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

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

#31
post #19

Earlier quoted context omitted.

You might be joking, but you're probably also not that far off from reality. I think more people should question all this nonsense about AI "solving" math problems. The details about human involvement are always hazy and the significance of the problems are opaque to most. We are very far away from the sensationalized and strongly implied idea that we are doing something miraculous here.

I am kind of joking, but I actually don't know where the flaw in my logic is. It's like one of those math proofs that 1 + 1 = 3. If I were to hazard a guess, I think that tokens spent thinking through hard math problems probably correspond to harder human thought than tokens spend thinking through React issues. I mean, LLMs have to expend hundreds of tokens to count the number of r's in strawberry. You can't tell me…

Some thoughts.

1. LLMs aren't "efficient", they seem to be as happy to spin in circles describing trivial things repeatedly as they are to spin in circles iterating on complicated things.

2. LLMs aren't "efficient", they use the same amount of compute for each token but sometimes all that compute is making an interesting decision about which token is the next one and sometimes there's really only one follow up to the phrase "and sometimes there's really only" and that compute is clearly unnecessary.

3. A (theoretical) efficient LLM still needs to emit tokens to tell the tools to do the obviously right things like "copy this giant file nearly verbatim except with every `if foo` replaced with `for foo in foo`. An efficient LLM might use less compute for those trivial tokens where it isn't making meaningful decisions, but if your metric is "tokens" and not "compute" that's never going to show up.

Until we get reasonably efficient LLMs that don't waste compute quite so freely I don't think there's any real point in trying to estimate task complexity by how long it takes an LLM.

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

#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.

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

#34
post #18

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.

There is no such thing. All new ideas are derived from previous experiences and concepts.

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

#35
post #18

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.

We call that Standing On The Shoulders Of Giants and revere Isaac Newton as clever, even though he himself stated that he was standing on the shoulders of giants.

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

#36

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.

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

#37

As someone with only passing exposure to serious math, this section was by far the most interesting to me: > The author assessed the problem as follows. > [number of mathematicians familiar, number trying, how long an expert would take, how notable, etc] How reliably can we know these things a-priori? Are these mostly guesses? I don't mean to diminish the value of guesses; I'm curious how reliable these kinds of gues…

For number of mathematicians familiar with and actively working on the problem, modern mathematics research is incredibly specialized, so it's easy to keep track of who's working on similar problems. You read each other's papers, go to the same conferences etc.

For "how long an expert would take" to solve a problem, for truly open problems I don't think you can usually answer this question with much confidence until the problem has been solved. But once it has been solved, people with experience have a good sense of how long it would have taken them (though most people underestimate how much time they need, since you always run into unanticipated challenges).

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

#38

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.

That's also the only way how humans solve hard problems.

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

#39

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.

No, that's precisely solving a problem.

Shotgunning it is an entirely valid approach to solving something. If AI proves to be particularly great at that approach, given the improvement runway that still remains, that's fantastic.

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

#40
post #38

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.

That's also the only way how humans solve hard problems.

There have been both inductive and deductive solutions to open math problems by humans in the past decade, including to fairly high-profile problems.
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