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Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

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Re: Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#161

Post by tmoertel »

madrox wrote: post #111
bitwize wrote: post #71

Earlier quoted context omitted.

The ownership class will be sharper. They will know how to exploit capital and turn it into more capital with vastly increased efficiency. Everybody else will be hosed.

I'm not sure if people will be more hosed than before. Historically, what makes people with capital able to turn things into more capital is its ability to buy someone's time and labor. Knowledge labor is becoming cheaper, easier, and more accessible. That changes the calculus for what is valuable, but not the mechanisms.

> Historically, what makes people with capital able to turn things into more capital is its ability to buy someone's time and labor.

You forgot to include resources:

What makes people with capital able to turn things into more capital is their ability to buy labor and resources. If people with more capital can generate capital faster than people with less capital, then (unless they are constrained, for example, by law or conscious) the people with the most capital will eventually own effectively all scarce resources, such as land. And that's likely to be a problem for everyone else.

Re: Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#162

Post by hodgehog11 »

throwaway27448 wrote: post #143
hodgehog11 wrote: post #87

Earlier quoted context omitted.

This argument, that LLMs can develop new crazy strategies using RLVR on math problems (like what happened with Chess), turns out to be false without a serious paradigm shift. Essentially, the search space is far too large, and the model will need help to explore better, probably with human feedback. https://arxiv.org/abs/2504.13837

I agree that LLMs are a bad fit for mathematical reasoning, but it's very hard for me to buy that humans are a better fit than a computational approach. Search will always beat our intuition.

Yes and no. I think we have vastly underestimated the extent of the search space for math problems. I also think we underestimate the degree to which our worldview influences the directions with which we attempt proofs. Problems are derived from constructions that we can relate to, often physically. Consequently, the technique in the solution often involves a construction that is similarly physical in its form. I think measure theory is a prime example of this, and it effectively unlocked solutions to a lot of long-standing statistical problems.

Re: Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#163

Post by DrewADesign »

portly wrote: post #131
amelius wrote: post #35

Earlier quoted context omitted.

> The goal should be to put everyone out of a job. Yeah, but why does it need to take the fun jobs first, like painting, writing poems, coding, making music, ... I want the AI to cook, do the dishes, take out the trash, etc.

> like painting, writing poems, coding, making music Citation needed. Do you have an example of someone in the arts losing their job because of AI?

Yes. The entire job markets for game concept art, stock photography, and storyboarding have been decimated and those were the lowest-hanging fruit for diffusion model applications.

Re: Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#164

Post by ori_b »

specvsimpl wrote: post #124
parineum wrote: post #122

Earlier quoted context omitted.

There is a kind of rubrik I use on stuff like this. If LLMs are discovering new math, why have I only read one or two articles where it's happening? Wouldn't it be happening with regularity? The most obvious example of this thinking is, if LLMs are replacing developers, why us open ai still hiring?

I can only say that at family meetings, I hear people talk about contracting with a shop that used to have 4 web designers, but now it's 1 guy, delivering 4x faster than before. So devs are being replaced.

Why aren't they delivering 4x more work? Does the world no longer need software?

Re: Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#165

Post by cyclopeanutopia »

podgorniy wrote: post #158
ansc wrote: post #155

Earlier quoted context omitted.

That's not just a great insight, but one that's worth carrying with us. That's why I built RememberBuddy. It's the one place for you to store your every-day insights so you don't forget.

What a great project idea, worth getting it clients. That's why I've build a platform for promoting young startapers to find theit niche audience. Give it a try and go to the moon!

What a great idea, that's why I'm building a platform to send you all to the moon.

Re: Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#166

Post by arcxi »

arjie wrote: post #102
amelius wrote: post #35

Earlier quoted context omitted.

> The goal should be to put everyone out of a job. Yeah, but why does it need to take the fun jobs first, like painting, writing poems, coding, making music, ... I want the AI to cook, do the dishes, take out the trash, etc.

Well, because consuming art, reading poems, having code written for you that solves a problem, and listening to music is also fun. Recently I wanted a grand elegy to Britain written as the Empire started failing and set to music in a specific style. I had it playing in the background while fixing some issues with some software. It truly was joyful to have this available to me. It didn’t have to have mass appeal or ne…

To me the image of a world where everyone does menial work while entertaining themselves with AI-generated "art" doesn't seem fun, it seems extremely depressing and dystopian. I guess we just have different values.

Re: Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#167

Post by 986aignan »

abcde666777 wrote: post #148
specvsimpl wrote: post #126

Earlier quoted context omitted.

You are aware of software verification? The AI can prove (mathematically) that its code implements the spec.

That just takes you back to the debate about the code being the spec.

The code lets you shoot yourself in the foot in a lot more ways than a spec does, though. Few people would make specs that include buffer overflows or SQL injection.

Re: Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#168

Post by [deleted] »

breatheoften wrote: post #89

Like so many things -- the evolution of AI math will I think follow trajectories hinted at in the 90s by the all time great sci-fi author Greg Egan. The nature of math won't change -- but the why of it definitely will. Egan imagined a future ai civilization in Diaspora where "math discovery" -- by nature in the future perhaps accurately described as "mechanistic math discovery" is modeled by society as a kind of salt…

[deleted]

Re: Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#169

Post by latentsea »

hodgehog11 wrote: post #138
threethirtytwo wrote: post #100

Earlier quoted context omitted.

But are you ok with the trendline of ai improvement? The speed of improvement indicates humans will only get further and further removed from the loop. I see posts like your all the time comforting themselves that humans still matter, and every-time people like you are describing a human owning an ever shrinking section of the problem space.

I used to be worried, but not so much anymore. It used to be the case that the labs were prioritising replacing human creativity, e.g. generative art, video, writing. However, they are coming to realise that just isn't a profitable approach. The most profitable goal is actually the most human-oriented one: the AI becomes an extraordinarily powerful tool that may be able to one-shot particular tasks. But the design of…

On the contrary the depth and breadth we're becoming able to handle agentically now in software is growing very rapidly, to the point where in the last 3 months the industry has undergone a big transformation and our job functions are fundamentally starting to change. As a software engineer I feel increasingly like AGI will be a real thing within the next few years, and it's going to affect everyone.

Re: Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#170

Post by gottheUIblues »

vatsachak wrote: post #61
slopinthebag wrote: post #59

Earlier quoted context omitted.

Yeah, it's hard to compare management and programming but they're both multimodal in very different ways. But there's gonna be entire domains in which AI dominates much like stockfish, but stockfish isn't managing franchises and there is no reason to expect that anytime soon. I feel like something people miss when they talk about intelligence is that humans have incredible breadth. This is really what differentiates…

Exactly. It's what the execs are missing. Also animals thrive in underspecified environments, while AIs like very specific environments. Math is the most specified field there is lol

So specified .. that it can actually prove it can't be completely specified by any single specification
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