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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

#191

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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

Oooh yeah that's really good framing. Humans have been building machines that outperform humans for hundreds of years at this point, but all in problems which are extremely well specified. It's not surprising LLM's are also great in these well specified domains. One difference between intelligence and artificial intelligence is that humans can thrive with extremely limited training data, whereas AI requires a massive…

Exactly. I would not want to have a pure math career or a performance engineering career in 10 years.

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

#192
post #133

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Yes but "the search space is too large" is something that has been said about innumerable AI-problems that were then solved. So it's not unreasonable that one doubts the merit of the statement when it's said for the umpteenth time.

I should have been more specific then. The problem isn't that the search space is too large to explore. The problem is that the search space is so large that the training procedure actively prefers to restrict the search space to maximise short term rewards, regardless of hyperparameter selection. There is a tradeoff here that could be ignored in the case of chess, but not for general math problems. This is far from…

The other trick could be bootstrapping through mathlib.

As you said brute forcing the search space as the starting procedure would take way too long for the AI to build intuition.

But if we could give it a million or so lemmas of human math, that would be a great starting point.

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

#193

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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.

"to the point where in the last 3 months the industry has undergone a big transformation "

Oh... this again.

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

#194
post #102
post #35

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> 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…

And if you consider art something to be consumed for light entertainment, that viewpoint makes sense. For people that consider art a way to express, and conversely experience, otherwise inexpressible things about our humanity, your wonderful world is a cheap, superficial, and sad way for tech companies to amalgamate and sell other people’s ideas and labor.

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

#195
post #21

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I kind of feel like software engineers working on improving AI are traitors working against other SE’s trying to make a living. However… I have to acknowledge my craft of SE has been putting people out of work for decades. I myself came up with business process improvement that directly let the company release about 20 people. I did this twice. So… fair play.

In the grand scheme it's good to invent things that replace human labor. It frees up people to do more interesting things. The goal should be to put everyone out of a job.

The problem is that most people consider doing art, writing, making music, and heck, even coding, “more interesting” than orchestrating a pile of knowledgeable but idiotic robot interns because that’s what’s profitable.

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

#196

Earlier quoted context omitted.

I kind of feel like software engineers working on improving AI are traitors working against other SE’s trying to make a living. However… I have to acknowledge my craft of SE has been putting people out of work for decades. I myself came up with business process improvement that directly let the company release about 20 people. I did this twice. So… fair play.

Sure, but that’s fine. I don’t have any allegiance to other software engineers.

Do you think other people’s sense of ethics should be so transactional towards you? Companies that might sell your data to shitty date brokers have no allegiance to you. Muggers have no allegiance to the people they mug. They’re both executing their professional tasks that benefit the people they have allegience to. They’re contributing to the velocity of money in our society. The data might even be used to market beneficial goods and service. So… thumbs up? Or would you feel differently if it was someone else profiting at your expense.

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

#197

Earlier quoted context omitted.

Sure, but that’s fine. I don’t have any allegiance to other software engineers.

Do you think other people’s sense of ethics should be so transactional towards you? Companies that might sell your data to shitty date brokers have no allegiance to you. Muggers have no allegiance to the people they mug. They’re both executing their professional tasks that benefit the people they have allegience to. They’re contributing to the velocity of money in our society. The data might even be used to market be…

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

#198

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"our new grad student made progress on the combinatorics problem we posed!" "oh awesome let's see if he can solve p!=np!"

Yes, too many people here do not understand the distance between the problems the article is discussing (and LLMs have solved) and the big problems in math and CS.

> Comments should get more thoughtful and substantive, not less, as a topic gets more divisive.

Do you have any good links on SoTA research in the provability of P!=NP?

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

#199
post #187

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AI doesn't change the equation; it makes the equation more brutal for people who don't have capital. If you don't have capital, the only way to get it is by trading resources or labor for it. Most poor people don't have resources, but they do have the ability to do labor that's valued. But AI is a substitute for labor. And as AI gets better, the value of many kinds of labor will go towards zero. If it was hard for po…

Ok, I'm following you. You're saying because labor gets cheaper it will be harder to make a living providing labor. Not disagreeing, but I wonder how much weight to give this argument. History shows a precedent of productivity revolutions changing the workforce, but not eliminating it, and lifting the quality of life of the population overall (though it does also create problems). Mixed bag with the arc bending towar…

Entire classes of workers have been put in the poorhouse on a near permanent basis due to technological changes, many tines during the past two centuries of industrial civilization. Without systemic structural changes to support the workforce this will happen/is already happening with AI.

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

#200
post #73

Earlier quoted context omitted.

But LLMs have proven themselves better at programming than most professional programmers. Don't argue. If you think Hackernews is a representative sample of the field then you haven't been in the field long enough. What LLMs have actually done is put the dream of software engineering within reach. Creativity is inimical to software engineering; the goal has long been to provide a universal set of reusable components…

Actually I will argue. Complex systems are akin to a graph, attributes of the system being the nodes and the relationships between those attributes being the edges. The type of mechanistic thinking you're espousing is akin to a directed acyclic graph or a tree, and converting an undirected cyclic graph into a tree requires you to disregard edges and probably nodes as well. This is called reductionism, and scientific…

> Saying that LLM's are better than most professional programmers is also trivially false, you do yourself no favours making such outlandish claims.

You grossly underestimate how awful one can be and still call themselves a "professional" in the field. Software engineering has effectively no standard certification of competence, which is part of why it's not actually an engineering field at all. So I stand by my statement that LLMs are better at writing code than most people working professionally as programmers. Again, Hackernews is not a representative sample, let alone the kind of programmer we admire and view as authoritative here on Hackernews. Most programmers require considerable oversight as well as detailed standards to follow in order to produce work without gumming up a code base. If you want to know why so much enterprise stuff is so bloated with heavy frameworks and a twisty maze of best practices like OO, SOLID, GoF patterns, etc. it's for this reason. The LLMs have access to a vast (if compressed/summarized) repository of knowledge about programming problems and commonly employed solutions in a variety of languages, and the ability to draw upon it instantly. Most humans, including myself, do not.

Anyway, as Tim Bryce observed in 2005, based on his father Milt's work in the 70s, most of the creativity and human in software development happens in the business/systems analysis phase, not programming, at least if you're employing a structured, rigorous, proven methodology. Milt Bryce turned systems design from an art into a proven, repeatable science, and with that a view of programming that's largely mechanistic. "There are very few true artists in programming; most programmers are just house painters."

> This might be besides the point, but I also wish AI boosters such as yourself would disclose any conflict of interests when it comes to discussing AI.

I'm not boosting squat. I'm telling it like it is, and talking about decisions in our field that have already been made. It is no longer up for debate that AI use is an integral part of software engineering now, and writing code "the old way", in an editor with maybe autocomplete, refactoring tools, etc., will soon go the way of punchcards. The business class that actually runs things has already decided this. If you're getting suspicious and demanding conflict-of-interest disclosures from someone who spells this out, your understanding is out of date.

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