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Epoch confirms GPT5.4 Pro solved a frontier math open problem

epoch.ai

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Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#51

Post by fxtentacle »

qnleigh wrote: post #43
tombert wrote: post #17

I was trying to get Claude and Codex to try and write a proof in Isabelle for the Collatz conjecture, but annoyingly it didn't solve it, and I don't feel like I'm any closer than I was when I started. AI is useless! In all seriousness, this is pretty cool. I suspect that there's a lot of theoretical math that haven't been solved simply because of the "size" of the proof. An AI feedback loop into something like Isabel…

I got Gemini to find a polynomial-time algorithm for integer factoring, but then I mysteriously got locked out of my Google account. They should at least refund me the tokens.

That sounds like the start of a very lucrative career. Are you sure it was Gemini and not an AI competitor offering affiliate commission? ;)

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#52

Post by ivalm »

kranner wrote: post #44
raincole wrote: post #41

Earlier quoted context omitted.

In other words, it's solving a problem.

Bet you didn't come up with that comment by first discarding a bunch of unsuitable comments.

because commenting is easy and solving hard problems is hard

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#53

Post by kelseyfrog »

himata4113 wrote: post #36
Validark wrote: post #33

I have long said I am an AI doubter until AI could print out the answers to hard problems or ones requiring tons of innovation. Assuming this is verified to be correct (not by AI) then I just became a believer. I would like to see a few more AI inventions to know for sure, but wow, it really is a new and exciting world. I really hope we use this intelligence resource to make the world better.

It's less of solving a problem, but trying every single solution until one works. Exhaustive search pretty much. It's pretty much how all the hard problems are solved by AI from my experience.

How do you think mathematicians solve problems?

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#54

Post by famouswaffles »

himata4113 wrote: post #36
Validark wrote: post #33

I have long said I am an AI doubter until AI could print out the answers to hard problems or ones requiring tons of innovation. Assuming this is verified to be correct (not by AI) then I just became a believer. I would like to see a few more AI inventions to know for sure, but wow, it really is a new and exciting world. I really hope we use this intelligence resource to make the world better.

It's less of solving a problem, but trying every single solution until one works. Exhaustive search pretty much. It's pretty much how all the hard problems are solved by AI from my experience.

If LLMs really solved hard problems by 'trying every single solution until one works', we'd be sitting here waiting until kingdom come for there to be any significant result at all. Instead this is just one of a few that has cropped up in recent months and likely the foretell of many to come.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#55

Post by storus »

Validark wrote: post #33

I have long said I am an AI doubter until AI could print out the answers to hard problems or ones requiring tons of innovation. Assuming this is verified to be correct (not by AI) then I just became a believer. I would like to see a few more AI inventions to know for sure, but wow, it really is a new and exciting world. I really hope we use this intelligence resource to make the world better.

AI is a remixer; it remixes all known ideas together. It won't come up with new ideas though; the LLMs just predict the most likely next token based on the context. That means the group of characters it outputs must have been quite common in the past. It won't add a new group of characters it has never seen before on its own.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#56

Post by virgildotcodes »

I don't know why I am still perpetually shocked that the default assumption is that humans are somehow unique.

It's this pervasive belief that underlies so much discussion around what it means to be intelligent. The null hypothesis goes out the window.

People constantly make comments like "well it's just trying a bunch of stuff until something works" and it seems that they do not pause for a moment to consider whether or not that also applies to humans.

If they do, they apply it in only the most restrictive way imaginable, some 2 dimensional caricature of reality, rather than considering all the ways that humans try and fail in all things throughout their lifetimes in the process of learning and discovery.

There's still this seeming belief in magic and human exceptionalism, deeply held, even in communities that otherwise tend to revolve around the sciences and the empirical.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#57

Post by [deleted] »

storus wrote: post #55
Validark wrote: post #33

I have long said I am an AI doubter until AI could print out the answers to hard problems or ones requiring tons of innovation. Assuming this is verified to be correct (not by AI) then I just became a believer. I would like to see a few more AI inventions to know for sure, but wow, it really is a new and exciting world. I really hope we use this intelligence resource to make the world better.

AI is a remixer; it remixes all known ideas together. It won't come up with new ideas though; the LLMs just predict the most likely next token based on the context. That means the group of characters it outputs must have been quite common in the past. It won't add a new group of characters it has never seen before on its own.

[deleted]

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#58

Post by qnleigh »

XCSme wrote: post #18
karmasimida wrote: post #4

No denial at this point, AI could produce something novel, and they will be doing more of this moving forward.

Not sure if AI can have clever or new ideas, it still seems to be it combines existing knowledge and executes algoritms. I am not necessarily saying humans do something different either, but I have yet to see a novel solution from an AI that is not simply an extrapolation of current knowledge.

Speaking as a researcher, the line between new ideas and existing knowledge is very blurry and maybe doesn't even exist. The vast majority of research papers get new results by combining existing ideas in novel ways. This process can lead to genuinely new ideas, because the results of a good project teach you unexpected things.

My biggest hesitation with AI research at the moment is that they may not be as good at this last step as humans. They may make novel observations, but will they internalize these results as deeply as a human researcher would? But this is just a theoretical argument; in practice, I see no signs of progress slowing down.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#59

Post by slopinthebag »

virgildotcodes wrote: post #56

I don't know why I am still perpetually shocked that the default assumption is that humans are somehow unique. It's this pervasive belief that underlies so much discussion around what it means to be intelligent. The null hypothesis goes out the window. People constantly make comments like "well it's just trying a bunch of stuff until something works" and it seems that they do not pause for a moment to consider whethe…

> I don't know why I am still perpetually shocked that the default assumption is that humans are somehow unique.

Uh, because up until and including now, we are...?

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#60

Post by slg »

raincole wrote: post #41
himata4113 wrote: post #36

Earlier quoted context omitted.

It's less of solving a problem, but trying every single solution until one works. Exhaustive search pretty much. It's pretty much how all the hard problems are solved by AI from my experience.

In other words, it's solving a problem.

Yes, but is it "intelligence" is a valid question. We have known for a long time that computers are a lot faster than humans. Get a dumb person who works fast enough and eventually they'll spit out enough good work to surpass a smart person of average speed.

It remains to be seen whether this is genuinely intelligence or an infinite monkeys at infinite typewriters situation. And I'm not sure why this specific example is worthy enough to sway people in one direction or another.

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