these problems if they were given enough time and were interested enough. What's notably different about 5.6 (and born out in benchmark after benchmark) is that it does seem to genuinely "reason" through stuff at all -- without that, persistence is pretty worthless because the LLM just goes wildly off the rails if it's put to work for long enough (5.6 itself will still do this if it can't find an answer in a reasonable amount of time).

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

#342
post #139

Earlier quoted context omitted.

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 th…

Unless you’re claiming that AIs will suddenly (and very soon) stop improving, they are obviously a threat to everyone’s job. Calling notable conjectures that have been open for decades “low-hanging fruit” is an act of desperation. Most professional mathematicians couldn’t have proved those conjectures if their lives depended on it.

> COUNTEREXAMPLE TO EULER'S CONJECTURE ON SUMS OF LIKE POWERS

> BY L. J. LANDER AND T. R. PARKIN

> A direct search on the CDC 6600 yielded:

    27⁵ + 84⁵ + 110⁵ + 133⁵ = 144⁵
> as the smallest instance in which four fifth powers sum to a fifth power. This is a counterexample to a conjecture by Euler that at least n nth powers are required to sum to an nth power, n>2.

https://www.ams.org/journals/bull/1966-72-06/S0002-9904-1966...

It is a conjecture whether grinding it out on Lean is a difference in kind, rather than degree. I say degree. But it remains to be seen.

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

#343

Earlier quoted context omitted.

This has always been the case though that "another avenue of human craftsmanship has been taken over by the machines." It's good if we can have robots building things instead of having humans slumped over a workbench in a sweatshop piecing things together. It's good if we can have LLMs spitting out code rather than CS grads working 15 hour days at fintech startups or whatever. The conditions were never (ever) good be…

Surgeons too now? Another avenue for human skill destroyed. I actually want to exit. I want to live in a society where humans flourish not AI. Actually one just needs to walk the streets of Japan and compare that to US. Tokyo has hundreds of small shops with humans doing specific niche stuff, perfecting their arts. That’s all so beautiful. America has massive warehouses and supermarkets, with completely uninterested…

What you write is what's profoundly depressing.

The only way you see people flourishing is through coercion, by society or by the world. You'd explicitly rather prolong this codependency for your aesthetic preferences even, as per your own words. We're already just circus monkeys in your world.

You cannot fathom people pursuing self-improvement because e.g. developing or being capable is inherently enjoyable. You only see a world where such activities are a must, or a manufactured must. That's your measuring stick and that's the entire pie for you.

I mean this in the least combative way possible, but it sounds like you have things to sort out on your end first, before charting a course for the world to follow.

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

#344

Earlier quoted context omitted.

[flagged]

I'm sorry this comment didn't sit well with you. My goal was to induce discussion by describing the claimed result (which was buried in the post), not to discourage it. If you have more specific feedback on what you found distasteful, I'd be happy to hear it.

I apologize. My comment was unfair and regretful.

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

#346
post #107

> 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…

I was trained as a mathematician and worked as a math researcher for a little while (now working as a private tutor), and based on my experience I'd say this description is basically right, with one extra wrinkle. In order to get a Ph.D., you have to do some sort of original research, so in that sense you're working on "previously unsolved stuff" basically right from the start. But that doesn't entail doing anything…

> In order to get a Ph.D., you have to do some sort of original research,

China has now introduced "practical PhDs" where you have to build some practical machine instead.

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

#347

Earlier quoted context omitted.

Sometimes I read a comment on HN that is so advanced that it's just as readable to me as Greek. Love reading it just to see someone work though!

> 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…

This is a great suggestion, use complex hard stuff for doing fun stuff.

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

#348

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?

ChatGPT pro will work 20-30 min in my experience pretty regularly in my experience. Never had 148min but it seems plausibly in the very right tail.

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

#349

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 bounde…

Yes, order d is the minimal number of evaluations of gradients needed for the same problem! That has actually been known since 1979 (Nemirovsky and Yudin showed that), and there are methods with the same complexity so this question in the gradient model has been solved for a long time. "because you can approximate a gradient with d function evaluations" was exactly why d^2 made sense as a lower bound for this case! Basically, the lower bound question can also be thought about as "can you do better than approxing a gradient?", so this result says no.

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

#350

> 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…

I would agree with your take. I (author of the post & paper) learned a ton from working on small parts of problems my PhD advisor was doing a lot of the heavy lifting on, and later also from getting some results that were essentially putting together the right pieces that already existed followed by some deep-in-the-weeds analysis.
Post reply on HN