Earlier quoted context omitted.
Manual labor
Even that is being automated now, it was one of the thing being automated very early on in factories..
And yet we still have human laborers. Robots are a lot more expensive than AI inference.
GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
421–430 of 467 posts
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#422Both impressive and terrifying. But as always, the methodology is buried: how many open problems were tried until they found a success? If they tried this on 1000 problems and this is the one that succeeded, it still means that there are 999 open problems that an LLM cannot one-shot. It seems likely that this would remain the situation until the next model. If this is the first one they tried, maybe we’re totally hos…
> But as always, the methodology is buried: how many open problems were tried until they found a success? Not only that, but they have like 500 world-leading experts in mathematics and IMO alumni, so how do we know one of the agents wasn't hardcoded to return a proof that the mathematicians had found? I'm a mathematician/graph theorist, and I've tried ChatGPT 5.3, 5.4, 5.5, and now 5.6 on a bunch of simple-ish open p…
What is a "simple-ish open problem". I guess it falls under "solving this open problem in mathemathics is left as an exercise to the reader" ;)
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#423Earlier quoted context omitted.
> However, it seems the proof is extremely concise so it seems that it is exploiting a clever trick that somehow all the experts missed. Why is that a "however"? My reading is that it found a genuinely new solution that is both elegant and previously missed. Seems like exactly the kind of result a human mathematician would aspire to.
clever tricks has value for sure. But the main way progress is done in mathematics is by building new theory, the proof of Fermat's Last Theorem is much more important because of the math it created to solve the problem, rather than actually solving the problem.
That depends on the branch of math. Combinatorics is trick-oriented. Maybe this is why AI has done well in that.
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#424Earlier quoted context omitted.
Sorry to be nihilist, but you never had any objective value if you're thinking in these terms. As far as we know, the universe "just is". There is no universal objective value of human beings, at all, any one of us. You have to make or find your own value in the universe. I try not to think too hard about the nihilist side and try to appreciate that for some unfathomable reason, I seem to have what I call consciousne…
> As far as we know, the universe "just is". I don't know this. In fact, billions of people around the world don't know this. In fact, all evidence points to the contrary. You have objective value being made in the image of a personal God. Denying that leads to a lot of pain, namely nihilistic suffering because it's on you to "pull yourself up by the bootstraps" in any endeavor involving your own self-worth.
> made in the image of a personal God
How does that work? The physical image? Or the mental image? Either has big problems. An omniscient god is so cognitively beyond a mere "7+-2" human that the latter claim makes no sense at all.
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#425Earlier quoted context omitted.
This is a great question. Thanks for asking it. It really got people talking. My $0.02: Your value as a person never had anything to do with your value to the economy. It's time to relearn that fact. Check out some of Tom Hodgkins books for more. Or maybe anxietyculture.com.
But it is. My worth is based on what my value is, what I can do. What when I can no longer have any value on the job market?
Your economic value and your value as human being are two different things.
Yeah, you gotta eat, but some of us have been slaves for so long that we've started to believe that our self worth is defined by what we will fetch at auction. It is not.
Read more about the Protestant work ethic, it's history, and what life was like before men began to assume it was the one true view of life. Not very long ago nobody had clocks, and the idea that work was an ethic was a fringe, almost cult-like belief system. Now most humans routinely take stimulants every morning to be better servants, and mistake their job for their purpose on earth. That's just nonsense our culture invented though.
If the master wants you to do something, force him get out the whip. Don't let him live in your head rent free by adopting his crazy belief system.
YOU decide what your value is. Don't abdicate the decision to someone else.
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#426Both impressive and terrifying. But as always, the methodology is buried: how many open problems were tried until they found a success? If they tried this on 1000 problems and this is the one that succeeded, it still means that there are 999 open problems that an LLM cannot one-shot. It seems likely that this would remain the situation until the next model. If this is the first one they tried, maybe we’re totally hos…
> But as always, the methodology is buried: how many open problems were tried until they found a success? Not only that, but they have like 500 world-leading experts in mathematics and IMO alumni, so how do we know one of the agents wasn't hardcoded to return a proof that the mathematicians had found? I'm a mathematician/graph theorist, and I've tried ChatGPT 5.3, 5.4, 5.5, and now 5.6 on a bunch of simple-ish open p…
I’ve had a similar experience in physics. Excellent domain knowledge and semantic search, but the intellectual sparkle and reasoning just isn’t there and it still often throws out a lot of wrong ideas. It is very useful for coding.
But there is a discrepancy between (the implication behind) these reports and how I subjectively feel talking to LLMs. Granted, I don’t have access to whatever cutting edge model is out there for as many credits, but I also don’t feel like I’m talking to an IMO silver medallist.
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#427Both impressive and terrifying. But as always, the methodology is buried: how many open problems were tried until they found a success? If they tried this on 1000 problems and this is the one that succeeded, it still means that there are 999 open problems that an LLM cannot one-shot. It seems likely that this would remain the situation until the next model. If this is the first one they tried, maybe we’re totally hos…
They have to feed the bubble.
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#428Earlier quoted context omitted.
i think most things can be automated, but not everything i think AI will just replace jobs with new jobs, and humans will continue with open-ended goal setting, and probably jobs where being human is necessary: responsibility and authenticity, so judges, politics, leaders, chefs, etc. so in a way, the above commenter was correct, anything a programmer can automate, AI can do
It is a little bit suspicious that the big replacement didn't happen, yet. If it was so valuable then AI companies would directly create valuable things, not just sell API tokens. A proof like this is a good effort at trying to provide value directly, but still far away from real use. When OpenAI cures cancer I'll accept the fate, but till then I'm still seeing a lot of gambling going on.
Reminds me of crypto. A lotta tokens. A lotta gambling. Very little supplanting of crypto from fiat. Very few use-cases that revolutionize society, etc.
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#429Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#430Earlier quoted context omitted.
Hear me out on this one: For a lot of math departments, that is exactly why they teach this. Education is rooted in application. We have entire careers that depend on certain aspects of mathematics, so most companies gatekeep that career by a degree. The degree requires the class. The student taking the class may not even be old enough to drink alcohol yet, and they can't possibly be expected to know of all the appli…
The ultimate goal of university education is to raise researchers , who are the people that investigate the knowledge frontier of their field and then advancing it. To do that they have to understand a large part of the existing field so they can communicate with their peers, avoid investigating things that have already been throroughly explored, and draw useful connections to other fields. Even in more applied field…
> The ultimate goal of university education is to raise researchers
The head of my CS department was quoted as saying, "our job is to produce researchers!"
This was in the context of a conversation about why the program wasn't better suited for industry.
It turned out that in our department 7% of students ended up going into research.
So he was openly declaring his intention to disregard the needs of 93% of his students.
(I'm not arguing against research, or on going deep with the theory. I just thought that was kind of funny, and it seemed a bit wrong to me.)